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On the interplay between US sectoral CDS, stock and VIX indices: Fresh insights from wavelet approaches
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Contents lists available at ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
On the interplay between US sectoral CDS, stock and VIX indices: Fresh insights from wavelet approaches Syed Jawad Hussain Shahzada, Chaker Alouib, , Rania Jammazic ⁎
a b c
Montpellier Business School, Montpellier, France South Ural State University, Russia College of Business Administration, Prince Sultan University, Riyadh, Saudi Arabia National School of Computer Science (ENSI), Tunis, Tunisia
ARTICLE INFO
ABSTRACT
Keywords: Credit default swaps Stock markets Volatility index Wavelet squared coherence
In this study, we examine the time and frequency connectedness between CDS-stock and CDS-VIX pairs as well as combinations of the three indices for eleven US sectors. The main novelty of the present study is the use of bivariate and multivariate wavelet approaches to explore credit risk hedging and arbitrage opportunities. The findings point to a significantly changing pattern in the dynamic linkage between the given assets in the time–frequency domain. A strong negative (positive) association is unveiled in the long-term horizon for CDS-stock (CDS-VIX) pairs. Three markets seem disconnected in the utilities and industrial sectors and highly connected in the cyclical sectors such as basic materials. The implications of the findings are discussed.
JEL classification: C58
1. Introduction Over the last two decades, the credit default swap (hereafter, CDS) market has been marked by a succession of substantial booms and busts, skyrocketing 68 fold from 180 billion US dollars in 1997 to 62 trillion in 2007. In its heyday, the CDS market's unprecedented development highlighted its phenomenal efficacy as a tool for both hedging and speculating on credit risk. Thereafter, the global CDS market shrank to around 40% of its historical high (ISDA, 2012). After this period of glory, the CDS market underwent into an irreversible tumble, as clearly testified by the Bloomberg report “The incredible shrinking credit default swap market” (Childs, 2014). These sweeping changes in the CDS market sounded the death knell for financial actors to explore, in a more comprehensive way, the interplay between CDS and other financial markets. For academics, the seminal paper by Merton (1974) lead to much literature related to CDS, equity returns and volatility. However, much attention has been paid to the credit risk after the global financial crisis (GFC). We can identify two main recent research strands. The first is concerned with the leading determinants deriving the CDS spread behaviour and co-movements. For instance, Shahzad et al. (2017) and Guesmi et al. (2018) investigate the asymmetric determinants of sectoral indices of the S&P500 and point out that sectoral CDS spreads are affected by positive and negative shocks in the corresponding industry stock price and the overall volatility of the stock market. Using wavelet methods, Hkiri et al. (2018) examine the co-movement between US financial sector CDS spreads and global risk factors including the market volatility index (VIX), oil prices and interest rates. The authors show that VIX is one of the leading risk factor driving the evolution of financial sector CDS spreads, which is also contingent on the frequency. The second strand of the literature is focused on the relative information efficiency of CDS, stock and bond markets. Longstaff et al. (2005) state that stock and bond markets exhibit similar speed of reaction to the arrival of credit market news. Recently, Tiwari et al. (2018),
⁎
Corresponding author. E-mail addresses: [email protected] (S.J.H. Shahzad), [email protected] (C. Aloui), [email protected] (R. Jammazi).
https://doi.org/10.1016/j.frl.2019.06.006 Received 22 January 2019; Received in revised form 5 May 2019; Accepted 19 June 2019 1544-6123/ © 2019 Published by Elsevier Inc.
Please cite this article as: Syed Jawad Hussain Shahzad, Chaker Aloui and Rania Jammazi, Finance Research Letters, https://doi.org/10.1016/j.frl.2019.06.006
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using the Diebold and Yilmaz (2012) spillover approach and wavelet coherence, examine the volatility spillovers among sovereign bonds, CDS spreads, stock market volatility and foreign exchange rates. The authors show that stocks and CDS are net transmitters of volatility. Given these findings, the financial services industry has started taking advantage of the possible significant interplay between CDS and equity markets by offering new products that help market participants in their decisions making. For instance, informed traders often prefer to trade in the CDS market than equities. This trading preference leads to a price discovery advantage in the CDS market. In this context, questions of whether the CDS market provides more accurate risk information than the stock market, and which markets leads and which lags, not only become relevant, but the answers can help provide information about future defaults. The sharp evolution of financial markets and the emergence of new financial products such as volatility futures underscore the paramount relevance of re-assessing the dynamic interaction between financial markets. Risk propagation and its transmission across economic sectors and financial markets has many implications for investors and policy-makers. In the context of financial crisis and economic recession, examining the interplay between credit, stock and volatility future markets across corporate sectors is increasingly important because it helps market participants understand how default probabilities evolve and spread during and after stress periods. Such an understanding provides information about the direction of future defaults, helping market participants price credit derivatives and hedge credit exposure in the sectoral credit market. Furthermore, information about the pricing efficiency and lead-lag relationships helps investors and portfolio managers switch between sectors and dynamically rebalance their credit portfolios. Uncovering these issues is important for policy-makers for the purpose of improving the surveillance of financial systems and reducing systemic risk during crisis periods. Given their heterogeneity and highly diversified nature, CDS and stock markets are obviously complex systems consisting of a multitude of heterogeneous agents operating over very different time horizons (from days to years), who collectively determine aggregate market behaviour. These market participants differ in terms of their expectations, trading strategies and risk profiles. They have asymmetric information sets, and thus heterogeneous beliefs. Therefore, it seems reasonable that the degree of connectedness of the CDS market with stock and volatility markets may vary across the timescales associated with investment horizons. In this context, wavelets offer a unique opportunity to study the dynamics of the co-movement between CDS-stock and CDS-VIX, providing a better picture than time domain methods (Bruzda, 2017; Aloui et al., 2016). Therefore, we rely on the flexible properties of the wavelet coherence and multiple coherence approaches to explore the interplay between pair-wise CDS-stock and CDS-VIX as well as the combination of the three indices. The rest of this article is organized as follows. Section 2 outlines the econometric methodology. Section 3 describes the dataset used and the empirical results of the wavelet approach. Section 4 offers concluding remarks. 2. Methodology In this section, we apply a three step procedure to investigate the interplays between pair-wise CDS-stock and CDS-VIX and the trivariate relationship between them. In doing so, the ARDL bound testing approach of Pesaran et al. (2001) is used to ascertain the existence of a long run relationship between the variables. The Granger non-causality test of Toda and Yamamoto (1995) is used to assess the time domain lead/lag effects between each pair. Finally, the bivariate and multivariate wavelet coherence approaches are used to explore the multi-scale interactions between the three markets. For the sake of brevity, we only provide a detailed description of the wavelet methods. 2.1. Bivariate and multivariate wavelet coherence approaches 2.1.1. Bivariate wavelet coherence Wavelets are ‘small waves’ that grow and decay over a limited time period. They result from a mother wavelet, ψ(t), that can be expressed as a function of two parameters. The first shows where the wavelet is centred (τ: translation parameter) while the second indicates the analysis resolution (s: dilation parameter). Formally, wavelets are defined as:
s , t (t )
t
A^ , s
s with
s
0
(1)
By convoluting the function ψs, t(t) with the time series x(t), we obtain the wavelet transform Wx,(s, τ)
W x ( , s) =
1 s
+
x (t )
t *
s
dt
(2)
where * is the complex conjugate. In recent literature, several wavelet functions are proposed including the Coiflet, Symmlet, Haar, Debauchies, and Gabor wavelets. Choosing the most suitable wavelet is critical, since wavelet coefficients Wx,(s, τ) contain combined information about both the function x(t) and the wavelet-based decompositions ψs,t(t). The most frequently used wavelet is the Morlet wavelet, introduced by Goupillaud et al. (1984). Formally, the Morlet wavelet is given by:
(t ) =
1 4
ei
t
e
2 2
e
t2 2 ,
(3) 2
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where the term e wavelet is:
(t ) =
1 4
2 2
guarantees the admissibility condition. Thus, for η ≥ 5, the term above becomes negligible and the Morlet
(e i t ) e
t2 2
(4)
According to Aguiar-Conraria et al. (2008), WTC is defined as the ratio of the cross-spectrum to the product of the spectrum for each series and can be seen as local correlation between two time series in the time-frequency dimension. Thus, a WTC value close to 1 shows a high degree of synchronization between time series, while a WTC value close to 0 implies no relationship. The WTC isolates regions in the time-frequency domain where the stated time series co-move, even if they do not exhibit a common high power. Following Goupillaud et al. (1984), the cross-wavelet transform of two time series x(t) and y(t) is defined as follows: (5)
Wxy ( , s ) = Wx ( , s ) W * y ( , s )
where Wx(τ, s) and Wy(τ, s) designate the CWTs of x(t) and y(t), respectively. The cross-wavelet power can easily be calculated using the cross-wavelet transform |Wxy(u, s)|. Torrence and Webster (1999) define the squared wavelet coherence (hereafter SWC) coefficient as:
Rt2 (s ) =
S (s 1WtXY (s )) S (s
1
X
2
Wt (s ) )· S (s
1
2
WtY (s ) 2 )
,
(6)
where S is a smoothing operator. WTC can be considered a correlation coefficient localized in the time–frequency domain with a value that ranges between 0 and 1. 2.1.2. Wavelet multiple coherence The multiple wavelet coherence (MWC) can be seen as a generalization of the bivariate coherence approach that enables us to depict the co-movement between a set of independent time series across timescales. Obviously the MWC is more flexible than the standard WC since it encompass a higher dimensionality of the data. Following Huang et al. (2016), the MWC is defined as:
RM 2 (x , y, z ) =
R2 (y, x ) + R2 (y , z ) 1
2Re [R (y, x ). R (y , z )*. R (x , z )*] R2 (y, z )
The ratio mentioned is the squared result of the MWC of the three time series (CDS, stock and VIX). R(y, x)2,R(y, z)2and R(x,z)2are the wavelet squared coherences between each combination of pairs. 3. Data and findings We examine the interplay between US sectoral 5-year industry CDS index spreads, U.S. sectoral equity indices and the VIX volatility index futures. The sectors are banking, financial, telecommunications, health care, oil and gas, basic materials, consumer goods, utilities, industrial, consumer services and technology. The VIX refers to the Chicago Board Options Exchange (CBOE) volatility index, which computes the implied volatility of the S&P500 index options for the next month. The VIX index gauges the fear and financial uncertainty in the US stock market. A higher index reflects greater uncertainty, which may increase the probability of default and therefore result in higher sector CDS spreads. All the data are collected from Thomson Reuters Datastream. The sample period is December 14, 2007 (the launch date of CDS indices by Datastream) to September 21, 2018.1 We use the autoregressive distributed-lagged (ARDL) bound test to examine the long-run relationship between the variables. Firstly, stationary test results (displayed in Table 1) from the augmented Dickey-Fuller test (ADF) and Phillips and Perron test (PP) indicate that the sectoral CDS and stock indices are I(I) while the VIX time series is I(0). Hence, we use the ARDL bound testing procedure, which is appropriate when the integration order of the variables is mixed. The results (reported in Table 2) indicate that cointegration relations exist at the conventional levels of significance. Perceptibly, we can affirm that the US CDS, stock and VIX markets are linked in the long-run. The Toda Yamamoto causality test results (shown in Table 3) indicate a unidirectional causality from stock to CDS, and from VIX to CDS indices. Therefore, both stock and VIX markets play a leading role in the CDS markets, hence the CDS markets are followers. In other words, the stock and VIX indices are the main drivers of the CDS, excepting the utilities sector. There are also feedback relationships in case of telecommunications and the oil and gas sectors between both CDS-stock and CDS-VIX pairs. The CDS market also causes VIX in the banking, basic materials and consumer services sectors. Before undertaking the wavelet approaches, we pay a great deal of attention to the so called ‘bias problem’ that may arise relative to the three indices. As pointed out by Veleda et al. (2012), the bias problem toward low frequency oscillations appears not only in the wavelet power spectra but also in the wavelet cross spectrum. To ensure the correct application of the wavelet methodology, following Ng and Chan (2012), the bias problem is remedied for each sectoral index. Fig. 1 shows the bias corrected wavelet spectrum for the banking sector.2 It is evident that the banking sector CDS spreads and stock prices exhibit high energy (variations) during the global financial crisis of 2007–09 and the CDS spreads in particular show high energy in the short-run (4–32 days frequency) toward 1 2
The descriptive statistics of the given data are available on request. Other figures are not reported to preserve space, but are available on request. 3
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Table 1 Unit root test results.
Panel A: CDS indices Banking Financial Telecommunications Healthcare Oil and Gas Basic Materials Consumer Goods Utilities Industrial Consumer Services Technology Panel B: Stock indices Banking Financial Telecommunications Healthcare Oil and Gas Basic Materials Consumer Goods Utilities Industrial Consumer Services Technology VIX
Augmented Dickey-Fuller (ADF) test Level 1st Diff.
Phillips and Perron (PP) test Level
1st Diff.
−1.734 −2.500 −1.915 −2.272 −2.079 −1.758 −1.449 −1.920 −1.623 −2.072 −2.140
−32.189*** −39.929*** −64.372*** −36.888*** −8.887*** −18.642*** −58.727*** −23.178*** −43.376*** −16.833*** −14.690***
−1.741 −2.183 −2.094 −2.529 −1.676 −1.907 −1.579 −2.118 −1.740 −2.181 −2.366
−48.399*** −84.574*** −64.387*** −71.198*** −81.381*** −67.792*** −58.469*** −57.842*** −62.191*** −80.425*** −93.394***
−1.410 −1.219 −1.898 0.369 −2.367 −1.268 −0.040 −0.812 −0.357 −0.285 0.503 −4.611***
−16.173*** −60.919*** −42.187*** −41.952*** −42.641*** −55.166*** −39.930*** −42.176*** −55.550*** −41.275*** −57.011*** −41.062***
−1.221 −1.076 −1.921 0.316 −2.510 −1.195 −0.040 −0.883 −0.284 −0.231 0.631 −4.056⁎⁎⁎
−61.434*** −62.364*** −55.540*** −56.818*** −59.132*** −55.167*** −54.646*** −59.039*** −55.565*** −56.078*** −57.321*** −64.723***
Note:. ***and ** denote rejection of the null hypothesis of a unit root at the 1% and 5% level of significance, respectively. Table 2 Results of ARDL bound test. Sector
Lag order
F-statistics
Banks Financial Telecom Healthcare Oil and Gas Basic Materials Consumer Goods Utilities Industrial Consumer Services Technology
(2,3,2) (4,4,4) (2,4,4) (4,4,2) (4,4,2) (3,4,1) (2,4,2) (1,0,3) (4,4,0) (4,4,4) (4,1,2)
5.857*† 9.279*** 6.527*** 9.254*** 7.647*** 17.72*** 8.286*** 5.194*** 7.076*** 9.627*** 12.51***
Note: lower I(0) bound upper I(I) bound. 99% 4.13 (4.99) 5.00 (5.85). 90% 2.63 (3.38) 3.35 (4.02). *** & * indicate that the F test value is significant at 1%, and 10% level of significance, respectively. † indicates that the ARDL specification has a linear trend. Pesaran et al. (2001) critical values without (with) linear trend.
the end of the sample period. The VIX volatility index shows various episodes of short-run high energy. The wavelet squared coherence plots for the eleven US sectors are shown in Fig. 2. The left panel corresponds to the CDS-stock pairs while the middle panel reflects the CDS-VIX pair-wise. In these figures arrows pointing left (right) means a negative (positive) relationship between the pairs. These figures show an overall negative relationship (arrows pointing left) between CDS spreads and stock prices and a positive relationship (arrows pointing right) between CDS spreads and the VIX volatility index. Specifically, a large area of negative coherence between CDS spread and stock prices is found in the case of basic material, and lowest wavelet coherence is found for the utilities sector. For the banking sector, the negative relationship between CDS spreads and stock prices is evident in the short to medium-run (2–64 days) and during the GFC and Eurozone sovereign debt crisis periods, whereas, for other financials, the relationship is more prominent in the long-run (more than 128 days). In other words, and as shown by the ARDL results, these markets tend to align in the long run regardless of the sector. For the CDS spreads and VIX volatility index, the utilities and industrial sectors seem unaffected by the equity market volatility, whereas healthcare, basic materials, and the banking and financial sectors appear to be most affected. These interactions are omnipresent at middle frequencies, since the red vortices are detected between 8 4
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Table 3 Toda Yamamoto Granger causality test results. Sector
Stock − / → CDS
CDS − / → Stock
VIX − / → CDS
CDS − / → VIX
Banks Financial Telecommunications Healthcare Oil and Gas Basic Materials Consumer Goods Utilities Industrial Consumer Services Technology
49.389⁎⁎⁎ 39.201⁎⁎⁎ 26.372⁎⁎⁎ 35.972⁎⁎⁎ 38.415⁎⁎⁎ 89.302⁎⁎⁎ 68.956⁎⁎⁎ 8.026 38.739⁎⁎⁎ 17.949⁎⁎⁎ 19.427⁎⁎
0.386 2.602 16.047⁎⁎⁎ 6.117 15.315* 3.769 7.885 4.684 4.535 4.662 14.551
21.735⁎⁎⁎ 33.936⁎⁎⁎ 35.656⁎⁎⁎ 19.992⁎⁎⁎ 21.163⁎⁎⁎ 32.994⁎⁎⁎ 17.642⁎⁎⁎ 9.204 19.373⁎⁎ 26.997⁎⁎⁎ 19.646⁎⁎
10.150⁎⁎ 2.989 26.246⁎⁎⁎ 7.227 18.187⁎⁎ 18.590⁎⁎ 10.069 6.409 6.583 16.487⁎⁎⁎ 13.083
Note: − / → implies no causality from first to second variable. ⁎ Rejection of null hypothesis of no causality at 10% level of significance. ⁎⁎ Rejection of null hypothesis of no causality at 5% level of significance. ⁎⁎⁎ Rejection of null hypothesis of no causality at 1% level of significance.
Fig. 1. Bias corrected wavelet transform of the banking sector CDS, equity and overall volatility index Note: The thick black contour depicts the 5% significance level against red noise, while the cone of influence (COI) where the edge effects might distort the picture is designated as a lighted shadow. The color code for power ranges goes from blue (low power) to red (high power). The x-axis denotes the studied time period and the y-axis represents the frequency (in days)3. We only report the figures for the banking sector to preserve space. The remaining graphs are available upon request from the corresponding author. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
and 128 days. Comparatively, these anomalies are smaller than those depicted at lower frequencies. The red areas are disconnected from each other, mixed with small blue zones (reflecting weak co-movements). Blue dominates, especially at high frequencies (tops of the figures), ranging from 4 to 16 trading days. Thus, we perceive a substantial change in the pattern of co-movement between the markets in the short-run. This result is important for investors operating in the US CDS-stock market sectors, since it allows them to not have a long-term outlook for a better appreciation of the diversification benefits when designing their portfolios. The WMC plots for the three assets are displayed on the right-hand panel of Fig. 2. Interestingly, the co-movement between the three variables follows a heterogeneous pattern over time and frequency. The strength of interactions varies moving from high frequency to low frequency. It is remarkable how the high frequency (2–16 days) is governed by a succession of small disconnected vortices with color migration from blue to yellow. The given anomalies reflect weak co-movements. The lowest frequencies are already governed by strong co-movements that reach their zenith when the color spectrum is dominated by red. These vortices sharply disintegrate at the highest frequencies and are dispersed over the whole sample period, proving the continuum of the CDSSTOCK-VIX interplays across timescales. Obviously, striking similarities are detected across sectors supporting the hypothesis of 5
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Fig. 2. Wavelet squared coherence and multiple coherence for the 11 US sectors. Note: The thick black contour depicts the 5% significance level estimated from Monte Carlo simulations by following phase randomized surrogate series, while the cone of influence (COI), where the edge effects might distort the picture, is shown as a lighted shadow. The color code for power ranges goes from blue (low power) to red (high power). The arrows denote the phase difference between the two time series. The variables are in phase when the arrows point to the right (positively related), and out of phase when the arrows point to the left (negatively related). The stock prices are leading when the arrows are oriented to the left and up, while the CDS spreads are leading when the arrows are oriented to the left and down. The CDS spreads are leading when the arrows are oriented to the right and down. Otherwise, VIX is leading when the arrows are pointed to the right and up. The x-axis denotes the studied time period, whereas the y-axis illustrates the frequency (in days). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 2. (continued)
market integration, excepting the utilities and industrial sectors. Overall, the results of both wavelet methods inform us that it may be possible to have some opportunities to generate profitable gains, especially in the mid and short term. Therefore, the investors interventions are short lived, given the reduced probability of potential diversification opportunities at lower frequencies. 4. Conclusion This study highlights the importance of the time and frequency co-movements between CDS, stock and volatility trading markets, based on bivariate and multivariate frameworks. Using wavelet bivariate and multivariate coherence approaches, this paper offers a complete picture of the interplay between these three markets across time and frequency. The results show a clear heterogeneity in 7
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Fig. 2. (continued)
the relationships between credit, stock and volatility markets across various sectors and trading frequencies. For instance, utilities and the industrial sector are less connected, whereas cyclical industries such as basic materials show higher coherence. These findings are important for credit risk hedging and to exploit arbitrage opportunities. In the sectors showing high coherence, investors can hedge credit risk by taking alternate positions in either market, for example a long exposure to credit risk might be hedged through a short position in volatility futures. The lack of connectedness between credit and stock markets in utilities and the industrial sectors indicates the possibility of mispricing credit risk and lack of information efficiency (or flow) in these sectors, which could be exploited for arbitrage profits. Acknowledgments The authors wish to thank the Editor-in-Chief Professor Jonathan A. Batten and two anonymous referees for their valuable inputs. C. Aloui would like to acknowledge Business, Society & Environment (BSE) Research Lab, Prince Sultan University, Saudi Arabia for their support. References Aguiar-Conraria, L., Azevedo, N., Soares, M.J., 2008. Using wavelets to decompose the time–frequency effects of monetary policy. Physica A 387 (12), 2863–2878. Aloui, C., Hkiri, B., Lau, C.K.M., Yarovaya, L., 2016. Investors’ sentiment and US Islamic and conventional indexes nexus: a time–frequency analysis. Finance Res. Lett. 19, 54–59. Bruzda, J., 2017. Real and complex wavelets in asset classification: an application to the US stock market. Finance Res. Lett. 21, 115–125. Childs, M., 2014. The incredible Shrinking credit-default swap market. Available on the link: https://www.bloomberg.com/news/articles/2014-01-30/credit-defaultswap-market-shrinks-by-half. Diebold, F.X., Yilmaz, K., 2012. Better to give than to receive: predictive directional measurement of volatility spillovers. Int. J. Forecast. 28 (1), 57–66.
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Goupillaud, P., Grossmann, A., Morlet, J., 1984. Cycle-octave and related transforms in seismic signal analysis. Geoexploration 23 (1), 85–102. Guesmi, K., Dhaoui, A., Goutte, S., Abid, I., 2018. On the determinants of industry-CDS index spreads: evidence from a nonlinear setting. J. Int. Financial Markets Inst. Money 56, 233–254. Hkiri, B., Hammoudeh, S., C., Aloui, Shahbaz, M., 2018. The interconnections between U.S. financial CDS spreads and control variables: new evidence using partial and multivariate wavelet coherences. Int. Rev. Econ. Finance 57, 237–257. Huang, S., An, H., Gao, X., Huang, X., 2016. Time–frequency featured co-movement between the stock and prices of crude oil and gold. Physica A 444, 985–995. ISDA (2012). OTC Derivatives Market Analysis, Mid-Year 2012. [electronic]. Available via: http://www2.isda.org/functional-areas/research/studies/. Longstaff, F.A., Mithal, S., Neis, E., 2005. Corporate yield Spreads: default risk or Liquidity? New evidence from the credit default swap market. J. Finance 60 (5), 2213–2253. http://dx.doi.org/10.1111/j.1540-6261.2005.00797. Merton, R., 1974). On the pricing of corporate debt: the risk structure of interest rates, J. Finance. 23 (2), 449–470. Ng, E.K., Chan, J.C., 2012. Geophysical applications of partial wavelet coherence and multiple wavelet coherence. J. Atm. Oceanic Technol. 29 (12), 1845–1853. https://doi.org/10.1175/JTECH-D-12-00056. Pesaran, M.H., Shin, Y., Smith, R.J., 2001. Bounds testing approaches to the analysis of level relationships. J. Appl. Econ. 16 (3), 289–326. Shahzad, S.J.H., Nor, S.M., Ferrer, R., Hammoudeh, S., 2017. Asymmetric determinants of CDS spreads: US industry-level evidence through the NARDL approach. Econ. Model. 60, 211–230. Tiwari, A.K., Cunado, J., Gupta, R., Wohar, M.E., 2018. Volatility spillovers across global asset classes: evidence from time and frequency domains. Q. Rev. Econ. Finance 70, 194–202. Toda, H.Y., Yamamoto, T., 1995. Statistical inference in vector autoregressions with possibly integrated processes. J. Econom. 66 (1), 225–250. Torrence, C., Webster, P.J., 1999. Interdecadal changes in the ENSO-monsoon system. J. Clim. 12 (8), 2679–2690. Veleda, D., Montagne, R., Araujo, M., 2012. Cross-wavelet bias corrected by normalizing scales. J. Atm. Oceanic Technol. 29 (9), 1401–1408. https://doi.org/10. 1175/JTECH-D-11-00140.1.
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Contents lists available at ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
On the interplay between US sectoral CDS, stock and VIX indices: Fresh insights from wavelet approaches Syed Jawad Hussain Shahzada, Chaker Alouib, , Rania Jammazic ⁎
a b c
Montpellier Business School, Montpellier, France South Ural State University, Russia College of Business Administration, Prince Sultan University, Riyadh, Saudi Arabia National School of Computer Science (ENSI), Tunis, Tunisia
ARTICLE INFO
ABSTRACT
Keywords: Credit default swaps Stock markets Volatility index Wavelet squared coherence
In this study, we examine the time and frequency connectedness between CDS-stock and CDS-VIX pairs as well as combinations of the three indices for eleven US sectors. The main novelty of the present study is the use of bivariate and multivariate wavelet approaches to explore credit risk hedging and arbitrage opportunities. The findings point to a significantly changing pattern in the dynamic linkage between the given assets in the time–frequency domain. A strong negative (positive) association is unveiled in the long-term horizon for CDS-stock (CDS-VIX) pairs. Three markets seem disconnected in the utilities and industrial sectors and highly connected in the cyclical sectors such as basic materials. The implications of the findings are discussed.
JEL classification: C58
1. Introduction Over the last two decades, the credit default swap (hereafter, CDS) market has been marked by a succession of substantial booms and busts, skyrocketing 68 fold from 180 billion US dollars in 1997 to 62 trillion in 2007. In its heyday, the CDS market's unprecedented development highlighted its phenomenal efficacy as a tool for both hedging and speculating on credit risk. Thereafter, the global CDS market shrank to around 40% of its historical high (ISDA, 2012). After this period of glory, the CDS market underwent into an irreversible tumble, as clearly testified by the Bloomberg report “The incredible shrinking credit default swap market” (Childs, 2014). These sweeping changes in the CDS market sounded the death knell for financial actors to explore, in a more comprehensive way, the interplay between CDS and other financial markets. For academics, the seminal paper by Merton (1974) lead to much literature related to CDS, equity returns and volatility. However, much attention has been paid to the credit risk after the global financial crisis (GFC). We can identify two main recent research strands. The first is concerned with the leading determinants deriving the CDS spread behaviour and co-movements. For instance, Shahzad et al. (2017) and Guesmi et al. (2018) investigate the asymmetric determinants of sectoral indices of the S&P500 and point out that sectoral CDS spreads are affected by positive and negative shocks in the corresponding industry stock price and the overall volatility of the stock market. Using wavelet methods, Hkiri et al. (2018) examine the co-movement between US financial sector CDS spreads and global risk factors including the market volatility index (VIX), oil prices and interest rates. The authors show that VIX is one of the leading risk factor driving the evolution of financial sector CDS spreads, which is also contingent on the frequency. The second strand of the literature is focused on the relative information efficiency of CDS, stock and bond markets. Longstaff et al. (2005) state that stock and bond markets exhibit similar speed of reaction to the arrival of credit market news. Recently, Tiwari et al. (2018),
⁎
Corresponding author. E-mail addresses: [email protected] (S.J.H. Shahzad), [email protected] (C. Aloui), [email protected] (R. Jammazi).
https://doi.org/10.1016/j.frl.2019.06.006 Received 22 January 2019; Received in revised form 5 May 2019; Accepted 19 June 2019 1544-6123/ © 2019 Published by Elsevier Inc.
Please cite this article as: Syed Jawad Hussain Shahzad, Chaker Aloui and Rania Jammazi, Finance Research Letters, https://doi.org/10.1016/j.frl.2019.06.006
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using the Diebold and Yilmaz (2012) spillover approach and wavelet coherence, examine the volatility spillovers among sovereign bonds, CDS spreads, stock market volatility and foreign exchange rates. The authors show that stocks and CDS are net transmitters of volatility. Given these findings, the financial services industry has started taking advantage of the possible significant interplay between CDS and equity markets by offering new products that help market participants in their decisions making. For instance, informed traders often prefer to trade in the CDS market than equities. This trading preference leads to a price discovery advantage in the CDS market. In this context, questions of whether the CDS market provides more accurate risk information than the stock market, and which markets leads and which lags, not only become relevant, but the answers can help provide information about future defaults. The sharp evolution of financial markets and the emergence of new financial products such as volatility futures underscore the paramount relevance of re-assessing the dynamic interaction between financial markets. Risk propagation and its transmission across economic sectors and financial markets has many implications for investors and policy-makers. In the context of financial crisis and economic recession, examining the interplay between credit, stock and volatility future markets across corporate sectors is increasingly important because it helps market participants understand how default probabilities evolve and spread during and after stress periods. Such an understanding provides information about the direction of future defaults, helping market participants price credit derivatives and hedge credit exposure in the sectoral credit market. Furthermore, information about the pricing efficiency and lead-lag relationships helps investors and portfolio managers switch between sectors and dynamically rebalance their credit portfolios. Uncovering these issues is important for policy-makers for the purpose of improving the surveillance of financial systems and reducing systemic risk during crisis periods. Given their heterogeneity and highly diversified nature, CDS and stock markets are obviously complex systems consisting of a multitude of heterogeneous agents operating over very different time horizons (from days to years), who collectively determine aggregate market behaviour. These market participants differ in terms of their expectations, trading strategies and risk profiles. They have asymmetric information sets, and thus heterogeneous beliefs. Therefore, it seems reasonable that the degree of connectedness of the CDS market with stock and volatility markets may vary across the timescales associated with investment horizons. In this context, wavelets offer a unique opportunity to study the dynamics of the co-movement between CDS-stock and CDS-VIX, providing a better picture than time domain methods (Bruzda, 2017; Aloui et al., 2016). Therefore, we rely on the flexible properties of the wavelet coherence and multiple coherence approaches to explore the interplay between pair-wise CDS-stock and CDS-VIX as well as the combination of the three indices. The rest of this article is organized as follows. Section 2 outlines the econometric methodology. Section 3 describes the dataset used and the empirical results of the wavelet approach. Section 4 offers concluding remarks. 2. Methodology In this section, we apply a three step procedure to investigate the interplays between pair-wise CDS-stock and CDS-VIX and the trivariate relationship between them. In doing so, the ARDL bound testing approach of Pesaran et al. (2001) is used to ascertain the existence of a long run relationship between the variables. The Granger non-causality test of Toda and Yamamoto (1995) is used to assess the time domain lead/lag effects between each pair. Finally, the bivariate and multivariate wavelet coherence approaches are used to explore the multi-scale interactions between the three markets. For the sake of brevity, we only provide a detailed description of the wavelet methods. 2.1. Bivariate and multivariate wavelet coherence approaches 2.1.1. Bivariate wavelet coherence Wavelets are ‘small waves’ that grow and decay over a limited time period. They result from a mother wavelet, ψ(t), that can be expressed as a function of two parameters. The first shows where the wavelet is centred (τ: translation parameter) while the second indicates the analysis resolution (s: dilation parameter). Formally, wavelets are defined as:
s , t (t )
t
A^ , s
s with
s
0
(1)
By convoluting the function ψs, t(t) with the time series x(t), we obtain the wavelet transform Wx,(s, τ)
W x ( , s) =
1 s
+
x (t )
t *
s
dt
(2)
where * is the complex conjugate. In recent literature, several wavelet functions are proposed including the Coiflet, Symmlet, Haar, Debauchies, and Gabor wavelets. Choosing the most suitable wavelet is critical, since wavelet coefficients Wx,(s, τ) contain combined information about both the function x(t) and the wavelet-based decompositions ψs,t(t). The most frequently used wavelet is the Morlet wavelet, introduced by Goupillaud et al. (1984). Formally, the Morlet wavelet is given by:
(t ) =
1 4
ei
t
e
2 2
e
t2 2 ,
(3) 2
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where the term e wavelet is:
(t ) =
1 4
2 2
guarantees the admissibility condition. Thus, for η ≥ 5, the term above becomes negligible and the Morlet
(e i t ) e
t2 2
(4)
According to Aguiar-Conraria et al. (2008), WTC is defined as the ratio of the cross-spectrum to the product of the spectrum for each series and can be seen as local correlation between two time series in the time-frequency dimension. Thus, a WTC value close to 1 shows a high degree of synchronization between time series, while a WTC value close to 0 implies no relationship. The WTC isolates regions in the time-frequency domain where the stated time series co-move, even if they do not exhibit a common high power. Following Goupillaud et al. (1984), the cross-wavelet transform of two time series x(t) and y(t) is defined as follows: (5)
Wxy ( , s ) = Wx ( , s ) W * y ( , s )
where Wx(τ, s) and Wy(τ, s) designate the CWTs of x(t) and y(t), respectively. The cross-wavelet power can easily be calculated using the cross-wavelet transform |Wxy(u, s)|. Torrence and Webster (1999) define the squared wavelet coherence (hereafter SWC) coefficient as:
Rt2 (s ) =
S (s 1WtXY (s )) S (s
1
X
2
Wt (s ) )· S (s
1
2
WtY (s ) 2 )
,
(6)
where S is a smoothing operator. WTC can be considered a correlation coefficient localized in the time–frequency domain with a value that ranges between 0 and 1. 2.1.2. Wavelet multiple coherence The multiple wavelet coherence (MWC) can be seen as a generalization of the bivariate coherence approach that enables us to depict the co-movement between a set of independent time series across timescales. Obviously the MWC is more flexible than the standard WC since it encompass a higher dimensionality of the data. Following Huang et al. (2016), the MWC is defined as:
RM 2 (x , y, z ) =
R2 (y, x ) + R2 (y , z ) 1
2Re [R (y, x ). R (y , z )*. R (x , z )*] R2 (y, z )
The ratio mentioned is the squared result of the MWC of the three time series (CDS, stock and VIX). R(y, x)2,R(y, z)2and R(x,z)2are the wavelet squared coherences between each combination of pairs. 3. Data and findings We examine the interplay between US sectoral 5-year industry CDS index spreads, U.S. sectoral equity indices and the VIX volatility index futures. The sectors are banking, financial, telecommunications, health care, oil and gas, basic materials, consumer goods, utilities, industrial, consumer services and technology. The VIX refers to the Chicago Board Options Exchange (CBOE) volatility index, which computes the implied volatility of the S&P500 index options for the next month. The VIX index gauges the fear and financial uncertainty in the US stock market. A higher index reflects greater uncertainty, which may increase the probability of default and therefore result in higher sector CDS spreads. All the data are collected from Thomson Reuters Datastream. The sample period is December 14, 2007 (the launch date of CDS indices by Datastream) to September 21, 2018.1 We use the autoregressive distributed-lagged (ARDL) bound test to examine the long-run relationship between the variables. Firstly, stationary test results (displayed in Table 1) from the augmented Dickey-Fuller test (ADF) and Phillips and Perron test (PP) indicate that the sectoral CDS and stock indices are I(I) while the VIX time series is I(0). Hence, we use the ARDL bound testing procedure, which is appropriate when the integration order of the variables is mixed. The results (reported in Table 2) indicate that cointegration relations exist at the conventional levels of significance. Perceptibly, we can affirm that the US CDS, stock and VIX markets are linked in the long-run. The Toda Yamamoto causality test results (shown in Table 3) indicate a unidirectional causality from stock to CDS, and from VIX to CDS indices. Therefore, both stock and VIX markets play a leading role in the CDS markets, hence the CDS markets are followers. In other words, the stock and VIX indices are the main drivers of the CDS, excepting the utilities sector. There are also feedback relationships in case of telecommunications and the oil and gas sectors between both CDS-stock and CDS-VIX pairs. The CDS market also causes VIX in the banking, basic materials and consumer services sectors. Before undertaking the wavelet approaches, we pay a great deal of attention to the so called ‘bias problem’ that may arise relative to the three indices. As pointed out by Veleda et al. (2012), the bias problem toward low frequency oscillations appears not only in the wavelet power spectra but also in the wavelet cross spectrum. To ensure the correct application of the wavelet methodology, following Ng and Chan (2012), the bias problem is remedied for each sectoral index. Fig. 1 shows the bias corrected wavelet spectrum for the banking sector.2 It is evident that the banking sector CDS spreads and stock prices exhibit high energy (variations) during the global financial crisis of 2007–09 and the CDS spreads in particular show high energy in the short-run (4–32 days frequency) toward 1 2
The descriptive statistics of the given data are available on request. Other figures are not reported to preserve space, but are available on request. 3
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Table 1 Unit root test results.
Panel A: CDS indices Banking Financial Telecommunications Healthcare Oil and Gas Basic Materials Consumer Goods Utilities Industrial Consumer Services Technology Panel B: Stock indices Banking Financial Telecommunications Healthcare Oil and Gas Basic Materials Consumer Goods Utilities Industrial Consumer Services Technology VIX
Augmented Dickey-Fuller (ADF) test Level 1st Diff.
Phillips and Perron (PP) test Level
1st Diff.
−1.734 −2.500 −1.915 −2.272 −2.079 −1.758 −1.449 −1.920 −1.623 −2.072 −2.140
−32.189*** −39.929*** −64.372*** −36.888*** −8.887*** −18.642*** −58.727*** −23.178*** −43.376*** −16.833*** −14.690***
−1.741 −2.183 −2.094 −2.529 −1.676 −1.907 −1.579 −2.118 −1.740 −2.181 −2.366
−48.399*** −84.574*** −64.387*** −71.198*** −81.381*** −67.792*** −58.469*** −57.842*** −62.191*** −80.425*** −93.394***
−1.410 −1.219 −1.898 0.369 −2.367 −1.268 −0.040 −0.812 −0.357 −0.285 0.503 −4.611***
−16.173*** −60.919*** −42.187*** −41.952*** −42.641*** −55.166*** −39.930*** −42.176*** −55.550*** −41.275*** −57.011*** −41.062***
−1.221 −1.076 −1.921 0.316 −2.510 −1.195 −0.040 −0.883 −0.284 −0.231 0.631 −4.056⁎⁎⁎
−61.434*** −62.364*** −55.540*** −56.818*** −59.132*** −55.167*** −54.646*** −59.039*** −55.565*** −56.078*** −57.321*** −64.723***
Note:. ***and ** denote rejection of the null hypothesis of a unit root at the 1% and 5% level of significance, respectively. Table 2 Results of ARDL bound test. Sector
Lag order
F-statistics
Banks Financial Telecom Healthcare Oil and Gas Basic Materials Consumer Goods Utilities Industrial Consumer Services Technology
(2,3,2) (4,4,4) (2,4,4) (4,4,2) (4,4,2) (3,4,1) (2,4,2) (1,0,3) (4,4,0) (4,4,4) (4,1,2)
5.857*† 9.279*** 6.527*** 9.254*** 7.647*** 17.72*** 8.286*** 5.194*** 7.076*** 9.627*** 12.51***
Note: lower I(0) bound upper I(I) bound. 99% 4.13 (4.99) 5.00 (5.85). 90% 2.63 (3.38) 3.35 (4.02). *** & * indicate that the F test value is significant at 1%, and 10% level of significance, respectively. † indicates that the ARDL specification has a linear trend. Pesaran et al. (2001) critical values without (with) linear trend.
the end of the sample period. The VIX volatility index shows various episodes of short-run high energy. The wavelet squared coherence plots for the eleven US sectors are shown in Fig. 2. The left panel corresponds to the CDS-stock pairs while the middle panel reflects the CDS-VIX pair-wise. In these figures arrows pointing left (right) means a negative (positive) relationship between the pairs. These figures show an overall negative relationship (arrows pointing left) between CDS spreads and stock prices and a positive relationship (arrows pointing right) between CDS spreads and the VIX volatility index. Specifically, a large area of negative coherence between CDS spread and stock prices is found in the case of basic material, and lowest wavelet coherence is found for the utilities sector. For the banking sector, the negative relationship between CDS spreads and stock prices is evident in the short to medium-run (2–64 days) and during the GFC and Eurozone sovereign debt crisis periods, whereas, for other financials, the relationship is more prominent in the long-run (more than 128 days). In other words, and as shown by the ARDL results, these markets tend to align in the long run regardless of the sector. For the CDS spreads and VIX volatility index, the utilities and industrial sectors seem unaffected by the equity market volatility, whereas healthcare, basic materials, and the banking and financial sectors appear to be most affected. These interactions are omnipresent at middle frequencies, since the red vortices are detected between 8 4
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Table 3 Toda Yamamoto Granger causality test results. Sector
Stock − / → CDS
CDS − / → Stock
VIX − / → CDS
CDS − / → VIX
Banks Financial Telecommunications Healthcare Oil and Gas Basic Materials Consumer Goods Utilities Industrial Consumer Services Technology
49.389⁎⁎⁎ 39.201⁎⁎⁎ 26.372⁎⁎⁎ 35.972⁎⁎⁎ 38.415⁎⁎⁎ 89.302⁎⁎⁎ 68.956⁎⁎⁎ 8.026 38.739⁎⁎⁎ 17.949⁎⁎⁎ 19.427⁎⁎
0.386 2.602 16.047⁎⁎⁎ 6.117 15.315* 3.769 7.885 4.684 4.535 4.662 14.551
21.735⁎⁎⁎ 33.936⁎⁎⁎ 35.656⁎⁎⁎ 19.992⁎⁎⁎ 21.163⁎⁎⁎ 32.994⁎⁎⁎ 17.642⁎⁎⁎ 9.204 19.373⁎⁎ 26.997⁎⁎⁎ 19.646⁎⁎
10.150⁎⁎ 2.989 26.246⁎⁎⁎ 7.227 18.187⁎⁎ 18.590⁎⁎ 10.069 6.409 6.583 16.487⁎⁎⁎ 13.083
Note: − / → implies no causality from first to second variable. ⁎ Rejection of null hypothesis of no causality at 10% level of significance. ⁎⁎ Rejection of null hypothesis of no causality at 5% level of significance. ⁎⁎⁎ Rejection of null hypothesis of no causality at 1% level of significance.
Fig. 1. Bias corrected wavelet transform of the banking sector CDS, equity and overall volatility index Note: The thick black contour depicts the 5% significance level against red noise, while the cone of influence (COI) where the edge effects might distort the picture is designated as a lighted shadow. The color code for power ranges goes from blue (low power) to red (high power). The x-axis denotes the studied time period and the y-axis represents the frequency (in days)3. We only report the figures for the banking sector to preserve space. The remaining graphs are available upon request from the corresponding author. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
and 128 days. Comparatively, these anomalies are smaller than those depicted at lower frequencies. The red areas are disconnected from each other, mixed with small blue zones (reflecting weak co-movements). Blue dominates, especially at high frequencies (tops of the figures), ranging from 4 to 16 trading days. Thus, we perceive a substantial change in the pattern of co-movement between the markets in the short-run. This result is important for investors operating in the US CDS-stock market sectors, since it allows them to not have a long-term outlook for a better appreciation of the diversification benefits when designing their portfolios. The WMC plots for the three assets are displayed on the right-hand panel of Fig. 2. Interestingly, the co-movement between the three variables follows a heterogeneous pattern over time and frequency. The strength of interactions varies moving from high frequency to low frequency. It is remarkable how the high frequency (2–16 days) is governed by a succession of small disconnected vortices with color migration from blue to yellow. The given anomalies reflect weak co-movements. The lowest frequencies are already governed by strong co-movements that reach their zenith when the color spectrum is dominated by red. These vortices sharply disintegrate at the highest frequencies and are dispersed over the whole sample period, proving the continuum of the CDSSTOCK-VIX interplays across timescales. Obviously, striking similarities are detected across sectors supporting the hypothesis of 5
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Fig. 2. Wavelet squared coherence and multiple coherence for the 11 US sectors. Note: The thick black contour depicts the 5% significance level estimated from Monte Carlo simulations by following phase randomized surrogate series, while the cone of influence (COI), where the edge effects might distort the picture, is shown as a lighted shadow. The color code for power ranges goes from blue (low power) to red (high power). The arrows denote the phase difference between the two time series. The variables are in phase when the arrows point to the right (positively related), and out of phase when the arrows point to the left (negatively related). The stock prices are leading when the arrows are oriented to the left and up, while the CDS spreads are leading when the arrows are oriented to the left and down. The CDS spreads are leading when the arrows are oriented to the right and down. Otherwise, VIX is leading when the arrows are pointed to the right and up. The x-axis denotes the studied time period, whereas the y-axis illustrates the frequency (in days). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 2. (continued)
market integration, excepting the utilities and industrial sectors. Overall, the results of both wavelet methods inform us that it may be possible to have some opportunities to generate profitable gains, especially in the mid and short term. Therefore, the investors interventions are short lived, given the reduced probability of potential diversification opportunities at lower frequencies. 4. Conclusion This study highlights the importance of the time and frequency co-movements between CDS, stock and volatility trading markets, based on bivariate and multivariate frameworks. Using wavelet bivariate and multivariate coherence approaches, this paper offers a complete picture of the interplay between these three markets across time and frequency. The results show a clear heterogeneity in 7
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Fig. 2. (continued)
the relationships between credit, stock and volatility markets across various sectors and trading frequencies. For instance, utilities and the industrial sector are less connected, whereas cyclical industries such as basic materials show higher coherence. These findings are important for credit risk hedging and to exploit arbitrage opportunities. In the sectors showing high coherence, investors can hedge credit risk by taking alternate positions in either market, for example a long exposure to credit risk might be hedged through a short position in volatility futures. The lack of connectedness between credit and stock markets in utilities and the industrial sectors indicates the possibility of mispricing credit risk and lack of information efficiency (or flow) in these sectors, which could be exploited for arbitrage profits. Acknowledgments The authors wish to thank the Editor-in-Chief Professor Jonathan A. Batten and two anonymous referees for their valuable inputs. C. Aloui would like to acknowledge Business, Society & Environment (BSE) Research Lab, Prince Sultan University, Saudi Arabia for their support. References Aguiar-Conraria, L., Azevedo, N., Soares, M.J., 2008. Using wavelets to decompose the time–frequency effects of monetary policy. Physica A 387 (12), 2863–2878. Aloui, C., Hkiri, B., Lau, C.K.M., Yarovaya, L., 2016. Investors’ sentiment and US Islamic and conventional indexes nexus: a time–frequency analysis. Finance Res. Lett. 19, 54–59. Bruzda, J., 2017. Real and complex wavelets in asset classification: an application to the US stock market. Finance Res. Lett. 21, 115–125. Childs, M., 2014. The incredible Shrinking credit-default swap market. Available on the link: https://www.bloomberg.com/news/articles/2014-01-30/credit-defaultswap-market-shrinks-by-half. Diebold, F.X., Yilmaz, K., 2012. Better to give than to receive: predictive directional measurement of volatility spillovers. Int. J. Forecast. 28 (1), 57–66.
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