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Overnight exchange rate risk based on multi-quantile and joint-shock CAViaR models
Accepted Manuscript Overnight exchange rate risk based on multi-quantile and joint-shock CAViaR models Wei Peng, Yufeng Zeng PII:
S0264-9993(18)30142-1
DOI:
https://doi.org/10.1016/j.econmod.2018.11.023
Reference:
ECMODE 4779
To appear in:
Economic Modelling
Received Date: 27 January 2018 Revised Date:
13 August 2018
Accepted Date: 27 November 2018
Please cite this article as: Peng, W., Zeng, Y., Overnight exchange rate risk based on multiquantile and joint-shock CAViaR models, Economic Modelling (2019), doi: https://doi.org/10.1016/ j.econmod.2018.11.023. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Overnight exchange rate risk based on multi-quantile and joint-shock CAViaR models
a
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Wei Penga(Corresponding author)
School of Finance, Zhongnan University of Economics and Law, 182# Nanhu Avenue,
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East Lake High-tech Development Zone, Wuhan 430-073, P.R. China
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Email: [email protected]
Yufeng Zengb
b
School of Economics, Fudan University , 220# Handan Road, Yangpu District ,
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Acknowledgments
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Shanghai 200-433, P.R. China
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This research was supported by the General Humanities and Social Sciences Research Project of Education Ministry“Research on Risk Conduction Measurement and Coordination Supervision Policy among Different Financial Sectors in China Based on Multi-quantile CAViaR”(Grant Number, 18YJC630132).
ACCEPTED MANUSCRIPT Overnight exchange rate risk based on multi-quantile and joint-shock CAViaR models
Abstract: Overnight risk of exchange rate is more and more important because the
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exchange rate trading time of various countries is inconsistent. Drawing on the multi-quantile CAViaR model for two markets, this study proposes a multi-quantile
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CAViaR model for three markets and a multi-quantile CAViaR model for joint shock. The two new models are used to measure the impact of the U.S. Dollar index and the
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Euro on the overnight risk for the exchange rate of the Japanese Yen, Hong Kong Dollar, and Chinese Renminbi. The results show that, first, a lag risk affects the overnight risk of the three exchange rates, of which the Renminbi exchange rate is subject to the largest risk. Second, the U.S. Dollar index and Euro exchange rate risks
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impact the overnight risk of the three exchange rates and this effect is highest for the overnight risk of the Yen’s exchange rate. In addition, the impact of the U.S.Dollar
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index risk is greater than that of the Euro. Third, the Euro and U.S.Dollar index produce a joint shock on the overnight risk of the three exchange rates, and here, the
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Yen’s exchange rate suffers the biggest shock. Finally, the multi-quantile CAViaR model for joint shock is more accurate than that for three markets, particularly when the Hong Kong Dollar exchange rate has a 5% VaR. These empirical results have meaningful implications for regulatory authorities.
Keywords: Value at Risk; exchange markets; overnight risk
JEL: C13, C14, C32, G10 1
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1. Introduction
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Exchange rate risks have critical implications for an economy: foreign countries could suffer the repercussions of a domestic crisis or a foreign crisis could impact a domestic economy [1–3]. In 1992, Soros sniped the pound and this led to the
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withdrawal of Britain from the European Union, which negatively impacted the British economy. The 1998 financial crisis in Southeast Asia was also due to a trade attack by
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Soros. The 2008 subprime mortgage crisis caused a major setback in the U.S. economy and resulted in the quantitative easing policy by the Federal Reserve [4, 5]. Subsequently, there was a worldwide influx of dollars, causing its value to depreciate
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[6, 7]. These aspects highlight that with intensifying global economic integration and regular financial fluctuations, effectively measuring and managing exchange rate risks have become a critical issue in various countries [8–11].
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In the global exchange rate markets, the U.S. Dollar index and Euro exchange rate
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occupy an important position and fluctuations in either are likely to affect major countries and economies [12–14]. In fact, both exchange rates have a peculiar impact on Asian countries and regions. The exchange markets for Asian countries and regions, particularly, Japan, Hong Kong, and China, close at 16:00 Beijing time, as per which the Euro and U.S.Dollar exchange rate markets open after 16:00 and close at night. In other words, exchange trade for the Euro and U.S.Dollar takes place outside the trading hours for the Asian foreign exchange markets [15–17]. Thus, the impact of 2
ACCEPTED MANUSCRIPT fluctuations in the Euro and U.S. Dollar index is reflected only the next trading day for the Asian exchange markets [18, 19]. This risk between foreign exchange closure and the next day’s opening is called the overnight risk of an exchange rate.
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This study attempts to answer the following questions. What is the impact of the U.S. Dollar index and Euro exchange rate on the exchange markets in Asian countries
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and regions? What are the differences between the impacts? Can foreign exchange regulators and management departments in Asian countries forecast and manage the
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trend of national exchange rate movements and overnight risk according to the volatility of the previous day’s exchange rate? Addressing these questions will not only help investors make optimal portfolio decisions in relevance to the foreign exchange market but also provide theoretical and practical guidance for policymakers
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and market regulators to more effectively manage overnight risk.
This study mainly employs the value-at-risk (VaR) method, which is based on the
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conditional autoregressive value at risk by regression (CAViaR) models, to measure
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overnight risk. The application of the VaR approach to estimate global risk was first proposed by JPMorgan Chase Bank in 1994. The Basel Accords are clearly defined by the use of VaR to calculate risks.
Koenker [20] proposed a quantile regression (QR) method to resolve the
optimization problem of loss function expectations and since then, numerous scholars have conducted related research. Engle and Manganelli [21] proposed CAViaR, which is a milestone in quantile regression given that its modeling challenges the general 3
ACCEPTED MANUSCRIPT idea and constructs VaR itself. The CAViaR model is divided into four quantile models: symmetric absolute value (SAV) model, asymmetric slope (AS) model, IG (indirect GARCH) model, and adaptive(AD) model, of which the AD model has been
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proven to be worst and no scholar conducts empirical research using it. Considerable recent research [22–25] has compared the CAViaR with the GARCH model and the historical data simulation method and shown that the VaR calculated using the
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CAViaR model is more accurate, a finding which has been supported by various
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additional studies. Kuester [26], Taylor [27], Frank and Masao [28], Sergio et al. [29], and Mauro and Leopoldo [30] improve the CAViaR model on the basis of the IG and AS models. The improved model is then compared with the GARCH model and the results show that the former is a better way to describe the evolution of market risk.
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Richard and Cathy [31] add the threshold function to the CAViaR model and prove that the improved model is more accurate. Drawing on Frank [28], Taylor [32] proposes a CAViaR model for threshold-weighted asymmetric AS and uses the model
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to analyze the Asian stock market. Simone and Halbert [33] adopt the CAViaR model
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to examine risk interactions between the two markets and accordingly, propose the multi-quantile CAViaR model.
This study mainly examines the impact of the U.S. Dollar index and Euro on the
overnight risk of the foreign exchange markets in Asian countries and regions. To do so, it focuses on the exchange rates of the Chinese Renminbi, Hong Kong Dollar, and Japanese Yen as research objects. The analysis makes two main contributions. First, the current literature lacks research on the overnight risk of exchange rates. By 4
ACCEPTED MANUSCRIPT drawing on Simone and Halbert’s [33] multi-quantile CAViaR model for two markets, this study proposes a multi-quantile CAViaR model for three markets to analyze the impact of the U.S. Dollar and Euro on the overnight risk of the three exchange rates.
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Second, the impact on the overnight risk for the Asian foreign exchange market is greater when the U.S. Dollar and Euro fall at the same time, as opposed to when they do not. Using the multi-quantile CAViaR model for three markets, this study further
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considers the effect of a joint shock, as suggested by David [34] and Kyoo [35], to
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propose a multi-quantile CAViaR model for joint shock.
2. Methodology
2.1 Conditional autoregressive value at risk by regression
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Following Koenker [20], Engle and Manganelli’s [21] CAViaR model can directly model the tail risk instead of estimating the tail distribution. According to Engle and Manganelli [21], the CAViaR model takes the form of a symmetric absolute
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value(SAV), asymmetric slope(AS), and indirect GARCH(IG)model.
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The symmetric absolute value(SAV) model is as follows:
f t (θ ) = β 1 + β 2 f t −1 (θ ) + β 3 yt −1 ,
(1)
where yt −1 is the market index rate of return, yt −1 is the absolute value of the
market index rate of return, ft (θ ) is the θ conditions quantile of y t , and ft (θ ) is the function of VaR.
The asymmetric slope(AS) model can be specified as 5
ACCEPTED MANUSCRIPT f t (θ ) = β1 + β 2 f t −1 (θ ) + β 3 yt −1 I ( yt −1 > 0) + β 4 yt −1 I ( yt −1 < 0) ,
(2)
where yt −1 is the market index rate of return, yt −1 is the absolute value of the market index rate of return, ft (θ ) is the θ conditions quantile of y t , and ft (θ ) is
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the function of VaR. Different from SAV model, the AS model incorporates the asymmetric term I () to denote the asymmetric effects of the threshold function on
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the market rate of return.
The indirect GARCH(IG) model is
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ft (θ ) = ( β1 + β 2 f 2t −1 (θ ) + β3 y 2t −1 )1/2 ,
(3)
where yt −1 is the market index rate of return, yt −1 is the absolute value of the
the function of VaR.
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market index rate of return, ft (θ ) is the θ conditions quantile of y t , and ft (θ ) is
However, the CAViaR model mainly analyzes dynamic risk characteristics in a
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single market and cannot capture the complex relationship of risk contagion among
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various markets.
To overcome this deficiency, Simone and Halbert [33] extend the traditional
CAViaR model to the multi-quantile CAViaR model for two markets by expanding the single-equation quantile regression concept to a structural-equation vector auto-regression and reveal that VaR in a single market is affected not only by its own market but also by risk spillovers from other markets.
Simone and Halbert’s [33] multi-quantile CAViaR model for two markets is as 6
ACCEPTED MANUSCRIPT follows:
f1,t (θ ) = c1 + a11 y1,t −1 + a12 y2,t −1 + b11 f1,t −1 (θ ) + b12 f 2,t −1 (θ ) ,
(4)
where y1,t −1 is a market index rate of return, y1,t −1 is the absolute value of the
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market index rate of return, f1,t (θ ) is the θ conditions quantiles of y 1,t , and
f1,t (θ ) is the function of the market VaR. In addition, y2,t −1 is another market index
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rate of return, y2,t −1 is the absolute value of another market index rate of return, f 2,t (θ ) is the θ conditions quantile of y 2 ,t , and f 2,t (θ ) is the function of another
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market’s VaR.
From eq. (4), we see that the multi-quantile CAViaR model for two markets explores the risk interaction between the two markets. The risk to any one market is
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affected by the return rate in the other market and a lag risk.
2.2 Model improvement
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The opening and closing time for foreign exchange markets globally differ. The closing time for foreign exchanges in China, Hong Kong, and Japan are 16:00 Beijing
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time. However, as per Beijing time, foreign exchange markets in the United States and Europe open post-16:00 and close during nighttime. Thus, the day’s trading in the U.S. and European foreign exchange markets are bound to impact the overnight risk in the foreign exchange markets of China, Hong Kong, and Japan, which open the following day.
The improved model is presented as follows. 7
ACCEPTED MANUSCRIPT First, drawing on Simone and Halbert’s [33] multi-quantile CAViaR model for two markets, this study proposes a multi-quantile CAViaR model for three markets to analyze the impact of the U.S. Dollar index and Euro on the overnight risk in Asian
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foreign exchange markets (i.e., China, Hong Kong, and Japan).
f1,t (θ ) = c1 + a11 y1,t −1 + a12 y2,t −1 + a13 y3,t −1 + b11 f1,t −1 (θ ) + b12 f 2,t −1 (θ ) + b13 f 3,t −1 (θ ) (5)
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where y1,t −1 is a market index overnight rate of return (China, Hong Kong, or Japan) and the logarithmic return percentage of the second day’s opening price for
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each exchange is divided by the first day’s closing price. y1,t −1 is the absolute value of the market index overnight rate of return, f1,t (θ ) is the θ conditions quantile of
y 1,t , and f1,t (θ ) is the VaR of the overnight risk for one exchange rate (RMB, HKD, or JPY). y2,t −1 is the U.S. Dollar’s day rate of return. f 2,t −1 (θ ) is the θ conditions
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quantile of y 2 , t − 1 and f 2,t −1 (θ ) is the day VaR for the U.S. Dollar. y3,t −1 is the Euro’s day rate of return. f 3,t −1 (θ ) is the θ conditions quantile of y 3 , t − 1 and
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f 3,t −1 (θ ) is the day VaR of the Euro.
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Second, this study further considers the impact of a joint shock. The influence of an overnight risk on the Asian foreign exchange market (i.e., China, Hong Kong, and Japan) is greater when the U.S. Dollar and Euro fall at the same time, rather than when they do not. Thus, as per the multi-quantile CAViaR model for three markets, this study further considers the effect of a joint shock, as suggested by David [34] and Kyoo [35], to propose a multi-quantile CAViaR model of joint shock.
, 8
ACCEPTED MANUSCRIPT f1,t (θ ) = c1 + a11 y1,t −1 + a12 y2,t −1 + a13 y3,t −1 + b11 f1,t −1 (θ ) + b12 f 2,t −1 (θ ) +b13 f 3,t −1 (θ ) + d1 y2,t −1 y3,t −1 I ( y2,t −1 < 0) I ( y3,t −1 < 0)
(6)
where y1,t −1 , f1,t −1 (θ ) , y2,t −1 , f 2,t −1 (θ ) , y3,t −1 , and f 3,t −1 (θ ) are the same as
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those in eq. (5). Threshold function I () denotes that the U.S. Dollar and Euro exchange rate return are less than zero, indicating that the U.S. Dollar and Euro fall at the same time.
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2.3 Model robustness test
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This analysis employs the RQ value, DQ test, and LR test to verify the estimations.
2.3.1 RQ value
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Referencing Engle and Manganelli [21], the objective function can be specified as
(7)
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n n min β∈Rk ∑ θ yt − ft (θ ) + ∑ (1 − θ ) yt − ft (θ ) . {t:yt > ft (θ )} {t: yt < ft (θ )}
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The RQ value is the objective function of eq. (7) and the lower the RQ value, the better the model.
2.3.2 DQ test
The DQ test can be organized as follows according to Engle and Manganelli [21]. If yt − f t (θ ) < 0 , ft (θ) denote VaR, then, VaR is insufficient to cover actual losses. This is called a “hit event.” 9
ACCEPTED MANUSCRIPT Hitt (θ) = I(yt < ft (θ)) −θ
.
(8)
Hit is uncorrelated with any variable belonging to information set Ω :
.
(9)
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E(Hittωt−1) = ωt−1E(Hitt ωt−1) = 0 ∀ωt−1 ∈Ωt−1
A good model should produce a sequence of unbiased and correlated hits, such that the explanatory power of this artificial regression should be zero.
{ I ( yt < ft (θ ))} . The null hypothesis is
is the
H0 :δ = 0 .
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indicator functions of
{It }
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Hitt (θ ) = δ0 + δ1Hitt −1 + .... + δ p Hitt − p + δ p+1 ft (θ ) + δ p+2 I year1,t + .... + δ p+2+n I yearn+1,t + µt . (10) Rewriting it in matrix form, we get
Hitt =Xδ + µt .
(11)
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The rewriting in matrix form of eq(10) is eq(11).X stands for vector of eq (10), δ stands for coefficient, µt stands for error term. The asymptotic distribution of the OLS estimator under the null can be easily
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established, invoking an appropriate central limit theorem: (12)
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δ OLS = ( X ' X ) −1 X ' Hit ~ N (0, θ (1 − θ )( X ' X ) −1 ) .
The DQ test statistics obey the chi-square distribution. Next, we derive the
dynamic quantile test statistic:
δ OLS X ' X δ OLS ~ χ 2 ( p + n + 2) θ (1 − θ ) . '
The null hypothesis is H 0 : δ = 0 . 2.3.3 LR test 10
(13)
ACCEPTED MANUSCRIPT The LR test includes LRuc , LRind , and LRcc . This study uses the unconditional coverage test statistic LRuc :
.
(14)
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LRuc = −2 ln[(1 − α ) k − m (α ) m ] + 2 ln[(1 − m / k ) k − m (m / k ) m ] ~ χ 2 (1)
The null hypotheses is m / k = α , where m is the total number of hits, k is the number of samples, and α is the significant level. The LR statistic obeys the
π0 =
(1 − π 0 )T00 (π 0 )T01 (1 − π 1 )T10 (π 1 ) T11 2 = 2 log[( ] ~ χ (1) T00 + T10 T00 + T11 (1 − π pool ) (π pool )
T01 T01 + T00
π1 =
T11 T11 + T10
π
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LRind
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chi-square distribution whose freedom is 1.
pool
=
T0 1
(15)
T 0 1 + T1 1 , + T 0 0 + T1 1 + T1 0
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where T00 is the number of no outliers for two consecutive days, T01 is the number of outliers after normal, T10 is the number of normal value after outliers, and
T11 is the number of outliers within two consecutive days
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2 LRcc = LRind + LRuc ~ χ (2) .
(16)
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3. Data
This study employs the RMB, HKD, and JPY exchange rates as research objects.
Exchange rate pricing is a direct price method that determines the equivalent value for a U.S. Dollar in local currency. A rising exchange rate denotes the appreciation of the U.S. Dollar, while a declining rate indicates the depreciation of the U.S. Dollar. This study focuses on the impact of the U.S.Dollar index and Euro exchange rate on the 11
ACCEPTED MANUSCRIPT overnight risk for the JPY, RMB, and HKD exchange rates.
Table 1 presents the trading hours for the exchange rate markets as per Beijing time. We see that the exchange markets for JPY, HKD, and RMB open during the
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morning and close in the afternoon, whereas the trading for the U.S. Dollar and the Euro takes place in the afternoon and evening. Thus, the U.S. Dollar index and Euro
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will inevitably affect the three exchange rates once the market opens the next day. .
Exchange rate market RMB, Hong Kong and Yen Euro
20
00
Time
8
00 16
16
00
00
24 00
4:00 the next morning
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U.S. Dollar
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Table 1 Trading hours for exchange rate market (Beijing time)
Therefore, the data for the three exchange rate markets in this study are the logarithmic return percentage of the second day’s opening price for each exchange
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divided by the first day’s closing price. The data for the U.S. Dollar index and Euro
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markets are the daily logarithmic return percentage. The full sample period is January 4, 2010–2018. To match the data sample, the non-trading days are eliminated, resulting in 2,060 observations. To test the robustness of the present model, all data samples are divided for in- and out-of-sample testing. Among them, 1,560 data samples are employed in the simulated empirical model and the remaining 500 are applied to out-of-sample backtesting. All the data are from the Flush iFinD financial database.
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ACCEPTED MANUSCRIPT Table 2 Summary statistics for returns U.S. Dollar
Euro
Yen
Hong
index
RMB
Kong
0.003656
0.004265
0.010949
0.000134
-0.004062
Max
1.947040
2.372358
2.509413
0.124377
1.071091
Min
-2.046598
-2.852691
-2.434121
-0.165909
-1.217969
St.D
0.465941
0.583086
0.177527
0.009147
0.100617
Skew
-0.002395
-0.045348
1.660918
-3.412024
-1.251197
p-value
0.000106
0.00028
0.00000
0.00000
0.00000
Kurtosis
4.523057
4.784520
63.20915
109.7397
42.16946
p-value
0.000118
0.000102
0.00000
0.00000
0.00000
JB test
199.1097
274.0433
311953.6
981450.8
132162.8
p-value
0.00000
0.000000
0.000000
0.000000
0.000000
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Mean
Notes: As per the p-value from the Jarque–Bera test, the distribution of the returns of
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exchange rate is not Gaussian.
Table 2 reports the log returns for each currency. In particular, the Euro shows
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highest volatility, while Hong Kong’s currency has the lowest. In addition, the Jarque–Bera statistics are significant, implying the returns for these variables do not follow the normal distribution. Therefore, employing the CAViaR approach is suitable for the present estimates.
4. Empirical results This study selects quantiles θ that equal 1% and 5%. By incorporating the U.S. 13
ACCEPTED MANUSCRIPT Dollar index and Euro, it is possible to compare and contrast the effects that both factors have on the overnight risk of these currencies.
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4.1 Quantile θ =1% Tables 3 and 4 present the results of the multi-quantile CAViaR model for three markets and the multi-quantile CAViaR model for joint shock.
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Table 3 Estimates of multi-quantile CAViaR model for three markets at 1% quantile Hong Kong
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Yen
RMB
1%--quantile
c1
0.1256(0.5120)
a11
0.0135(0.0211)
a12
1.8926**(0.0035)
a13 b11
1.6404**(0.0266)
1.3813(1.0297)
0.8836**(0.0124)
0.9012**(0.0119)
0.8809(0.9297)
0.0586**(0.0108)
0.0186**(0.0024)
0.1515**(0.0152)
0.4233**(0.0227)
0.2783*(0.1587)
0.2536**(0.0815)
0.3784*(0.1958)
0.1568**(0.0489)
0.0465**(0.0082)
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1.0894*(0.5397)
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b13
0.0778(0.2690)
1.8318**(0.0115)
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b12
0.4048(0.3458)
Notes
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level. The null
hypothesis is that the coefficient is 0.The numbers in parentheses are standard errors.
Tables 3 and 4 show that coefficients a12 for the three exchange rates are significant, indicating the U.S. Dollar index rate of return has an impact on overnight risks. Of the three exchange rates, the U.S. Dollar has the most prominent impact on 14
ACCEPTED MANUSCRIPT the overnight risk for JPY and the least effect on that for RMB. The results in Table 3 show that coefficients a13 for the exchange rates for JPY and HKD are significant, indicating that the Euro exchange rate of return impacts the
suggesting no effect by the Euro exchange rate of return.
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overnight risk for both currencies. However, coefficient a13 for RMB is insignificant,
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Table 4 Estimates of multi-quantile CAViaR model for joint shock at 1% quantile Yen
Hong Kong
RMB
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1%--quantile
0.1952(0.2088)
0.5063(1.8251)
0.0779(0.7839)
a11
0.1133**(0.0065)
1.3407(2.5633)
1.2058(1.6622)
a12
1.2527*(0.6682)
1.0838**(0.0206)
1.0393*(0.5869)
a13
0.6866**(0.0127)
0.6062(1.0383)
0.4866(0.8033)
b11
0.1886**(0.1814)
0.2586**(0.0433)
0.4566**(0.0339)
0.6253**(0.1929)
0.4585**(0.0839)
0.2776**(0.0869)
0.1538**(0.0482)
0.0425**(0.0155)
0.6708**(0.2055)
0.1066**(0.0421)
0.2734*(0.1314)
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b13
EP
b12
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c1
d1
Notes
0.7892**(0.0925)
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level. The null
hypothesis is that the coefficient is 0.The numbers in parentheses are standard errors.
Tabled 3 and 4 suggest that coefficients b11 are significant for the three exchange rates; that is, the overnight risk for the three exchange rates is affected by the lag risk. Among these, the impact is highest on the RMB exchange rate. 15
ACCEPTED MANUSCRIPT In addition, coefficients b12 for the three exchange rates are all significant, indicating that the U.S. Dollar index impacts the overnight risk for all three exchange rates. Of these, it has the strongest impact on the overnight risk for the Yen’s exchange
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rate and least effect on that of the renminbi. Coefficients b13 are equally significant for the three exchange rates, suggesting
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the Euro influences the overnight risks for all three exchange rates, of which it has the greatest effect on the Yen’s exchange rate and the least impact on that of the RMB.
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Thus, Tables 3 and 4 demonstrate that, compared to the Euro, the U.S. Dollar index has a greater impact on the overnight risk of the three exchange rates. Coefficients d1 for the three exchange rates (Table 4) are all significant,
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indicating that the overnight risks for all three rates are affected by the joint shock from the U.S. Dollar index and Euro. More specifically, the impact on the overnight risk for the three exchange rates is greater when the U.S. Dollar index and Euro fall at
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the same time rather than when they do not. Further, the joint shock has a higher
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effect on the overnight risk for the Yen than that for Hong Kong Dollar and renminbi, which is affected the least. This can be mainly attributed to China’s strict control system for foreign exchange. 4.2 Quantile θ =5%
Tables 5 and 6 present the results of the multi-quantile CAViaR models for three markets and joint shock.
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ACCEPTED MANUSCRIPT Table 5 Estimates of multi-quantile CAViaR model for three markets at 5% quantile Yen
Hong Kong
RMB
0.7289(0.8652)
a11
0.0188**(0.0047)
a12
1.8024**(0.0861)
1.8501**(0.1772)
1.0393(1.825)
a13
0.8434**(0.2802)
0.9244**(0.0052)
0.8070(0.8855)
b11
0.0468**(0.0158)
0.0896**(0.0774)
0.2333**(0.0554)
b12 b13 Notes
0.4333(0.1282)
0.3730(0.7866)
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c1
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5%--quantile
1.5818(1.2308)
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1.8408**(0.1665)
0.5908**(0.1559)
0.4563*(0.2290)
0.2088**(0.0288)
0.3988*(0.2206)
0.2343**(0.0032)
0.1687**(0.0115)
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level. The null
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hypothesis is that the coefficient is 0.The numbers in parentheses are standard errors.
As shown in Table 5, coefficients a12 are significant for the exchange rate of the
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Japanese Yen and Hong Kong Dollar, indicating that the overnight risks for the
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exchange rates of both currencies are affected by the U.S. Dollar index rate of return .In addition, coefficients a13 for the Japanese Yen and Hong Kong Dollar are significant, indicating that the Euro exchange rate of return affects the overnight risk of both currencies, of which it has a greater effect on the Hong Kong Dollar. Coefficients b11 for the three exchange rates (Tables 5 and 6) are all significant, indicating that the lag risk affects the overnight risk for the three rates. The impact of lag risk is highest for the overnight risk of the RMB exchange rate. 17
ACCEPTED MANUSCRIPT Table 6 Estimates of multi-quantile CAViaR model for joint shock at 5% quantile Yen
Hong Kong
RMB
5%--quantile 0.2355*(0.1282)
0.4454(0.6028)
a11
0.5887(0.7299)
1.5902(1.1220)
a12
0.8096**(0.0083)
0.3609(0.0698)
a13
0.5434(0.7098)
0.6062**(0.0522)
b11
0.2478**(0.0042)
0.4089**(0.0371)
0.9084(0.6988)
1.0393(0.8077)
M AN U
SC
0.5080(0.7754)
0.5886**(0.0764)
0.7690**(0.0148)
0.5880*(0.2808)
0.3792**(0.0238)
b13
0.5754*(0.0240)
0.4509**(0.0533)
0.2643*(0.1288)
d1
0.6809**(0.0301)
0.4363**(0.1059)
0.3311**(0.0261)
b12
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level. The null
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Notes
0.0871(0.7041)
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c1
hypothesis is that the coefficient is 0.The numbers in parentheses are standard errors.
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Coefficients b12 (Tables 5 and 6) for the three exchange rates are all significant,
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suggesting that the U.S. Dollar index affects the overnight risk for all three exchange rates. The U.S.Dollar index risk has the strongest impact on the Yen’s exchange rate and the least impact on the RMB exchange rate.
From Tables 5 and Table 6, we see that the impact of the U.S.Dollar index on the
overnight risk of the three exchange rates is greater than that of the Euro. Coefficients b13 for the three exchange rates are equally significant, indicating that the Euro risk affects the overnight risks of the three exchange rates (Tables 5 and 18
ACCEPTED MANUSCRIPT 6). Among the three, the Euro risk has the greatest effect the Yen’s exchange rate and the least influence on that of the RMB. ～ Finally, coefficients d1 of the three exchange rates in Table 6 are all significant,
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suggesting that the overnight risks for all three exchange rates are affected by the joint shock of the U.S. Dollar index and Euro. Further, the impact on overnight risk of the
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three exchange rates is greater when the U.S.Dollar index and Euro fall at the same time than when they do not. The joint shock on the overnight risk for the Yen is
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greater and the least for the RMB exchange rate. This is also mainly due to China’s strict control system for foreign exchange.
5. Model robustness test
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Tables 7 and 8 present the results for the RQ and DQ tests of the multi-quantile CAViaR models for three markets and joint shock.
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Table 7 RQ and DQ tests of multi-quantile CAViaR model for three markets
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Yen
Hong Kong
RMB
1%--quantile
RQ
6.5043[0.2369]
1.1174[0.6089]
4.8063[0.3025]
DQ test (IS)
0.1098[0.9650]
0.1970[0.7938]
0.6702[0.2760]
DQ test (OS)
0.1507[0.8756]
0.1298[0.9268]
0.1259[0.9371]
5%--quantile RQ
9.3433[0.1208]
5.5437[0.2562]
7.4327[0.2162]
DQ test (IS)
0.1186[0.9554]
0.2052[0.7451]
0.5862[0.3263]
19
ACCEPTED MANUSCRIPT DQ test (OS)
0.3169[0.6366]
0.1045[0.9663]
0.1032[0.9673]
Notes The numbers in square brackets are p-values. IS and OS denote in- and out-of-sample.
Table 8 RQ and DQ tests of multi-quantile CAViaR model for joint shock Hong Kong 1%--quantile
RMB
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Yen
6.4045[0.2374]
1.1071[0.6377]
4.4060[0.3251]
DQ test (IS)
0.1283[0.9352]
0.1925[0.7968]
0.1711[0.8250]
DQ test (OS)
0.1871[0.8136]
0.1136[0.9561]
0.1622[0.8344]
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SC
RQ
5%--quantile
8.0967[0.1422]
5.1439[0.2680]
7.3321[0.2189]
DQ test (IS)
0.3284[0.5476]
0.1397[0.8906]
0.1647[0.8327]
DQ test (OS)
0.1026[0.9802]
0.1307[0.9061]
0.3260[0.5691]
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RQ
Notes The numbers in square brackets are p-values. IS and OS denote in- and out-of-sample.
As indicated in Tables 7 and 8, irrespective of 1% or 5% quantiles θ , the
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multi-quantile CAViaR models for three markets and joint shock pass the DQ test.
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However, the RQ values for the multi-quantile CAViaR model for joint shock are smaller than those of the multi-quantile CAViaR model for three markets. Thus, the former model for joint shock is better than the latter for three markets.
20
ACCEPTED MANUSCRIPT Table 9 LR test ( θ = 1% ) the multi-quantile
CAViaR model of three markets
CAViaR model of joint-shock
1%--quantile
P-value
0.9353
LRind
2.1565
P-value
0.1420
LRcc
2.1631
P-value Hong
Notes
2.4052
0.1209
2.5199 0.2837
0.7753
0.7027
0.3786
0.4019
LRind
1.2205
1.5331
P-value
0.2693
0.2156
LRcc
1.9958
2.2358
P-value
0.3687
0.3270
LRuc
0.0029
0.5681
P-value
0.9571
0.4510
LRind
2.0388
1.2550
P-value
0.1533
0.2626
LRcc
2.0417
1.8231
P
0.3603
0.4019
LRuc P-value
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RMB
0.7349
0.3391
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Kong
0.1147
SC
0.0066
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LRuc
EP
Yen
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the multi-quantile
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level.
21
ACCEPTED MANUSCRIPT Table 10 LR test ( θ = 5% ) the multi-quantile
CAViaR model of three markets
CAViaR model of joint-shock
5%--quantile
P-value
0.7023
LRind
0.7621
P-value
0.3827
LRcc
0.9082
P-value Hong
Notes
0.6533
0.4189
0.6875 0.7091
1.1691
2.8092
0.2796
0.0937
LRind
9.4735**
2.6640
P-value
0.0000
0.1026
LRcc
10.6426**
5.4732
P-value
0.0000
0.0648
LRuc
2.7098
2.4485
P-value
0.0997
0.1176
LRind
1.0805
1.4309
P-value
0.2986
0.2316
LRcc
3.7903
3.8794
P-value
0.1503
0.1437
LRuc P-value
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RMB
0.8533
0.6350
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Kong
0.0342
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0.1461
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LRuc
EP
Yen
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the multi-quantile
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level.
22
ACCEPTED MANUSCRIPT Tables 9 and 10 list the LR test results for the three exchange rates. We see that the values of the multi-quantile CAViaR model for joint shock pass the test. When θ = 1%, the multi-quantile CAViaR model for three markets passes the LR test. However,
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when θ = 5%, the LRind and LRcc statistics for the Hong Kong exchange rate are significant. Thus, the multi-quantile CAViaR model for three markets fails the LRind and LRcc tests, indicating that the multi-quantile CAViaR model for joint shocks is
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better.
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From the DQ test, RQ value, and LR test, we see that the multi-quantile CAViaR model for joint shock is better than the multi-quantile CAViaR model for three markets; however, when θ is 5% , the multi-quantile CAViaR model for joint shocks
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has more advantages for the Hong Kong exchange rate.
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1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
Yen
2015/7/31 2015/12/3 2016/4/6 2016/8/9 2016/12/12 2017/4/14 2017/8/17 2017/12/20
2010/9/20 2011/1/21 2011/5/26 2011/9/28 2012/2/6 2012/6/11 2012/10/15 2013/2/18 2013/6/25 2013/11/6 2014/3/18 2014/7/22 2014/11/24 2015/3/27
2010/1/5 2010/5/14
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1%～VaR 5%～VaR
Fig. 1 Overnight risk in multi-quantile CAViaR model for joint shock (Yen)
23
0.5
0 RMB
2.5
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Fig. 2 Overnight risk in multi-quantile CAViaR model for joint shock (Hong Kong)
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24
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0 2015/7/31 2015/12/3 2016/4/6 2016/8/9 2016/12/12 2017/4/14 2017/8/17 2017/12/20
2010/9/20 2011/1/21 2011/5/26 2011/9/28 2012/2/6 2012/6/11 2012/10/15 2013/2/18 2013/6/25 2013/11/6 2014/3/18 2014/7/22 2014/11/24 2015/3/27
2010/1/5 2010/5/14
0.5
2015/7/31 2015/12/3 2016/4/6 2016/8/9 2016/12/12 2017/4/14 2017/8/17 2017/12/20
1
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1.5
2010/9/20 2011/1/21 2011/5/26 2011/9/28 2012/2/6 2012/6/11 2012/10/15 2013/2/18 2013/6/25 2013/11/6 2014/3/18 2014/7/22 2014/11/24 2015/3/27
2
EP
2010/1/5 2010/5/14
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ACCEPTED MANUSCRIPT HongKong
3
2.5
2
1.5 1%～VaR 5%～VaR
1
1%～VaR 5%～VaR
Fig. 3 Overnight risk in multi-quantile CAViaR model for joint shock (RMB)
ACCEPTED MANUSCRIPT 0 Yen HongKong RMB
-0.02
-0.04
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-0.06
-0.08
-0.1
0
20
40
60
80
100
120
140
160
M AN U
-0.14
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-0.12
180
200
Fig. 4 Impulse response of market shocks (1%)
0 -0.01
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-0.02
Yen HongKong RMB
-0.03 -0.04
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-0.05 -0.06
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-0.07 -0.08 -0.09
0
20
40
60
80
100
120
140
160
180
200
Fig. 5 Impulse response of market shocks (5%)
Note: Figs. 4 and 5 depict the response of the future 200 periods for the Yen, Hong Kong Dollar, and renminbi in the multi-quantile CAViaR model of joint shocks when the three exchange rates are simultaneously given one unit of standard deviation of new information shock. The estimation is
25
ACCEPTED MANUSCRIPT performed using Simone and Halbert’s [33] quantile impulse response function (QIRF). The abscissa represents the period,the ordinate represents the impact value.
Figs.1-3 show the VaR of overnight risk. The impact of the Dollar index and the
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Euro exchange rate on the exchange markets of Yen,Hong Kong Dollar and RMB is our topic. Everyday VaR is calculated through the multi-quantile CAViaR model for
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three markets and the multi-quantile CAViaR model for joint shock proposed in this paper, so we can obtain the VaR series.
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Figs. 4 and 5 depict the response of the future 200 periods for the Yen, Hong Kong Dollar, and Renminbi in the multi-quantile CAViaR model of joint shocks when the three exchange rates are simultaneously given one unit of standard deviation of new
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information shock.Whether it is 1% or 5%, the the response of the renminbi will first disappear, and Japan Yen and Hong Kong Dollar will be disappeared closer.
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6. Conclusions
This study examines the impact of the U.S. Dollar index and Euro on the overnight
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risk of the foreign exchange markets in Asian countries and regions, particularly the RMB, HKD, and JPY exchange rates. Referencing Simone and Halbert’s [33] multi-quantile CAViaR model for two markets, a multi-quantile CAViaR model for three markets is proposed. The model for three markets is then used to further consider the effect of a joint shock, as suggested by David [34] and Kyoo [35], to propose a multivariate quantile CAViaR model for joint shock. The two new models are applied to measure the impact of the U.S.Dollar index and Euro on the overnight 26
ACCEPTED MANUSCRIPT risk for the Yen’s, Hong Kong Dollars, and Renminbi’s exchange rate for 2010–2018.
The study presents the following empirical results, and accordingly, policy implications. First, the lag risk affects the overnight risk for all three exchange rates,
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of which the RMB exchange rate suffers the highest risk. Thus, it is important that foreign exchange administrations in Japan, Hong Kong, and particularly, China pay
SC
close attention to the lagging risk of their exchange rates. Second, the U.S.Dollar index risk and Euro exchange rate risk impact the overnight risk for the three
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exchange rates, of which it has largest effect on the overnight risk of the Yen’s exchange rate and the smallest on the RMB exchange rate. In this case, Japanese regulators must pay close attention to the day’s volatility in the U.S. Dollar index and Euro given that both exchange rate risks have the highest impact on the overnight risk
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of the Yen. In addition, the forecast and management of the opening exchange rate for the Japanese Yen should be based on the day’s movements in the U.S. Dollar index
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and Euro. In comparison, given the strict exchange rate control in China, the impact
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on the overnight risk of the RMB is smaller.
Third, the impact of the U.S.Dollar index risk on the overnight risk for the three
exchange rates is greater than that of the Euro. Therefore, Japan, Hong Kong, and China’s foreign exchange administrations should more closely monitor the movements of the U.S. Dollar index than those of the Euro. Fourth, the overnight risk of the three exchange rates is affected by the joint shock of the Euro and U.S. Dollar index. More specifically, the Yen’s exchange rate suffered the biggest shock, followed
27
ACCEPTED MANUSCRIPT by the exchange rates for the HKD and RMB. Thus, when the Euro and U.S. Dollar index fall at the same time, it seems imperative to focus on the effect of combined shocks on the next day’s opening of the domestic exchange rate. Further, risk
RI PT
management departments must be well prepared to effectively forecast and manage domestic exchange rate fluctuations, promote capital stability, and prevent large-scale capital outflows. Finally, the multi-quantile CAViaR model for joint shocks is more
SC
accurate than that for three markets and has more advantages when θ of the Hong
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Kong exchange rate is 5%.
References
[1] Srideep,G., Janice,B., 2010. Nominal exchange rate volatility, relative price
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volatility and the real exchange rate. Journal of International Money and Finance. 29, 840–856.
[2] Gabaix,X.,Maggiori,M.,2015.International liquidity and exchange rate dynamics.
EP
The Quarterly Journal of Economics. 130(3), 1369–1420.
AC C
[3] Joseph, M.L., Lambertides, N., Savva, C.S.,2015. Short-horizon excess returns and exchange rate and interest rate effects. Journal of International Financial
Markets, Institutions & Money. 7, 54–76.
[4] Thomas ,J., Lisa,S.,2015.The role of U.S. subprime mortgage-backed assets in propagating the crisis:contagion or interdependence?.The North American Journal of Economics and Finance. 34,167–186.
28
ACCEPTED MANUSCRIPT [5] Hassen, C., 2015. The US home mortgage market during the financial crisis. International Journal of Computational Economics and Econometrics. 5(4), 122–138.
RI PT
[6] Muthucattu,T.P., James,D.K., 2016. The linkages,persistence,asymmetry in the volatility, the price discovery and efficiency, and the effect of the US subprime
India. Applied Economics. 48, 669–683.
SC
mortgage financial crisis on the spot and the futures market’s returns: the case of
M AN U
[7] Manuel ,A.W., Scott,F., Kristopher,G.,2017.The effect of large investors on asset quality: evidence from subprime mortgage securities. Journal of Monetary Economics. 87, 34–51.
TE D
[8] Ding, D., 2012. Exchange rate risk in the US stock market. Journal of International Financial Markets, Institutions & Money. 22, 137–150.
EP
[9] Su,J.B.,2015.Value-at-risk estimates of the stock indices in developed and emerging markets including the spillover effects of currency market. Economic
AC C
Modelling. 46, 204-224.
[10] Ivo, J.M., 2016. IMF Support and Inter-Regime Exchange Rate Volatility. Open Econnomics Review. 23, 193–211.
[11] David, P., 2017. Gauging exchange rate targeting. Journal of International Money and Finance. 43, 155–166.
29
ACCEPTED MANUSCRIPT [12] Gabriela, O., 2016. Statistical analysis regarding the evolutions of the euro exchange rate and the dollar exchange rate, in Romania. Economics and Applied Informatics. 4, 80–91.
Computational Economics. 48(3), 463–472.
RI PT
[13] Fernando,V., 2016. On the historical exchange rates Euro/US dollar.
SC
[14] Corte, P.D.,Ramadorai, T., Sarno, L., 2016. Volatility risk premia and exchange
M AN U
rate predictability. Journal of Financial Economics. 120, 21–40.
[15] Cornell, W. B., Dietrich, J. K.,1978. The efficiency of the market for foreign exchange under floating exchange rates. The Review of Economics and Statistics. 60(1), 111–120.
TE D
[16] Neely, C. J., Weller, P. A. ,2003. Intraday technical trading in the foreign exchange market. Journal of International Money and Finance. 22(2), 223–237.
EP
[17] Petr, Z.,2014. Technical trading and testing of intra-day market efficiency in the foreign exchange market. Acta Universitatis Bohemiae Meridionales. 17(1), 3–
AC C
13.
[18] Panayotocv,G.,Bakshi,G.,2013.Predictability of currency carry trades and asset pricing implications. Journal of Financial Economics. 110, 139–163.
[19] Samuel,W.M.,Robert,B.G., Enrique,H., 2016.Timing foreign exchange markets. Econometrics. 4(15), 22–45.
30
ACCEPTED MANUSCRIPT [20] Koenker, R. ,1978. Regression quantiles. Econometrica. 1, 33–50.
[21] Engle, R., Manganelli, S., 2004. CAViaR: Conditional Autoregressive Value at Risk by regression quantiles. Journal of Business and Economic Statistics. 4,
RI PT
367–381.
[22] James,W.,2005.Generating volatility forecasts from Value at Risk estimates.
SC
Management Science. 51,712–725.
M AN U
[23] Allen, D., Powell, L., 2015. A Gourmet's delight: CAViaR and the Australian stock market. Applied Economics Letters. 19, 1493–1498.
[24] Keith,K., Stefan,M., Marc,S.,2016.Value-at-Risk prediction: a comparison of alternative strategies. Journal of Financial Econometrics. 4,53–89.
TE D
[25] Eugene, S., 2017. Extreme risk spillover network:application to financial institutions. Quantitative Finance.17(9), 58–79.
EP
[26] Kuster, L., 2006. Value-at-Risk prediction: a Comparison of alternative
AC C
strategies. Journal of Financial Econometric. 4, 53–89.
[27] Taylor,W.,2008.Using exponentially weighted quantile regression to estimate Value at Risk and expected shortfall. Journal of Financial Econometrics. 6, 382– 406.
[28] Frank, J., Masao, F., 2009. CAViaR-based forecast for oil price risk. Energy Economics. 31, 511–518.
31
ACCEPTED MANUSCRIPT [29] Sergio,F.,Masao,F., Zudi,L.,2010.Index-exciting CAViaR: a new empirical timevarying risk model. Studies in Nonlinear Dynamics & Econometrics. 14, 38–52.
RI PT
[30] Mauro,B., Leopoldo,C.,2016. Comparison of Value-at-Risk models using the MCS approach. Computational Statistics. 31(2), 579–608.
SC
[31] Richard,H.,Cathy,W.S.,2014.Bayesian time-varying quantile forecasting for Value at Risk in financial markets. Journal of Business & Economic Statistics. 29,
M AN U
481–492.
[32] Taylor,W.,2013.Using CAViaR models with implied volatility for Value-at-Risk estimation. Journal of Forecasting. 32, 62–74.
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[33] Simone,M.,Halbert,W.,2015.VAR for VaR: measuring tail dependence using multivariate regression quantiles. Journal of Econometrics.187, 169–188.
EP
[34] David, G., 2016. The Systemic Risk of Cross-Border Banking: Evidence from the Sudden Stop and Interbank Stress Contagion in East Asia. Emerging Markets
AC C
Finance and Trade. 52, 237–254.
[35] Kyoo, K., 2017. Estimating production functions with control functions when capital is measured with error. Journal of Econometrics. 190, 267–279.
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ACCEPTED MANUSCRIPT This paper mainly studies the impact of the US dollar index and the euro on the overnight risk of the foreign exchange markets of Asian countries and regions. We select the RMB exchange rate, the Hong Kong exchange rate and the Japanese Yen
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exchange rate as the research objects. Overnight risk is the risk of the exchange rate closing up to the opening of the next day. The main contribution of this paper has the following aspects:
SC
1. The current literature lacks the study of the overnight risk of exchange rates.
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Based on the multi-quantile CAViaR model of the two markets which was proposed by Simone and Halbert(2015), this paper proposes a multi-quantile CAViaR model of three markets to analyze the impact of the US Dollar and the Euro on the overnight risk of the Asian foreign exchange market;
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2. The impact on the overnight risk of the Asian foreign exchange market when the Dollar and the Euro fall at the same time is greater than that when they do not fall at the same time, so based on the multi-quantile CAViaR model of three markets, this
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paper further consider the effect of joint-shock impact from the idea of David(2016)
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and Kyoo(2017) to propose a multi-quantile CAViaR model for joint shock. 3. Furthermore, the conclusions of the this study have important policy
implications for how to management the overnight risk.
S0264-9993(18)30142-1
DOI:
https://doi.org/10.1016/j.econmod.2018.11.023
Reference:
ECMODE 4779
To appear in:
Economic Modelling
Received Date: 27 January 2018 Revised Date:
13 August 2018
Accepted Date: 27 November 2018
Please cite this article as: Peng, W., Zeng, Y., Overnight exchange rate risk based on multiquantile and joint-shock CAViaR models, Economic Modelling (2019), doi: https://doi.org/10.1016/ j.econmod.2018.11.023. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Overnight exchange rate risk based on multi-quantile and joint-shock CAViaR models
a
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Wei Penga(Corresponding author)
School of Finance, Zhongnan University of Economics and Law, 182# Nanhu Avenue,
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East Lake High-tech Development Zone, Wuhan 430-073, P.R. China
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Email: [email protected]
Yufeng Zengb
b
School of Economics, Fudan University , 220# Handan Road, Yangpu District ,
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Acknowledgments
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Shanghai 200-433, P.R. China
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This research was supported by the General Humanities and Social Sciences Research Project of Education Ministry“Research on Risk Conduction Measurement and Coordination Supervision Policy among Different Financial Sectors in China Based on Multi-quantile CAViaR”(Grant Number, 18YJC630132).
ACCEPTED MANUSCRIPT Overnight exchange rate risk based on multi-quantile and joint-shock CAViaR models
Abstract: Overnight risk of exchange rate is more and more important because the
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exchange rate trading time of various countries is inconsistent. Drawing on the multi-quantile CAViaR model for two markets, this study proposes a multi-quantile
SC
CAViaR model for three markets and a multi-quantile CAViaR model for joint shock. The two new models are used to measure the impact of the U.S. Dollar index and the
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Euro on the overnight risk for the exchange rate of the Japanese Yen, Hong Kong Dollar, and Chinese Renminbi. The results show that, first, a lag risk affects the overnight risk of the three exchange rates, of which the Renminbi exchange rate is subject to the largest risk. Second, the U.S. Dollar index and Euro exchange rate risks
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impact the overnight risk of the three exchange rates and this effect is highest for the overnight risk of the Yen’s exchange rate. In addition, the impact of the U.S.Dollar
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index risk is greater than that of the Euro. Third, the Euro and U.S.Dollar index produce a joint shock on the overnight risk of the three exchange rates, and here, the
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Yen’s exchange rate suffers the biggest shock. Finally, the multi-quantile CAViaR model for joint shock is more accurate than that for three markets, particularly when the Hong Kong Dollar exchange rate has a 5% VaR. These empirical results have meaningful implications for regulatory authorities.
Keywords: Value at Risk; exchange markets; overnight risk
JEL: C13, C14, C32, G10 1
ACCEPTED MANUSCRIPT
1. Introduction
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Exchange rate risks have critical implications for an economy: foreign countries could suffer the repercussions of a domestic crisis or a foreign crisis could impact a domestic economy [1–3]. In 1992, Soros sniped the pound and this led to the
SC
withdrawal of Britain from the European Union, which negatively impacted the British economy. The 1998 financial crisis in Southeast Asia was also due to a trade attack by
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Soros. The 2008 subprime mortgage crisis caused a major setback in the U.S. economy and resulted in the quantitative easing policy by the Federal Reserve [4, 5]. Subsequently, there was a worldwide influx of dollars, causing its value to depreciate
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[6, 7]. These aspects highlight that with intensifying global economic integration and regular financial fluctuations, effectively measuring and managing exchange rate risks have become a critical issue in various countries [8–11].
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In the global exchange rate markets, the U.S. Dollar index and Euro exchange rate
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occupy an important position and fluctuations in either are likely to affect major countries and economies [12–14]. In fact, both exchange rates have a peculiar impact on Asian countries and regions. The exchange markets for Asian countries and regions, particularly, Japan, Hong Kong, and China, close at 16:00 Beijing time, as per which the Euro and U.S.Dollar exchange rate markets open after 16:00 and close at night. In other words, exchange trade for the Euro and U.S.Dollar takes place outside the trading hours for the Asian foreign exchange markets [15–17]. Thus, the impact of 2
ACCEPTED MANUSCRIPT fluctuations in the Euro and U.S. Dollar index is reflected only the next trading day for the Asian exchange markets [18, 19]. This risk between foreign exchange closure and the next day’s opening is called the overnight risk of an exchange rate.
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This study attempts to answer the following questions. What is the impact of the U.S. Dollar index and Euro exchange rate on the exchange markets in Asian countries
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and regions? What are the differences between the impacts? Can foreign exchange regulators and management departments in Asian countries forecast and manage the
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trend of national exchange rate movements and overnight risk according to the volatility of the previous day’s exchange rate? Addressing these questions will not only help investors make optimal portfolio decisions in relevance to the foreign exchange market but also provide theoretical and practical guidance for policymakers
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and market regulators to more effectively manage overnight risk.
This study mainly employs the value-at-risk (VaR) method, which is based on the
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conditional autoregressive value at risk by regression (CAViaR) models, to measure
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overnight risk. The application of the VaR approach to estimate global risk was first proposed by JPMorgan Chase Bank in 1994. The Basel Accords are clearly defined by the use of VaR to calculate risks.
Koenker [20] proposed a quantile regression (QR) method to resolve the
optimization problem of loss function expectations and since then, numerous scholars have conducted related research. Engle and Manganelli [21] proposed CAViaR, which is a milestone in quantile regression given that its modeling challenges the general 3
ACCEPTED MANUSCRIPT idea and constructs VaR itself. The CAViaR model is divided into four quantile models: symmetric absolute value (SAV) model, asymmetric slope (AS) model, IG (indirect GARCH) model, and adaptive(AD) model, of which the AD model has been
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proven to be worst and no scholar conducts empirical research using it. Considerable recent research [22–25] has compared the CAViaR with the GARCH model and the historical data simulation method and shown that the VaR calculated using the
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CAViaR model is more accurate, a finding which has been supported by various
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additional studies. Kuester [26], Taylor [27], Frank and Masao [28], Sergio et al. [29], and Mauro and Leopoldo [30] improve the CAViaR model on the basis of the IG and AS models. The improved model is then compared with the GARCH model and the results show that the former is a better way to describe the evolution of market risk.
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Richard and Cathy [31] add the threshold function to the CAViaR model and prove that the improved model is more accurate. Drawing on Frank [28], Taylor [32] proposes a CAViaR model for threshold-weighted asymmetric AS and uses the model
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to analyze the Asian stock market. Simone and Halbert [33] adopt the CAViaR model
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to examine risk interactions between the two markets and accordingly, propose the multi-quantile CAViaR model.
This study mainly examines the impact of the U.S. Dollar index and Euro on the
overnight risk of the foreign exchange markets in Asian countries and regions. To do so, it focuses on the exchange rates of the Chinese Renminbi, Hong Kong Dollar, and Japanese Yen as research objects. The analysis makes two main contributions. First, the current literature lacks research on the overnight risk of exchange rates. By 4
ACCEPTED MANUSCRIPT drawing on Simone and Halbert’s [33] multi-quantile CAViaR model for two markets, this study proposes a multi-quantile CAViaR model for three markets to analyze the impact of the U.S. Dollar and Euro on the overnight risk of the three exchange rates.
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Second, the impact on the overnight risk for the Asian foreign exchange market is greater when the U.S. Dollar and Euro fall at the same time, as opposed to when they do not. Using the multi-quantile CAViaR model for three markets, this study further
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considers the effect of a joint shock, as suggested by David [34] and Kyoo [35], to
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propose a multi-quantile CAViaR model for joint shock.
2. Methodology
2.1 Conditional autoregressive value at risk by regression
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Following Koenker [20], Engle and Manganelli’s [21] CAViaR model can directly model the tail risk instead of estimating the tail distribution. According to Engle and Manganelli [21], the CAViaR model takes the form of a symmetric absolute
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value(SAV), asymmetric slope(AS), and indirect GARCH(IG)model.
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The symmetric absolute value(SAV) model is as follows:
f t (θ ) = β 1 + β 2 f t −1 (θ ) + β 3 yt −1 ,
(1)
where yt −1 is the market index rate of return, yt −1 is the absolute value of the
market index rate of return, ft (θ ) is the θ conditions quantile of y t , and ft (θ ) is the function of VaR.
The asymmetric slope(AS) model can be specified as 5
ACCEPTED MANUSCRIPT f t (θ ) = β1 + β 2 f t −1 (θ ) + β 3 yt −1 I ( yt −1 > 0) + β 4 yt −1 I ( yt −1 < 0) ,
(2)
where yt −1 is the market index rate of return, yt −1 is the absolute value of the market index rate of return, ft (θ ) is the θ conditions quantile of y t , and ft (θ ) is
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the function of VaR. Different from SAV model, the AS model incorporates the asymmetric term I () to denote the asymmetric effects of the threshold function on
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the market rate of return.
The indirect GARCH(IG) model is
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ft (θ ) = ( β1 + β 2 f 2t −1 (θ ) + β3 y 2t −1 )1/2 ,
(3)
where yt −1 is the market index rate of return, yt −1 is the absolute value of the
the function of VaR.
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market index rate of return, ft (θ ) is the θ conditions quantile of y t , and ft (θ ) is
However, the CAViaR model mainly analyzes dynamic risk characteristics in a
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single market and cannot capture the complex relationship of risk contagion among
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various markets.
To overcome this deficiency, Simone and Halbert [33] extend the traditional
CAViaR model to the multi-quantile CAViaR model for two markets by expanding the single-equation quantile regression concept to a structural-equation vector auto-regression and reveal that VaR in a single market is affected not only by its own market but also by risk spillovers from other markets.
Simone and Halbert’s [33] multi-quantile CAViaR model for two markets is as 6
ACCEPTED MANUSCRIPT follows:
f1,t (θ ) = c1 + a11 y1,t −1 + a12 y2,t −1 + b11 f1,t −1 (θ ) + b12 f 2,t −1 (θ ) ,
(4)
where y1,t −1 is a market index rate of return, y1,t −1 is the absolute value of the
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market index rate of return, f1,t (θ ) is the θ conditions quantiles of y 1,t , and
f1,t (θ ) is the function of the market VaR. In addition, y2,t −1 is another market index
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rate of return, y2,t −1 is the absolute value of another market index rate of return, f 2,t (θ ) is the θ conditions quantile of y 2 ,t , and f 2,t (θ ) is the function of another
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market’s VaR.
From eq. (4), we see that the multi-quantile CAViaR model for two markets explores the risk interaction between the two markets. The risk to any one market is
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affected by the return rate in the other market and a lag risk.
2.2 Model improvement
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The opening and closing time for foreign exchange markets globally differ. The closing time for foreign exchanges in China, Hong Kong, and Japan are 16:00 Beijing
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time. However, as per Beijing time, foreign exchange markets in the United States and Europe open post-16:00 and close during nighttime. Thus, the day’s trading in the U.S. and European foreign exchange markets are bound to impact the overnight risk in the foreign exchange markets of China, Hong Kong, and Japan, which open the following day.
The improved model is presented as follows. 7
ACCEPTED MANUSCRIPT First, drawing on Simone and Halbert’s [33] multi-quantile CAViaR model for two markets, this study proposes a multi-quantile CAViaR model for three markets to analyze the impact of the U.S. Dollar index and Euro on the overnight risk in Asian
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foreign exchange markets (i.e., China, Hong Kong, and Japan).
f1,t (θ ) = c1 + a11 y1,t −1 + a12 y2,t −1 + a13 y3,t −1 + b11 f1,t −1 (θ ) + b12 f 2,t −1 (θ ) + b13 f 3,t −1 (θ ) (5)
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where y1,t −1 is a market index overnight rate of return (China, Hong Kong, or Japan) and the logarithmic return percentage of the second day’s opening price for
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each exchange is divided by the first day’s closing price. y1,t −1 is the absolute value of the market index overnight rate of return, f1,t (θ ) is the θ conditions quantile of
y 1,t , and f1,t (θ ) is the VaR of the overnight risk for one exchange rate (RMB, HKD, or JPY). y2,t −1 is the U.S. Dollar’s day rate of return. f 2,t −1 (θ ) is the θ conditions
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quantile of y 2 , t − 1 and f 2,t −1 (θ ) is the day VaR for the U.S. Dollar. y3,t −1 is the Euro’s day rate of return. f 3,t −1 (θ ) is the θ conditions quantile of y 3 , t − 1 and
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f 3,t −1 (θ ) is the day VaR of the Euro.
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Second, this study further considers the impact of a joint shock. The influence of an overnight risk on the Asian foreign exchange market (i.e., China, Hong Kong, and Japan) is greater when the U.S. Dollar and Euro fall at the same time, rather than when they do not. Thus, as per the multi-quantile CAViaR model for three markets, this study further considers the effect of a joint shock, as suggested by David [34] and Kyoo [35], to propose a multi-quantile CAViaR model of joint shock.
, 8
ACCEPTED MANUSCRIPT f1,t (θ ) = c1 + a11 y1,t −1 + a12 y2,t −1 + a13 y3,t −1 + b11 f1,t −1 (θ ) + b12 f 2,t −1 (θ ) +b13 f 3,t −1 (θ ) + d1 y2,t −1 y3,t −1 I ( y2,t −1 < 0) I ( y3,t −1 < 0)
(6)
where y1,t −1 , f1,t −1 (θ ) , y2,t −1 , f 2,t −1 (θ ) , y3,t −1 , and f 3,t −1 (θ ) are the same as
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those in eq. (5). Threshold function I () denotes that the U.S. Dollar and Euro exchange rate return are less than zero, indicating that the U.S. Dollar and Euro fall at the same time.
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2.3 Model robustness test
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This analysis employs the RQ value, DQ test, and LR test to verify the estimations.
2.3.1 RQ value
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Referencing Engle and Manganelli [21], the objective function can be specified as
(7)
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n n min β∈Rk ∑ θ yt − ft (θ ) + ∑ (1 − θ ) yt − ft (θ ) . {t:yt > ft (θ )} {t: yt < ft (θ )}
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The RQ value is the objective function of eq. (7) and the lower the RQ value, the better the model.
2.3.2 DQ test
The DQ test can be organized as follows according to Engle and Manganelli [21]. If yt − f t (θ ) < 0 , ft (θ) denote VaR, then, VaR is insufficient to cover actual losses. This is called a “hit event.” 9
ACCEPTED MANUSCRIPT Hitt (θ) = I(yt < ft (θ)) −θ
.
(8)
Hit is uncorrelated with any variable belonging to information set Ω :
.
(9)
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E(Hittωt−1) = ωt−1E(Hitt ωt−1) = 0 ∀ωt−1 ∈Ωt−1
A good model should produce a sequence of unbiased and correlated hits, such that the explanatory power of this artificial regression should be zero.
{ I ( yt < ft (θ ))} . The null hypothesis is
is the
H0 :δ = 0 .
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indicator functions of
{It }
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Hitt (θ ) = δ0 + δ1Hitt −1 + .... + δ p Hitt − p + δ p+1 ft (θ ) + δ p+2 I year1,t + .... + δ p+2+n I yearn+1,t + µt . (10) Rewriting it in matrix form, we get
Hitt =Xδ + µt .
(11)
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The rewriting in matrix form of eq(10) is eq(11).X stands for vector of eq (10), δ stands for coefficient, µt stands for error term. The asymptotic distribution of the OLS estimator under the null can be easily
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established, invoking an appropriate central limit theorem: (12)
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δ OLS = ( X ' X ) −1 X ' Hit ~ N (0, θ (1 − θ )( X ' X ) −1 ) .
The DQ test statistics obey the chi-square distribution. Next, we derive the
dynamic quantile test statistic:
δ OLS X ' X δ OLS ~ χ 2 ( p + n + 2) θ (1 − θ ) . '
The null hypothesis is H 0 : δ = 0 . 2.3.3 LR test 10
(13)
ACCEPTED MANUSCRIPT The LR test includes LRuc , LRind , and LRcc . This study uses the unconditional coverage test statistic LRuc :
.
(14)
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LRuc = −2 ln[(1 − α ) k − m (α ) m ] + 2 ln[(1 − m / k ) k − m (m / k ) m ] ~ χ 2 (1)
The null hypotheses is m / k = α , where m is the total number of hits, k is the number of samples, and α is the significant level. The LR statistic obeys the
π0 =
(1 − π 0 )T00 (π 0 )T01 (1 − π 1 )T10 (π 1 ) T11 2 = 2 log[( ] ~ χ (1) T00 + T10 T00 + T11 (1 − π pool ) (π pool )
T01 T01 + T00
π1 =
T11 T11 + T10
π
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LRind
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chi-square distribution whose freedom is 1.
pool
=
T0 1
(15)
T 0 1 + T1 1 , + T 0 0 + T1 1 + T1 0
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where T00 is the number of no outliers for two consecutive days, T01 is the number of outliers after normal, T10 is the number of normal value after outliers, and
T11 is the number of outliers within two consecutive days
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2 LRcc = LRind + LRuc ~ χ (2) .
(16)
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3. Data
This study employs the RMB, HKD, and JPY exchange rates as research objects.
Exchange rate pricing is a direct price method that determines the equivalent value for a U.S. Dollar in local currency. A rising exchange rate denotes the appreciation of the U.S. Dollar, while a declining rate indicates the depreciation of the U.S. Dollar. This study focuses on the impact of the U.S.Dollar index and Euro exchange rate on the 11
ACCEPTED MANUSCRIPT overnight risk for the JPY, RMB, and HKD exchange rates.
Table 1 presents the trading hours for the exchange rate markets as per Beijing time. We see that the exchange markets for JPY, HKD, and RMB open during the
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morning and close in the afternoon, whereas the trading for the U.S. Dollar and the Euro takes place in the afternoon and evening. Thus, the U.S. Dollar index and Euro
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will inevitably affect the three exchange rates once the market opens the next day. .
Exchange rate market RMB, Hong Kong and Yen Euro
20
00
Time
8
00 16
16
00
00
24 00
4:00 the next morning
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U.S. Dollar
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Table 1 Trading hours for exchange rate market (Beijing time)
Therefore, the data for the three exchange rate markets in this study are the logarithmic return percentage of the second day’s opening price for each exchange
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divided by the first day’s closing price. The data for the U.S. Dollar index and Euro
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markets are the daily logarithmic return percentage. The full sample period is January 4, 2010–2018. To match the data sample, the non-trading days are eliminated, resulting in 2,060 observations. To test the robustness of the present model, all data samples are divided for in- and out-of-sample testing. Among them, 1,560 data samples are employed in the simulated empirical model and the remaining 500 are applied to out-of-sample backtesting. All the data are from the Flush iFinD financial database.
12
ACCEPTED MANUSCRIPT Table 2 Summary statistics for returns U.S. Dollar
Euro
Yen
Hong
index
RMB
Kong
0.003656
0.004265
0.010949
0.000134
-0.004062
Max
1.947040
2.372358
2.509413
0.124377
1.071091
Min
-2.046598
-2.852691
-2.434121
-0.165909
-1.217969
St.D
0.465941
0.583086
0.177527
0.009147
0.100617
Skew
-0.002395
-0.045348
1.660918
-3.412024
-1.251197
p-value
0.000106
0.00028
0.00000
0.00000
0.00000
Kurtosis
4.523057
4.784520
63.20915
109.7397
42.16946
p-value
0.000118
0.000102
0.00000
0.00000
0.00000
JB test
199.1097
274.0433
311953.6
981450.8
132162.8
p-value
0.00000
0.000000
0.000000
0.000000
0.000000
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Mean
Notes: As per the p-value from the Jarque–Bera test, the distribution of the returns of
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exchange rate is not Gaussian.
Table 2 reports the log returns for each currency. In particular, the Euro shows
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highest volatility, while Hong Kong’s currency has the lowest. In addition, the Jarque–Bera statistics are significant, implying the returns for these variables do not follow the normal distribution. Therefore, employing the CAViaR approach is suitable for the present estimates.
4. Empirical results This study selects quantiles θ that equal 1% and 5%. By incorporating the U.S. 13
ACCEPTED MANUSCRIPT Dollar index and Euro, it is possible to compare and contrast the effects that both factors have on the overnight risk of these currencies.
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4.1 Quantile θ =1% Tables 3 and 4 present the results of the multi-quantile CAViaR model for three markets and the multi-quantile CAViaR model for joint shock.
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Table 3 Estimates of multi-quantile CAViaR model for three markets at 1% quantile Hong Kong
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Yen
RMB
1%--quantile
c1
0.1256(0.5120)
a11
0.0135(0.0211)
a12
1.8926**(0.0035)
a13 b11
1.6404**(0.0266)
1.3813(1.0297)
0.8836**(0.0124)
0.9012**(0.0119)
0.8809(0.9297)
0.0586**(0.0108)
0.0186**(0.0024)
0.1515**(0.0152)
0.4233**(0.0227)
0.2783*(0.1587)
0.2536**(0.0815)
0.3784*(0.1958)
0.1568**(0.0489)
0.0465**(0.0082)
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1.0894*(0.5397)
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b13
0.0778(0.2690)
1.8318**(0.0115)
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b12
0.4048(0.3458)
Notes
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level. The null
hypothesis is that the coefficient is 0.The numbers in parentheses are standard errors.
Tables 3 and 4 show that coefficients a12 for the three exchange rates are significant, indicating the U.S. Dollar index rate of return has an impact on overnight risks. Of the three exchange rates, the U.S. Dollar has the most prominent impact on 14
ACCEPTED MANUSCRIPT the overnight risk for JPY and the least effect on that for RMB. The results in Table 3 show that coefficients a13 for the exchange rates for JPY and HKD are significant, indicating that the Euro exchange rate of return impacts the
suggesting no effect by the Euro exchange rate of return.
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overnight risk for both currencies. However, coefficient a13 for RMB is insignificant,
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Table 4 Estimates of multi-quantile CAViaR model for joint shock at 1% quantile Yen
Hong Kong
RMB
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1%--quantile
0.1952(0.2088)
0.5063(1.8251)
0.0779(0.7839)
a11
0.1133**(0.0065)
1.3407(2.5633)
1.2058(1.6622)
a12
1.2527*(0.6682)
1.0838**(0.0206)
1.0393*(0.5869)
a13
0.6866**(0.0127)
0.6062(1.0383)
0.4866(0.8033)
b11
0.1886**(0.1814)
0.2586**(0.0433)
0.4566**(0.0339)
0.6253**(0.1929)
0.4585**(0.0839)
0.2776**(0.0869)
0.1538**(0.0482)
0.0425**(0.0155)
0.6708**(0.2055)
0.1066**(0.0421)
0.2734*(0.1314)
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b13
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b12
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c1
d1
Notes
0.7892**(0.0925)
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level. The null
hypothesis is that the coefficient is 0.The numbers in parentheses are standard errors.
Tabled 3 and 4 suggest that coefficients b11 are significant for the three exchange rates; that is, the overnight risk for the three exchange rates is affected by the lag risk. Among these, the impact is highest on the RMB exchange rate. 15
ACCEPTED MANUSCRIPT In addition, coefficients b12 for the three exchange rates are all significant, indicating that the U.S. Dollar index impacts the overnight risk for all three exchange rates. Of these, it has the strongest impact on the overnight risk for the Yen’s exchange
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rate and least effect on that of the renminbi. Coefficients b13 are equally significant for the three exchange rates, suggesting
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the Euro influences the overnight risks for all three exchange rates, of which it has the greatest effect on the Yen’s exchange rate and the least impact on that of the RMB.
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Thus, Tables 3 and 4 demonstrate that, compared to the Euro, the U.S. Dollar index has a greater impact on the overnight risk of the three exchange rates. Coefficients d1 for the three exchange rates (Table 4) are all significant,
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indicating that the overnight risks for all three rates are affected by the joint shock from the U.S. Dollar index and Euro. More specifically, the impact on the overnight risk for the three exchange rates is greater when the U.S. Dollar index and Euro fall at
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the same time rather than when they do not. Further, the joint shock has a higher
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effect on the overnight risk for the Yen than that for Hong Kong Dollar and renminbi, which is affected the least. This can be mainly attributed to China’s strict control system for foreign exchange. 4.2 Quantile θ =5%
Tables 5 and 6 present the results of the multi-quantile CAViaR models for three markets and joint shock.
16
ACCEPTED MANUSCRIPT Table 5 Estimates of multi-quantile CAViaR model for three markets at 5% quantile Yen
Hong Kong
RMB
0.7289(0.8652)
a11
0.0188**(0.0047)
a12
1.8024**(0.0861)
1.8501**(0.1772)
1.0393(1.825)
a13
0.8434**(0.2802)
0.9244**(0.0052)
0.8070(0.8855)
b11
0.0468**(0.0158)
0.0896**(0.0774)
0.2333**(0.0554)
b12 b13 Notes
0.4333(0.1282)
0.3730(0.7866)
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c1
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5%--quantile
1.5818(1.2308)
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1.8408**(0.1665)
0.5908**(0.1559)
0.4563*(0.2290)
0.2088**(0.0288)
0.3988*(0.2206)
0.2343**(0.0032)
0.1687**(0.0115)
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level. The null
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hypothesis is that the coefficient is 0.The numbers in parentheses are standard errors.
As shown in Table 5, coefficients a12 are significant for the exchange rate of the
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Japanese Yen and Hong Kong Dollar, indicating that the overnight risks for the
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exchange rates of both currencies are affected by the U.S. Dollar index rate of return .In addition, coefficients a13 for the Japanese Yen and Hong Kong Dollar are significant, indicating that the Euro exchange rate of return affects the overnight risk of both currencies, of which it has a greater effect on the Hong Kong Dollar. Coefficients b11 for the three exchange rates (Tables 5 and 6) are all significant, indicating that the lag risk affects the overnight risk for the three rates. The impact of lag risk is highest for the overnight risk of the RMB exchange rate. 17
ACCEPTED MANUSCRIPT Table 6 Estimates of multi-quantile CAViaR model for joint shock at 5% quantile Yen
Hong Kong
RMB
5%--quantile 0.2355*(0.1282)
0.4454(0.6028)
a11
0.5887(0.7299)
1.5902(1.1220)
a12
0.8096**(0.0083)
0.3609(0.0698)
a13
0.5434(0.7098)
0.6062**(0.0522)
b11
0.2478**(0.0042)
0.4089**(0.0371)
0.9084(0.6988)
1.0393(0.8077)
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0.5080(0.7754)
0.5886**(0.0764)
0.7690**(0.0148)
0.5880*(0.2808)
0.3792**(0.0238)
b13
0.5754*(0.0240)
0.4509**(0.0533)
0.2643*(0.1288)
d1
0.6809**(0.0301)
0.4363**(0.1059)
0.3311**(0.0261)
b12
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level. The null
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Notes
0.0871(0.7041)
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c1
hypothesis is that the coefficient is 0.The numbers in parentheses are standard errors.
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Coefficients b12 (Tables 5 and 6) for the three exchange rates are all significant,
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suggesting that the U.S. Dollar index affects the overnight risk for all three exchange rates. The U.S.Dollar index risk has the strongest impact on the Yen’s exchange rate and the least impact on the RMB exchange rate.
From Tables 5 and Table 6, we see that the impact of the U.S.Dollar index on the
overnight risk of the three exchange rates is greater than that of the Euro. Coefficients b13 for the three exchange rates are equally significant, indicating that the Euro risk affects the overnight risks of the three exchange rates (Tables 5 and 18
ACCEPTED MANUSCRIPT 6). Among the three, the Euro risk has the greatest effect the Yen’s exchange rate and the least influence on that of the RMB. ～ Finally, coefficients d1 of the three exchange rates in Table 6 are all significant,
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suggesting that the overnight risks for all three exchange rates are affected by the joint shock of the U.S. Dollar index and Euro. Further, the impact on overnight risk of the
SC
three exchange rates is greater when the U.S.Dollar index and Euro fall at the same time than when they do not. The joint shock on the overnight risk for the Yen is
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greater and the least for the RMB exchange rate. This is also mainly due to China’s strict control system for foreign exchange.
5. Model robustness test
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Tables 7 and 8 present the results for the RQ and DQ tests of the multi-quantile CAViaR models for three markets and joint shock.
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Table 7 RQ and DQ tests of multi-quantile CAViaR model for three markets
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Yen
Hong Kong
RMB
1%--quantile
RQ
6.5043[0.2369]
1.1174[0.6089]
4.8063[0.3025]
DQ test (IS)
0.1098[0.9650]
0.1970[0.7938]
0.6702[0.2760]
DQ test (OS)
0.1507[0.8756]
0.1298[0.9268]
0.1259[0.9371]
5%--quantile RQ
9.3433[0.1208]
5.5437[0.2562]
7.4327[0.2162]
DQ test (IS)
0.1186[0.9554]
0.2052[0.7451]
0.5862[0.3263]
19
ACCEPTED MANUSCRIPT DQ test (OS)
0.3169[0.6366]
0.1045[0.9663]
0.1032[0.9673]
Notes The numbers in square brackets are p-values. IS and OS denote in- and out-of-sample.
Table 8 RQ and DQ tests of multi-quantile CAViaR model for joint shock Hong Kong 1%--quantile
RMB
RI PT
Yen
6.4045[0.2374]
1.1071[0.6377]
4.4060[0.3251]
DQ test (IS)
0.1283[0.9352]
0.1925[0.7968]
0.1711[0.8250]
DQ test (OS)
0.1871[0.8136]
0.1136[0.9561]
0.1622[0.8344]
M AN U
SC
RQ
5%--quantile
8.0967[0.1422]
5.1439[0.2680]
7.3321[0.2189]
DQ test (IS)
0.3284[0.5476]
0.1397[0.8906]
0.1647[0.8327]
DQ test (OS)
0.1026[0.9802]
0.1307[0.9061]
0.3260[0.5691]
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RQ
Notes The numbers in square brackets are p-values. IS and OS denote in- and out-of-sample.
As indicated in Tables 7 and 8, irrespective of 1% or 5% quantiles θ , the
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multi-quantile CAViaR models for three markets and joint shock pass the DQ test.
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However, the RQ values for the multi-quantile CAViaR model for joint shock are smaller than those of the multi-quantile CAViaR model for three markets. Thus, the former model for joint shock is better than the latter for three markets.
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ACCEPTED MANUSCRIPT Table 9 LR test ( θ = 1% ) the multi-quantile
CAViaR model of three markets
CAViaR model of joint-shock
1%--quantile
P-value
0.9353
LRind
2.1565
P-value
0.1420
LRcc
2.1631
P-value Hong
Notes
2.4052
0.1209
2.5199 0.2837
0.7753
0.7027
0.3786
0.4019
LRind
1.2205
1.5331
P-value
0.2693
0.2156
LRcc
1.9958
2.2358
P-value
0.3687
0.3270
LRuc
0.0029
0.5681
P-value
0.9571
0.4510
LRind
2.0388
1.2550
P-value
0.1533
0.2626
LRcc
2.0417
1.8231
P
0.3603
0.4019
LRuc P-value
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RMB
0.7349
0.3391
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Kong
0.1147
SC
0.0066
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LRuc
EP
Yen
RI PT
the multi-quantile
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level.
21
ACCEPTED MANUSCRIPT Table 10 LR test ( θ = 5% ) the multi-quantile
CAViaR model of three markets
CAViaR model of joint-shock
5%--quantile
P-value
0.7023
LRind
0.7621
P-value
0.3827
LRcc
0.9082
P-value Hong
Notes
0.6533
0.4189
0.6875 0.7091
1.1691
2.8092
0.2796
0.0937
LRind
9.4735**
2.6640
P-value
0.0000
0.1026
LRcc
10.6426**
5.4732
P-value
0.0000
0.0648
LRuc
2.7098
2.4485
P-value
0.0997
0.1176
LRind
1.0805
1.4309
P-value
0.2986
0.2316
LRcc
3.7903
3.8794
P-value
0.1503
0.1437
LRuc P-value
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RMB
0.8533
0.6350
TE D
Kong
0.0342
SC
0.1461
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LRuc
EP
Yen
RI PT
the multi-quantile
* and ** indicate rejection of the null hypothesis at the 5% and 1% significance level.
22
ACCEPTED MANUSCRIPT Tables 9 and 10 list the LR test results for the three exchange rates. We see that the values of the multi-quantile CAViaR model for joint shock pass the test. When θ = 1%, the multi-quantile CAViaR model for three markets passes the LR test. However,
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when θ = 5%, the LRind and LRcc statistics for the Hong Kong exchange rate are significant. Thus, the multi-quantile CAViaR model for three markets fails the LRind and LRcc tests, indicating that the multi-quantile CAViaR model for joint shocks is
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better.
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From the DQ test, RQ value, and LR test, we see that the multi-quantile CAViaR model for joint shock is better than the multi-quantile CAViaR model for three markets; however, when θ is 5% , the multi-quantile CAViaR model for joint shocks
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has more advantages for the Hong Kong exchange rate.
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1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
Yen
2015/7/31 2015/12/3 2016/4/6 2016/8/9 2016/12/12 2017/4/14 2017/8/17 2017/12/20
2010/9/20 2011/1/21 2011/5/26 2011/9/28 2012/2/6 2012/6/11 2012/10/15 2013/2/18 2013/6/25 2013/11/6 2014/3/18 2014/7/22 2014/11/24 2015/3/27
2010/1/5 2010/5/14
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1%～VaR 5%～VaR
Fig. 1 Overnight risk in multi-quantile CAViaR model for joint shock (Yen)
23
0.5
0 RMB
2.5
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Fig. 2 Overnight risk in multi-quantile CAViaR model for joint shock (Hong Kong)
SC
24
RI PT
0 2015/7/31 2015/12/3 2016/4/6 2016/8/9 2016/12/12 2017/4/14 2017/8/17 2017/12/20
2010/9/20 2011/1/21 2011/5/26 2011/9/28 2012/2/6 2012/6/11 2012/10/15 2013/2/18 2013/6/25 2013/11/6 2014/3/18 2014/7/22 2014/11/24 2015/3/27
2010/1/5 2010/5/14
0.5
2015/7/31 2015/12/3 2016/4/6 2016/8/9 2016/12/12 2017/4/14 2017/8/17 2017/12/20
1
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1.5
2010/9/20 2011/1/21 2011/5/26 2011/9/28 2012/2/6 2012/6/11 2012/10/15 2013/2/18 2013/6/25 2013/11/6 2014/3/18 2014/7/22 2014/11/24 2015/3/27
2
EP
2010/1/5 2010/5/14
AC C
ACCEPTED MANUSCRIPT HongKong
3
2.5
2
1.5 1%～VaR 5%～VaR
1
1%～VaR 5%～VaR
Fig. 3 Overnight risk in multi-quantile CAViaR model for joint shock (RMB)
ACCEPTED MANUSCRIPT 0 Yen HongKong RMB
-0.02
-0.04
RI PT
-0.06
-0.08
-0.1
0
20
40
60
80
100
120
140
160
M AN U
-0.14
SC
-0.12
180
200
Fig. 4 Impulse response of market shocks (1%)
0 -0.01
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-0.02
Yen HongKong RMB
-0.03 -0.04
EP
-0.05 -0.06
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-0.07 -0.08 -0.09
0
20
40
60
80
100
120
140
160
180
200
Fig. 5 Impulse response of market shocks (5%)
Note: Figs. 4 and 5 depict the response of the future 200 periods for the Yen, Hong Kong Dollar, and renminbi in the multi-quantile CAViaR model of joint shocks when the three exchange rates are simultaneously given one unit of standard deviation of new information shock. The estimation is
25
ACCEPTED MANUSCRIPT performed using Simone and Halbert’s [33] quantile impulse response function (QIRF). The abscissa represents the period,the ordinate represents the impact value.
Figs.1-3 show the VaR of overnight risk. The impact of the Dollar index and the
RI PT
Euro exchange rate on the exchange markets of Yen,Hong Kong Dollar and RMB is our topic. Everyday VaR is calculated through the multi-quantile CAViaR model for
SC
three markets and the multi-quantile CAViaR model for joint shock proposed in this paper, so we can obtain the VaR series.
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Figs. 4 and 5 depict the response of the future 200 periods for the Yen, Hong Kong Dollar, and Renminbi in the multi-quantile CAViaR model of joint shocks when the three exchange rates are simultaneously given one unit of standard deviation of new
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information shock.Whether it is 1% or 5%, the the response of the renminbi will first disappear, and Japan Yen and Hong Kong Dollar will be disappeared closer.
EP
6. Conclusions
This study examines the impact of the U.S. Dollar index and Euro on the overnight
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risk of the foreign exchange markets in Asian countries and regions, particularly the RMB, HKD, and JPY exchange rates. Referencing Simone and Halbert’s [33] multi-quantile CAViaR model for two markets, a multi-quantile CAViaR model for three markets is proposed. The model for three markets is then used to further consider the effect of a joint shock, as suggested by David [34] and Kyoo [35], to propose a multivariate quantile CAViaR model for joint shock. The two new models are applied to measure the impact of the U.S.Dollar index and Euro on the overnight 26
ACCEPTED MANUSCRIPT risk for the Yen’s, Hong Kong Dollars, and Renminbi’s exchange rate for 2010–2018.
The study presents the following empirical results, and accordingly, policy implications. First, the lag risk affects the overnight risk for all three exchange rates,
RI PT
of which the RMB exchange rate suffers the highest risk. Thus, it is important that foreign exchange administrations in Japan, Hong Kong, and particularly, China pay
SC
close attention to the lagging risk of their exchange rates. Second, the U.S.Dollar index risk and Euro exchange rate risk impact the overnight risk for the three
M AN U
exchange rates, of which it has largest effect on the overnight risk of the Yen’s exchange rate and the smallest on the RMB exchange rate. In this case, Japanese regulators must pay close attention to the day’s volatility in the U.S. Dollar index and Euro given that both exchange rate risks have the highest impact on the overnight risk
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of the Yen. In addition, the forecast and management of the opening exchange rate for the Japanese Yen should be based on the day’s movements in the U.S. Dollar index
EP
and Euro. In comparison, given the strict exchange rate control in China, the impact
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on the overnight risk of the RMB is smaller.
Third, the impact of the U.S.Dollar index risk on the overnight risk for the three
exchange rates is greater than that of the Euro. Therefore, Japan, Hong Kong, and China’s foreign exchange administrations should more closely monitor the movements of the U.S. Dollar index than those of the Euro. Fourth, the overnight risk of the three exchange rates is affected by the joint shock of the Euro and U.S. Dollar index. More specifically, the Yen’s exchange rate suffered the biggest shock, followed
27
ACCEPTED MANUSCRIPT by the exchange rates for the HKD and RMB. Thus, when the Euro and U.S. Dollar index fall at the same time, it seems imperative to focus on the effect of combined shocks on the next day’s opening of the domestic exchange rate. Further, risk
RI PT
management departments must be well prepared to effectively forecast and manage domestic exchange rate fluctuations, promote capital stability, and prevent large-scale capital outflows. Finally, the multi-quantile CAViaR model for joint shocks is more
SC
accurate than that for three markets and has more advantages when θ of the Hong
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Kong exchange rate is 5%.
References
[1] Srideep,G., Janice,B., 2010. Nominal exchange rate volatility, relative price
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volatility and the real exchange rate. Journal of International Money and Finance. 29, 840–856.
[2] Gabaix,X.,Maggiori,M.,2015.International liquidity and exchange rate dynamics.
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The Quarterly Journal of Economics. 130(3), 1369–1420.
AC C
[3] Joseph, M.L., Lambertides, N., Savva, C.S.,2015. Short-horizon excess returns and exchange rate and interest rate effects. Journal of International Financial
Markets, Institutions & Money. 7, 54–76.
[4] Thomas ,J., Lisa,S.,2015.The role of U.S. subprime mortgage-backed assets in propagating the crisis:contagion or interdependence?.The North American Journal of Economics and Finance. 34,167–186.
28
ACCEPTED MANUSCRIPT [5] Hassen, C., 2015. The US home mortgage market during the financial crisis. International Journal of Computational Economics and Econometrics. 5(4), 122–138.
RI PT
[6] Muthucattu,T.P., James,D.K., 2016. The linkages,persistence,asymmetry in the volatility, the price discovery and efficiency, and the effect of the US subprime
India. Applied Economics. 48, 669–683.
SC
mortgage financial crisis on the spot and the futures market’s returns: the case of
M AN U
[7] Manuel ,A.W., Scott,F., Kristopher,G.,2017.The effect of large investors on asset quality: evidence from subprime mortgage securities. Journal of Monetary Economics. 87, 34–51.
TE D
[8] Ding, D., 2012. Exchange rate risk in the US stock market. Journal of International Financial Markets, Institutions & Money. 22, 137–150.
EP
[9] Su,J.B.,2015.Value-at-risk estimates of the stock indices in developed and emerging markets including the spillover effects of currency market. Economic
AC C
Modelling. 46, 204-224.
[10] Ivo, J.M., 2016. IMF Support and Inter-Regime Exchange Rate Volatility. Open Econnomics Review. 23, 193–211.
[11] David, P., 2017. Gauging exchange rate targeting. Journal of International Money and Finance. 43, 155–166.
29
ACCEPTED MANUSCRIPT [12] Gabriela, O., 2016. Statistical analysis regarding the evolutions of the euro exchange rate and the dollar exchange rate, in Romania. Economics and Applied Informatics. 4, 80–91.
Computational Economics. 48(3), 463–472.
RI PT
[13] Fernando,V., 2016. On the historical exchange rates Euro/US dollar.
SC
[14] Corte, P.D.,Ramadorai, T., Sarno, L., 2016. Volatility risk premia and exchange
M AN U
rate predictability. Journal of Financial Economics. 120, 21–40.
[15] Cornell, W. B., Dietrich, J. K.,1978. The efficiency of the market for foreign exchange under floating exchange rates. The Review of Economics and Statistics. 60(1), 111–120.
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[16] Neely, C. J., Weller, P. A. ,2003. Intraday technical trading in the foreign exchange market. Journal of International Money and Finance. 22(2), 223–237.
EP
[17] Petr, Z.,2014. Technical trading and testing of intra-day market efficiency in the foreign exchange market. Acta Universitatis Bohemiae Meridionales. 17(1), 3–
AC C
13.
[18] Panayotocv,G.,Bakshi,G.,2013.Predictability of currency carry trades and asset pricing implications. Journal of Financial Economics. 110, 139–163.
[19] Samuel,W.M.,Robert,B.G., Enrique,H., 2016.Timing foreign exchange markets. Econometrics. 4(15), 22–45.
30
ACCEPTED MANUSCRIPT [20] Koenker, R. ,1978. Regression quantiles. Econometrica. 1, 33–50.
[21] Engle, R., Manganelli, S., 2004. CAViaR: Conditional Autoregressive Value at Risk by regression quantiles. Journal of Business and Economic Statistics. 4,
RI PT
367–381.
[22] James,W.,2005.Generating volatility forecasts from Value at Risk estimates.
SC
Management Science. 51,712–725.
M AN U
[23] Allen, D., Powell, L., 2015. A Gourmet's delight: CAViaR and the Australian stock market. Applied Economics Letters. 19, 1493–1498.
[24] Keith,K., Stefan,M., Marc,S.,2016.Value-at-Risk prediction: a comparison of alternative strategies. Journal of Financial Econometrics. 4,53–89.
TE D
[25] Eugene, S., 2017. Extreme risk spillover network:application to financial institutions. Quantitative Finance.17(9), 58–79.
EP
[26] Kuster, L., 2006. Value-at-Risk prediction: a Comparison of alternative
AC C
strategies. Journal of Financial Econometric. 4, 53–89.
[27] Taylor,W.,2008.Using exponentially weighted quantile regression to estimate Value at Risk and expected shortfall. Journal of Financial Econometrics. 6, 382– 406.
[28] Frank, J., Masao, F., 2009. CAViaR-based forecast for oil price risk. Energy Economics. 31, 511–518.
31
ACCEPTED MANUSCRIPT [29] Sergio,F.,Masao,F., Zudi,L.,2010.Index-exciting CAViaR: a new empirical timevarying risk model. Studies in Nonlinear Dynamics & Econometrics. 14, 38–52.
RI PT
[30] Mauro,B., Leopoldo,C.,2016. Comparison of Value-at-Risk models using the MCS approach. Computational Statistics. 31(2), 579–608.
SC
[31] Richard,H.,Cathy,W.S.,2014.Bayesian time-varying quantile forecasting for Value at Risk in financial markets. Journal of Business & Economic Statistics. 29,
M AN U
481–492.
[32] Taylor,W.,2013.Using CAViaR models with implied volatility for Value-at-Risk estimation. Journal of Forecasting. 32, 62–74.
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[33] Simone,M.,Halbert,W.,2015.VAR for VaR: measuring tail dependence using multivariate regression quantiles. Journal of Econometrics.187, 169–188.
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[34] David, G., 2016. The Systemic Risk of Cross-Border Banking: Evidence from the Sudden Stop and Interbank Stress Contagion in East Asia. Emerging Markets
AC C
Finance and Trade. 52, 237–254.
[35] Kyoo, K., 2017. Estimating production functions with control functions when capital is measured with error. Journal of Econometrics. 190, 267–279.
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ACCEPTED MANUSCRIPT This paper mainly studies the impact of the US dollar index and the euro on the overnight risk of the foreign exchange markets of Asian countries and regions. We select the RMB exchange rate, the Hong Kong exchange rate and the Japanese Yen
RI PT
exchange rate as the research objects. Overnight risk is the risk of the exchange rate closing up to the opening of the next day. The main contribution of this paper has the following aspects:
SC
1. The current literature lacks the study of the overnight risk of exchange rates.
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Based on the multi-quantile CAViaR model of the two markets which was proposed by Simone and Halbert(2015), this paper proposes a multi-quantile CAViaR model of three markets to analyze the impact of the US Dollar and the Euro on the overnight risk of the Asian foreign exchange market;
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2. The impact on the overnight risk of the Asian foreign exchange market when the Dollar and the Euro fall at the same time is greater than that when they do not fall at the same time, so based on the multi-quantile CAViaR model of three markets, this
EP
paper further consider the effect of joint-shock impact from the idea of David(2016)
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and Kyoo(2017) to propose a multi-quantile CAViaR model for joint shock. 3. Furthermore, the conclusions of the this study have important policy
implications for how to management the overnight risk.