Currency crisis prediction using ADR market data: An options-based approach

International Journal of Forecasting 26 (2010) 858–884 www.elsevier.com/locate/ijforecast

Currency crisis prediction using ADR market data: An options-based approach Dominik Maltritz ∗ , Stefan Eichler Faculty of Business and Economics, TU Dresden, Muenchner Platz 1-3, 01062 Dresden, Germany

Abstract During capital control episodes, large price deviations between American Depositary Receipts (ADR) and their underlying stocks signal that a currency crisis is about to occur. We interpret this price spread as the price of a call option. Using option pricing theory we derive detailed information about both the probability of a currency crisis and the expected magnitude of devaluation. Analyzing daily ADR market data preceding the Venezuelan crisis (1996), our approach predicts crisis probabilities of almost 100% and forecasts the exchange rate after floating quite accurately. During the Argentine crisis (2002), the estimated exchange rates are similar to the actual ones. c 2009 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

Keywords: Exchange rates; Finance; Financial markets; Probability forecasting; Stock market data

1. Introduction Over the past few decades, many developing countries have fallen victim to financial crises. Due to their harmful effects, the literature has thus put an increasing amount of effort into developing models to predict the occurrence of such crises. This paper presents an approach for forecasting currency crises that relies on option pricing theory and uses highfrequency stock market data. In particular, we consider the price spreads between American Depositary Receipts (ADRs) and their underlying stocks in the emerging market. ∗ Corresponding author. Tel.: +49 351 46335905.

E-mail address: [email protected] (D. Maltritz).

The most important branches of the literature on forecasting currency crises are based on either logit/probit models – which Eichengreen, Rose, and Wyplosz (1995, 1996) and Frankel and Rose (1996) promote – or the signal or early warning indicator system put forward by Kaminsky, Lizondo, and Reinhart (1998) and Kaminsky and Reinhart (1999). Both types of model use observable economic and sociopolitical variables that presumably lead to currency crises. This body of literature not only provides useful insights into the nature and causes of currency crises, but also shows that currency crisis prediction in general is possible. Indeed, it appears that it would be possible to predict the occurrence of a currency crisis up to two years in advance with some accuracy.

c 2009 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved. 0169-2070/$ - see front matter doi:10.1016/j.ijforecast.2009.05.028

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We focus on short term crisis prediction. The use of stock market data may yield noticeably more accurate forecasts than the models mentioned above, which are based on past observations of economic data describing the causes of a crisis. On the eve of a currency crisis, economic conditions change quickly and dramatically. The data used in existing models are generally observed infrequently and are often outdated. In contrast to these backward-looking approaches, the use of market data is forwardlooking, since these data reflect market participants’ expectations. Moreover, the high frequency of stock market data more accurately represents changing conditions and makes daily crisis forecasts possible. The use of market data is based on the assumption that financial markets are able to efficiently process information about the value of the securities being traded, which implies that market prices should reflect all information available in this context, and that market participants are able to correctly anticipate exchange rate movements, at least on average. The market prices of securities whose value depends on the exchange rate can thus be used as input data to derive an assessment of currency crisis risk and the unobservable value of the exchange rate. Even if the markets themselves are not perfect in a theoretical sense, market data may still be superior to other sources of information. The ADR market in particular reveals information about exchange rate expectations, since the price difference between an ADR stock and its “original” stock is driven by the exchange rate. An ADR stock represents the ownership of a specific number of “underlying” or “original” shares in the home market on which the ADR stock is written.1 While the ADR stock is traded at a US stock exchange and is denominated in US dollars, the “original” stock is denominated in the currency and traded at the stock exchange of the home market. Every ADR stock can be converted into its respective “original” stock (and vice versa) through ADR conversion using custodian banks. Since the ADR stock and its corresponding “original” stock are substitutes through ADR conversion, and incorporate equivalent rights and dividend claims, both types of a company’s 1 See Karolyi (1998) for an excellent survey on the ADR market.

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stock should exhibit the same price in exchange rateadjusted terms. Previous to several currency crises, large and persistent price spreads developed between “original” stocks and their cross-listed ADR stocks. This happens when capital controls impede arbitrage forces and induce price segmentation. In this case, the law that an ADR stock and its “original” stock must have the same price no longer holds. Contemporaneously with the establishment of liquid ADR markets and the growing importance of ADR securities over the past decades, a comprehensive body of literature on ADR pricing has emerged. With respect to our topic, papers that are concerned with the relation between ADR prices and currency (crisis) risk are especially important. In analyzing daily data for a broad set of crisis episodes – including the United Kingdom (1992), Mexico (1994), Southeast Asia (1997), Russia (1998), and Brazil (1999) – Bin, Blenman, and Chen (2004), for example, find that the outbreak of a currency crisis in a given country leads to significantly negative abnormal returns on ADRs in that country. Bailey, Chan, and Chung (2000) analyze intraday ADR prices during the Mexican crisis of 1994/1995, and also report that ADR returns were (negatively) affected by news about the Mexican exchange rate regime and actual depreciations of the peso. Liang and Mougoue (2001) examine monthly data for 110 firms located in the UK, Japan, and South Africa from 1976 to 1990, and confirm that exchange rate fluctuations affect ADR prices. Several interesting studies, such as Arquette, Brown, and Burdekin (2008), Auguste, Dominguez, Kamil, and Tesar (2006), Levy Yeyati, Schmukler, and van Horen (2004) and Melvin (2003), consider the spreads between ADR and corresponding domestic stock prices, rather than the ADR prices themselves. They argue that these ADR spreads reflect the risk of a devaluation, since market participants can use the ADR market to hedge their funds (denominated in the domestic currency) against devaluation losses during periods in which capital control exists. Thus, they interpret the ADR spread as an indicator of devaluation risk, and discuss the development of this risk indicator during crisis periods. Some authors, such as Arquette et al. (2008) and Auguste et al. (2006), also analyze the determinants of ADR spreads. Our paper is inspired by these interesting contributions, but has a different focus. Instead of discussing

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the risk indication of ADR spreads during crisis periods and analyzing the underlying causes, we use the spreads to infer more detailed information about the crisis risk. We quantify crisis probabilities and the underlying value of the currency, which is unobservable because the exchange rate is pegged, by showing that an ADR portfolio – consisting of a short sold ADR stock and a (number of) corresponding domestic stock(s) – can be interpreted as either an option on the true value of the currency or a future on the actual currency value. Using the future approach, we estimate the actual value of the currency from observed values of the ADR portfolio. Based on the option approach, we derive the crisis probability on the one hand and the “true” value of the currency on the other. The use of ADR spreads for the estimation of the currency crisis risk and the true currency value using option pricing theory relies on the following considerations. To avoid a currency crisis, governments typically impose capital controls to impede crossborder capital flows. ADR conversion, however, provides a legal option to hedge proceeds – denominated in the emerging market’s currency – against devaluation losses during periods of capital controls. A call option position can be created by buying an emerging market (“original”) stock and selling short the corresponding ADR stock. For this call option position, the true exchange rate, or, more precisely, the value of the emerging market’s currency, represents the underlying instrument. Normally, if a currency is pegged, we do not know its “true” value. We can derive this value, however, using the option pricing formula. Then, we can use the estimated exchange rate series to derive the probability of devaluation, as well as the expected magnitude of the devaluation. Other input parameters for these calculations, such as the drift and volatility of the exchange rate, are derived simultaneously, where the estimated exchange rates are based on time series of ADR market data. To do this, we employ a maximum likelihood approach which relies purely on the model’s features and avoids additional assumptions.2 2 Here, we adapt the estimation approach first proposed by Duan (1994), who considers the estimation of insurance contracts of bank deposits and the Vasicek (1977) model. In his paper, Duan provides a maximum likelihood-based approach for estimating the model parameters from market data. This approach relies only on the model’s assumptions and avoids some of the problems of other approaches where additional assumptions are required for the estimation. See Duan (1994) for further discussion.

This options-based approach provides detailed information about the two dimensions of currency crisis risk: the probability that a currency crisis will occur and the expected magnitude of the devaluation, i.e. the “true” value of the currency. This information is critical for policymakers. If the probability of a currency crisis continues to increase, policymakers can implement the necessary measures to strengthen their currency and avoid a crisis. While the forecast approaches mentioned above serve a similar purpose, our approach additionally helps in the event that such actions fail or are not even undertaken. If the government prefers a pegged currency to a free float, it can realign the peg rate by an amount that our approach estimates as being appropriate for meeting market participants’ devaluation expectations. In doing so, the government can sustain the peg regime (with an adjusted peg exchange rate) and avoid a currency crisis. The turmoil caused by the Mexican crisis (1994/95), for example, could have been avoided. This crisis was triggered by a 15% devaluation of the peso, which was much lower than what market participants demanded, resulting in a speculative attack on the peso and eventually forcing the government to abandon the peg and allow the peso to float. Options-based approaches are widely used in other fields to forecast events influencing the value of financial claims related to different types of financial crises. When applied to banks and (the insurance of) their deposits, as Merton (1977) first proposed, option pricing theory can be used to forecast bank failures. Recent papers apply options-based (or structural) models to bank failures (see, e.g., Chan-Lau, Jobert, & Kong, 2004; Gropp, Vesala, & Vulpes, 2002; Gunther, Levonian, & Moore, 2001) and to bank deposit insurance (see, e.g., Duan, Moreau, & Sealey, 1995; Duan & Simonato, 2002). Options-based models are also used in debt crisis forecasting and in estimating country default risk. Early examples are Clark (1991) and Claessens and van Wijnbergen (1993). These authors demonstrate that options-based approaches can be applied successfully by using economic fundamentals rather than market data. Examples of papers that apply market data to estimating optionsbased models of debt-crisis risk are Claessens and Pennacchi (1996), Huschens, Karmann, Maltritz, and Vogl (2007) and Keswani (2000).

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An influential and comprehensive body of literature deals with deriving information about future exchange rates based on market-traded currency options. By using option prices, the market’s expectations of future exchange rates (Campa, Chang, & Reider, 1998) or the correlations between exchange rates (Campa & Chang, 1998) can be estimated. Some pioneering papers have used market-traded currency options to forecast the occurrence of devaluations in managed exchange rate regimes. Campa and Chang (1996) and Malz (1996) use data on currency options to assess the realignment risk prior to the crisis of the European Exchange Rate Mechanism (ERM) in 1992–93. The authors find that option prices implied that the target zones of the mark-lira band and the mark-pound band lost credibility well before the lira and the pound were devalued. Campa, Chang, and Refalo (2002) were the first to apply option pricing theory to evaluate realignment risk in an emerging market. Using data on market-traded real-dollar options, the authors find that the market anticipated the steady realignments of the real-dollar exchange rate during Brazil’s crawling peg regime (1994–99). These papers show that it is possible to evaluate the risk of devaluation using data on markettraded currency options. We present an options-based approach that relies on the prices of synthetic currency options derived from price spreads between ADRs and their underlying stocks, which can be applied if no market-traded currency options exist. In fact, for many pegged currencies no market-traded currency options are available – be it because the emerging country is too small or because the currency peg is so credible that no demand for currency options exists – and, thus, the approaches mentioned above cannot be applied. In the last decade, however, many emerging market companies have begun to issue ADRs. Using the price spread between ADRs and their underlying stocks during capital controls, we can calculate the prices of artificial currency options and, thus, apply the options-based framework to estimate the probability of a currency crisis and the expected magnitude of the devaluation. We demonstrate the applicability of our framework for two currency crisis episodes: Venezuela in 1996 and Argentina in 2002. The remainder of the paper is organized as follows: Section 2 outlines a theoretical approach for inferring the price of a synthetic call option from

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price differences between ADR and “original” stocks. Section 3 introduces an option pricing framework that will enable us to derive the devaluation probability and expected exchange rates using the call option series. It also describes the estimation approach. Section 4 applies the approach and presents our findings, and Section 5 concludes. 2. Calculating prices of the synthetic call option from ADR market data 2.1. ADR market, capital controls and exchange rate expectations The following presents a formal representation of the price relationship between ADR stocks and their corresponding “original” stocks in the emerging market, and how this information can signal a devaluation. The starting point of our discussion is ADR conversion. ADR conversion means that one ADR stock, traded in the US and quoted in US dollars at price pitADR , can be converted into γi shares of the emerging market stock, traded in the emerging market and quoted in the emerging market currency at price pitEM . The variable γi is called the conversion ratio and is specific to the ADR stock of each company i. ADR conversion may also be executed in the reverse direction, i.e. one emerging market stock can be converted into 1/γi ADR stocks. Since ADR conversion can be conducted at any point in time, the ADR stock and its corresponding emerging market stock are perfect substitutes. Thus, assuming perfect capital markets with zero transaction costs (like broker or conversion fees), both types of stock should exhibit the same exchange rate-adjusted price, where St 3 is the market exchange rate.4 In the absence of capital controls, arbitrage forces ensure the validity of the following arbitrage-consistent price parity: pitEM =

pitADR St . γi

(1)

3 The exchange rate is defined as the price of one US dollar in terms of the emerging market currency. 4 This assumption may be somewhat idealized. However, similar assumptions are well accepted and widely used in various important contributions to modern finance theory, such as the option pricing models, real option theory, and structural models of both corporate and sovereign default risk cited in the introduction.

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As long as the currency is pegged at a fixed exchange rate, S ∗ , and no capital controls are in place, the arbitrage-consistent ADR pricing (Eq. (1)) can be rewritten as: pitEM =

pitADR S ∗ . γi

(2)

Since arbitrage forces guarantee that the two types of stock are worth the same amount, an investor will be indifferent as to where he allocates his capital. It is important to realize, however, that the price parity equations (Eqs. (1) and (2)) are only binding as long as round-trip ADR arbitrage is possible and cross-border capital flows are not being restricted. The imposition of capital controls can result in a permanent violation of the arbitrage-consistent pricing (Eqs. (1) and (2)): since financial proceeds cannot be transferred across borders and ADR arbitrage is thus impossible, discrepancies between the price of ADR stocks and the price of emerging market stocks can arise and persist over time. If market participants anticipate a devaluation of the emerging market currency, S˜ > S ∗ , the price relationship between the ADR stock and the emerging market stock should incorporate this expectation. The observable market price of the emerging market stock, pitEM , therefore seems to be overvalued, since it is higher than the right-hand side of the arbitrage condition (2) would indicate5 : pitEM =

pitADR S˜ p ADR S ∗ > it . γi γi

(3)

Actually, the price spread presented in Eq. (3) is reasonable in the context of information efficiency, as it reflects all publicly available information concerning the sustainability of the peg regime. The price spread will change as soon as the market receives new information on the peg’s credibility. Rising spreads, for example, point to a deteriorating credibility of the peg, i.e. higher currency crisis probabilities and higher expected exchange rates. Eq. (3) and the following inferences and equations only hold, 5 In the case of the Argentine crisis of 2001/02, Melvin (2003), Levy Yeyati et al. (2004), and Auguste et al. (2006), for example, observe exploding premiums of 40%–45% for Argentine underlying stocks over their ADR stocks prior to the devaluation of the Argentine peso on January 11, 2002.

however, if capital controls are installed and crossborder arbitrage cannot take place. By trading ADRs and emerging market stocks, the market participants reveal their “true” assessments of what a reasonable exchange rate would be, because as soon as capital controls are lifted, ADR arbitrage resumes, the price relationship between the ADR stock and the emerging market stock is again determined by Eq. (1), and the market exchange rate St applies. Thus, any “false” expectations would hurt shareholders of either the ADR stock or the emerging market stock, and should therefore be speculated away. Even if capital controls are in place, the emerging market stock and the ADR stock may have the same value. This is true if market participants do not expect depreciation, i.e., they are certain that if capital controls were removed, the true value of the currency would be greater than or equal to the value corresponding to the pegged rate. In this case, the government maintains the peg, and the ADR prices equal the prices of the corresponding domestic stocks. Our approach is not applicable in such situations, where participants in markets do not have depreciation expectations, and thus the spread between ADR and domestic stocks is zero. By contrast, if capital controls are imposed and expectations of depreciation arise, the spread between the ADR and domestic stock prices is positive, and we can determine the probability of depreciation and the expected value of the currency after the collapse of the peg. For this purpose we apply option pricing theory, as is explained in the following sections. 2.2. The synthetic currency option From Eq. (3) we know that the emerging market stock seems to be overvalued if devaluation expectations arise during capital controls. This price deviation emerges endogenously as a result of creating a synthetic currency option, as explained in the following. During capital controls, cross-border capital transfers are prohibited, but ADR conversion is still possible. Thus, by buying the emerging market stock i for pitEM emerging market currency units on day t, the investor acquires the right to convert this stock into 1/γi ADRs worth pitADR /γi US dollars at any time in the future. The right of ADR conversion – i.e., the right to convert an emerging market currency-denominated asset

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into a US dollar denominated-asset – may serve as a hedging instrument for the emerging market shareholder against the risk of devaluation of the emerging market currency against the US dollar. Holding the emerging market stock, the investor can eliminate the risk of future price movements of the stock pair i – not induced by a change in devaluation expectations – by shorting 1/γi corresponding ADRs worth pitADR /γi US dollars. The resulting portfolio establishes a synthetic currency call option worth Cit , where the call option’s underlying instrument St is the true value of the domestic currency, and the strike price of the currency option represents the pegged rate, S ∗ . On the day T when capital controls are lifted – which resembles the maturity of the option – the payout of the portfolio equals the payout of a call option at maturity:
CiT = max ST − S ∗ , 0 . (4) To explain the shape of the pay-out function at T , we distinguish between two situations. In the first situation, the true value of the domestic currency is less than the value that corresponds to the pegged rate on day T when capital controls are lifted, i.e. the true exchange rate is higher than the pegged rate (since the exchange rate is expressed as domestic currency over anchor currency). In this case, the realized or observed exchange rate will be higher than the pegged rate, ST > S ∗ , since the government cannot maintain the peg without capital controls.6 The ADR portfolio has a positive value in the amount of the difference between the realized rate after allowing the currency to float and the pegged rate: ST − S ∗ > 0. In the second scenario, the true value of the currency is greater than (or at least equal to) the corresponding pegged rate, which means that the true exchange rate is lower than (or equal to) the pegged rate. In this case, the government can maintain the peg (at its original rate). This is possible even without capital controls because market participants will not attack the domestic currency if it is undervalued at the pegged rate. Thus, the actual exchange rate is equal to the pegged rate, and the value of the ADR portfolio 6 As was shown in the seminal paper by Flood and Garber (1984), a speculative attack will lead to an immediate breakdown of the peg as soon as the value of the domestic currency is below that of the anchor currency, and the true exchange rate will prevail.

is zero. Even if the true exchange rate falls below the pegged rate, the value of the portfolio is not negative because the government can maintain the peg. Thus, we obtain the truncated pay-out function of a call option (see Eq. (4)). It is reasonable to assume that the government will maintain the peg if it is able to do so. In fact, since the reason for capital controls is to defend the peg, it would be unrealistic for the government to give up the peg unless it is forced to do so. We want to emphasize that the underlying of the hypothetical option generated by the portfolio is the true exchange rate, which reflects the true value of the currency, and not the actual exchange rate; the two are equal only in the absence of capital controls and interventions of the central bank. Otherwise the two values may differ. The call option contract is set up the day capital controls are installed. The call option matures on day T when capital controls are lifted, because thenceforward, capital can legally be transferred abroad, and the option contract loses its purpose as a legal instrument for hedging emerging market currency-denominated funds against a devaluation loss. This synthetic currency option gives the investor the right to transfer emerging market currency units into US dollars at the pegged exchange rate, S ∗ , by accomplishing ADR conversion up until the option matures. In other words, the call option enables the investor to “buy” the “true” value of the currency expected by ADR market participants, St , at time t (the underlying instrument), by delivering the pegged exchange rate S ∗ (the strike price). 2.3. Deriving the price of the synthetic call option from ADR market data To acquire one synthetic call option of the ADR stock pair i, the investor buys one emerging market stock for pitEM emerging market currency units at the emerging market’s stock exchange, and shorts 1/γi ADR stocks at pitADR US dollars in the United States. Applying the fixed exchange rate S ∗ , the short-selling p ADR S ∗

proceeds can be expressed as it γi in terms of the emerging market currency. Since a portfolio created in this way resembles a call option in the absence of arbitrage opportunities, the value of the call option at any date before maturity can be derived from the observed prices of the ADR and its underlying stock,

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as shown in Eq. (5):7 Cit = pitEM −

The synthetic call option, priced at Cit , as outlined in Eqs. (5) and (6), gives the holder the right to

pitADR S ∗ . γi

(5)

The creation of this synthetic currency option – i.e., buying the emerging market stock and shorting the ADR – endogenously determines the price spread represented by Eq. (3). Rearranging Eq. (5), we can split the price of the emerging market stock, pitEM , into two components, as outlined in Eq. (6): pitEM =

pitADR S ∗ + Cit . γi

(6) p ADR S ∗

p ADR S ∗

of emerging market exchange the amount it γi currency units into US dollars at the fixed rate S ∗ , up until the option matures. Since ADR stocks of the i individual corporations exhibit different levels of stock prices pitADR and conversion ratios γi , it seems reasonable to standardize the call option by dividing p ADR

Eq. (6) by the factor itγi , which is specific to the ADR stock of each company i. Eq. (7) represents the standardized call option price: Cit =

γi pitEM pitADR

− S∗.

(7)

The first component, it γi , is the short-selling proceed, which equals the arbitrage-consistent value of the emerging market stock in the absence of capital controls.8 It reflects the “fundamental” value of the emerging market stock calculated using the arbitrageconsistent pricing (Eq. (2)), which holds when no capital controls are installed. The second component, Cit , represents the value of the synthetic call option. Fig. 1 displays both price components of the Argentine stock Perez Companc, as defined in Eq. (6). The grey area shows the arbitrage-consistent value,

Using the pricing formula (7), we can infer the standardized call option price, CitS , from the observed price relationship between the ADR stock and the emerging market stock. The major advantage of the standardization is that the call option prices – which are derived from the ADR stocks and emerging market stocks of i different companies – are comparable and interpretable in the same manner.9

pitADR S ∗ , γi

So far, we have argued that the ADR portfolio – made up of a long position in the emerging market stock and the equivalent number of short sold ADR stocks – represents an option on the true value of the currency. The ADR portfolio can also, however, be considered as a currency future,10 with the actual or realized exchange rate as the underlying rather than the true or fundamental value of the currency. The ADR portfolio still has the truncated pay-out function described by Eq. (4), however, because the actual exchange rate – the underlying value of the future – is itself truncated: if on day T (when capital controls are lifted), the true exchange rate is below the pegged rate (i.e. the true value of the currency is above the value that corresponds to the pegged rate), the government can maintain the peg. This means that

i.e. the conversion ratio-adjusted ADR price translated into pesos at the pegged rate of S ∗ = 1 peso per US dollar. The black area shows the call option component Cit . The rising values of the call option prior to the outbreak of the currency crisis on January 11, 2002, indicate that investors were willing to pay a higher risk premium to hedge their peso funds against a devaluation. Thus, by establishing the synthetic currency option, i.e. simultaneously buying the Argentine stock and short-selling the corresponding ADR, investors caused Argentine stock quotes to rise and ADR quotes to fall. 7 It is important to point out that company-specific news does not affect the call option price, since stock price movements, which do not reflect the reassessment of the devaluation risk, cancel each other out. On a day with good company-specific news, for example, pitEM will rise by the same amount as pitADR S ∗ /γi , leaving the call option price unchanged. Hence, changes in the call option price only reflect variations in the devaluation risk. 8 Note that the fixed exchange rate S ∗ holds until the currency is allowed to float.

2.4. The ADR portfolio as a currency future

9 Note that establishing a call option by taking a long position in the emerging market stock and a short position in the ADR stock is unaffected by deriving standardized call option prices. 10 We would like to thank an anonymous referee for pointing out the interpretation of the ADR portfolio as a future on the actual value of the currency.

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Fig. 1. Components of the Perez Companc Argentine stock price.

the actual exchange rate is equal to the pegged rate and not to the true exchange rate. If the true exchange rate is above the pegged rate, the peg will break down and the actual exchange rate will equal the true rate. In this way, the actual exchange rate is itself contingent on the true exchange rate. The value of the future contract equals the value of the option contract described above (where both contracts have a different underlying): Fit = Cit =

γi pitEM pitADR

− S∗.

(7a)

The pricing equation of a future contract with the actual exchange rate, Stact , as the underlying for any date t before T is given by:11 Ft = Stact e−r f (T −t) − S ∗ e−r (T −t) .

(8)

By rearranging Eq. (8) we can estimate the current value of the actual exchange rate from the future value and the pegged rate: Ft + S ∗ e−r (T −t) . (8a) e−r f (T −t) By calculating the future value, Ft , from observed stock prices using (7a) and inserting it in (8a), we Stact =

11 For simplicity we drop the firm index i, since the value of the future contract analyzed in the empirical section is obtained from a portfolio of firms.

can estimate the current value (at t) of the exchange rate that will be realized at T . Thus, the underlying value of the future gives us the best estimate at t of the exchange rate that will prevail at T . This value differs from the true, or fundamental, value of the exchange rate because the actual value of the exchange rate at T (when capital controls are lifted) may be truncated, as was explained above: when the true value of the currency is above the value that corresponds to the pegged rate, the government is able to maintain the peg, and the actual exchange (the pegged rate) is higher than the true exchange rate. Otherwise the peg collapses and the true value equals the actual value. Since the true value of the currency and the actual value of the currency are not necessarily the same at T, their current values at any date t before T also differ. Implicit in the current value of the actual exchange rate, which is derived using the future approach, is the possibility that we end up in a situation where the actual exchange rate – which is then the pegged rate – is above the true value because the peg is still intact. Thus, the underlying of the future, i.e. the current estimate of the actual exchange rate at T , must be higher than the true exchange rate (the underlying of the option contract). We can interpret the ADR portfolio as a future even without making the assumption that the government will maintain the peg if the true exchange rate is below the pegged rate, which implies a truncated pay-

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out function. The future approach is thus less restrictive. Returning to the more restrictive assumption, we are able to derive valuable additional information by using the option approach. While the underlying of the future gives us the best estimation of the exchange rate at t that will actually prevail at T , we can infer further information from ADR spreads by interpreting the ADR portfolio as an option. Whereas the underlying of the future, i.e. the current value of the actual exchange rate, reflects both the true value of the currency and the probability of devaluation in combination, the option approach allows us to infer separate information on the true value of the exchange rate, on the one hand, and on the devaluation probability, on the other. As was explained in the introduction, these separate estimates may provide important information for policymakers and investors alike. 3. Deriving the probability of devaluation and expected true exchange rates from ADR market data 3.1. Option-pricing framework, probability and magnitude of devaluation In this section, we explain the option pricing framework which is later used to derive the probability of a future devaluation, as well as the value of the true exchange rates. We assume that the true exchange rate, i.e. the underlying of our option contract, can be described as a stochastic variable. In doing so, we consider that future values of the true exchange rate are not known with certainty at the present date, t. To model future movements of the true exchange rate, we use the following Ito process: dS = µ S Sdt + σ S SdZ ,

(9)

where µ S and σ S are constant parameters and Z follows a standard Wiener process. This implies that log-changes (growth rates), st,1t = ln(St /St−1t ), of the exchange rate at equidistant intervals 1t are independently identically normally distributed: " ! # √ σ S2 st,1t ∼ i.i.n. µ S − 1t; σ S 1t . (10) 2 The assumption that the underlying can be described by a stochastic (Ito) process, as given by

Eq. (9) – which implies constant parameters for volatility and drift – is widely used and well-accepted in the literature. Examples of this include all of the papers mentioned in the introduction, where market perceptions about an unknown quantity are derived from observed market prices using option pricing theory. In addition, this assumption is typically made with respect to the exchange rate in the contributions where currency options are considered. Important theoretical contributions on currency crises (see e.g., (Flood & Garber, 1984)) also assume a constant growth rate of the (true value of the) exchange rate, which they call the shadow exchange rate. The extent to which the assumption of constant parameters is supported by empirical findings is discussed in Section 4. Furthermore, we adapt the typical assumptions of option pricing theory to our problem.12 This means that securities are traded without arbitrage opportunities on frictionless markets where one constant, riskless interest rate for borrowing and lending exists in every country.13 Although they are idealized, these assumptions are well accepted and widely used, for example, in option pricing theory, real options theory, structural models on corporate credit risk, and, in particular, currency options. The main differences between the various issues concern the types of securities examined. Black and Scholes (1973), for example, consider an option and the underlying stock. Merton (1974), in his credit risk model, considers the stock and the value of the firm. In our case, the underlying is the true exchange rate and the derivative security is the standardized call option derived from the price spread between the emerging market stock and the ADR stock. Based on these assumptions, we can use a pricing formula for the call option on exchange rates to link the value of the call option contract, Ct , at any point in time, t, to the underlying, i.e. the true exchange rate,

12 See Black and Scholes (1973, p. 640) for a detailed discussion. 13 In the following, r means the riskless interest rate in the country whose devaluation risk and exchange rate are forecasted (i.e. Argentina and Venezuela), whereas r f means the interest rate in the country that provides the anchor currency (i.e. the US).

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St :14,15 p Ct = St e−r f (T −t) N (d + σ S T − t,) − S ∗ · e−r (T −t) N (d),

(11)

where d=

ln(St /S ∗ ) + (r − r f − σ S2 /2)(T − t) . √ σS T − t

Here, N (x) is the value of the standard normal distribution for the argument in parentheses. T is the maturity of the option contract, i.e. the date at which the capital controls are lifted. At any date t before T , we can determine the probability of a devaluation, i.e. the probability that the true exchange rate ST at maturity T (the lifting of capital controls) will be above the peg exchange rate S ∗ , and, thus, that the currency will be devalued. Based on the assumed stochastic nature of the exchange rate, the probability of devaluation can be calculated using the exchange rate on day t, St , as follows:16 

smax

mean



}| { z }| { z  ln(S ∗ /S ) − (µ − σ 2 /2) (T − t)  t S   S Pt,T = 1 − N  √ .   σS T − t | {z } standard deviation

(12) For a better understanding of Eq. (12), we look at the log-changes of the state variable. The second term on the right-hand side, N (x), describes the probability that no devaluation will occur. The peg will be maintained if the true exchange rate at T is less than or, at most, equal to the peg exchange rate, i.e. ST ≤ S ∗ . This means that the maximum change between the true exchange rates at t and at T has to be smaller than

14 The pricing formula for an exchange rate option is the same as the formula for a call option on a stock that pays a constant dividend, which was derived by Merton (1973). 15 The firm index i can be dropped in the following, since we study a call option portfolio in the empirical section discussed below. 16 Here, we use the results outlined by Delianedis and Geske (1998). They also provide a discussion of actual and risk-neutral probabilities. The valuation of the securities, and hence the pricing formula (11), are based on risk-neutral probabilities, since it is assumed that a riskless portfolio can be created (Merton, 1974). Thus, the future drift of the underlying, µ S , does not influence the value of the option. Since we are interested in the actual devaluation probabilities, we use an estimator of the actual drift instead of the riskless interest rate.

867

smax = ln(S ∗ /St ). Otherwise, the true exchange rate at T is above S ∗ , and the currency will be devalued. Since the assumed stochastic features of the true exchange rate yield log-changes at equidistant time intervals that are independently identically normally distributed (see Eq. (10)), the probability of not devaluing can be calculated by using the standard normal distribution, N (x), on the standardized maximum log-change. In doing so, we use the mean and the standard deviation of the log-changes (see Eq. (10)), as shown in Eq. (12). Given the standardized change, we can calculate the probability of not devaluing by using the standard normal distribution. The opposite is the probability of devaluation. Using the stochastic properties of the true exchange rate (see Eq. (9)) we can derive the true exchange rate ST we expect for day T, given the true exchange rate St estimated on the day the forecast was made and the drift of the stochastic process µ S : E t [ST ] = St eµ S (T −t) .

(13)

The expected magnitude of devaluation can be derived by subtracting the peg exchange rate from the expected exchange rate after the lifting of capital controls: E t [ST ] − S ∗ . The option pricing framework used here assumes that the parameters of the stochastic process, µ S and σ S , are constant. A constant drift, µ S , means that the expected growth rate is constant over a future time interval. Nevertheless, expectations about the future exchange rate do change over time: changes in expectations about the future exchange rate, E t [ST ], are directly reflected by a change in the exchange rate’s current value St . If St changes, the expected value also changes (as can be seen in formula (13)), even if the parameters are constant. Assuming constant parameters, we can estimate the exchange rate from observed option prices. 3.2. Deriving the true exchange rate and its parameters from observable data using a maximum likelihood approach So far we have assumed that the values of the true exchange rate St and the parameters of the stochastic process, µ S and σ S , are observable and known.17 17 If a time series of values of the exchange rate is given, we can easily determine the values of the stochastic parameters µ S and σ S .

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In this case, we could calculate the devaluation probability and the expected exchange rate E t [ST ] by using Eqs. (12) and (13), respectively. These formulas follow directly from the assumption concerning the stochastic process: no additional assumption would be needed. The other assumptions above are only made in order to derive the option-pricing formula (11). If the formula is valid and both the true exchange rate St and its volatility σ S are given, one could calculate the fair option value. In this paper, however, we use the pricing formula to tackle another problem. In many cases, capital controls are used to maintain a fixed exchange rate which deviates from the true exchange rate that would result without central bank intervention. We derive the true but unobservable value of the exchange rate (and its stochastic parameters) from observable prices of the synthetic call option described above, i.e., from market prices of local currency-denominated stocks and their corresponding ADR stocks. This relies on the assumption that the stock markets process information efficiently, i.e., that all available information relevant to pricing is actually reflected in the prices. With respect to spreads between ADRs and the corresponding local stocks this concerns information on the exchange rate in particular, since the exchange rate determines the ADR spread, as is explained in Section 2. Even if the markets are not perfectly efficient in the theoretical sense, the use of market data may provide better results than alternative approaches relying on economic data, which are only available at a low frequency, and are thus often outdated. These publicly observable data are known to market participants, and are thus also reflected in the stock prices. Stock prices should, however, comprise more current and more accurate information. Market participants process and evaluate this information, whereby we assume that they correctly anticipate the consequences for the exchange rate, at least on average. In the following, we present an approach for deriving the values of the unobservable true exchange rate at any point in time t (
eters simultaneously. As can be seen in Eqs. (12) and (13), these quantities are needed to calculate the devaluation probability and to forecast exchange rate values for future dates. As outlined in Eq. (7), we use quotes of ADR stock and emerging market stock as input data to derive the market value of the call option, Ct .18 The call option price depends on the true exchange rate St , as specified by Eq. (11). We apply this equation to derive the unobservable true exchange rate, St , by using the empirically observed call option price, Ct . If all other input data on the right hand side of Eq. (11) were known, one could easily derive the exchange rate from given market data on option prices by solving the formula iteratively. While the peg exchange rate, S ∗ , (i.e. the strike price of the option), the riskless interest rates r and r f , and the time to maturity, T − t, are observable and known, the volatility of the exchange rate, σ S , is an unobservable parameter when the true exchange rate itself is a latent variable. In other words, we have two unknown quantities but only one equation. Consequently we must add more structure to the problem: we refrain from adding new assumptions, and instead use our assumption about the stochastic properties of the exchange rate to develop a maximum likelihood approach to infer the unknown quantities.19 In this approach we use a time series of observed option values Ctn , with n = 0, . . . , N observations derived from Eq. (7). If the volatility parameter σ S were known, we could use Eq. (11) to determine the corresponding value of the exchange rate Stn for each option value Ctn in the time series. The properties of the stochastic process (see Eq. (9)) require σ S to be constant over time. Thus, its value, though unknown, remains the same for the whole time series. Based on this consideration we back out the exchange rate from the time series of observable option prices in several steps. In the first step, we choose an arbitrary value for the volatility and solve Eq. (11) (iteratively) for the exchange rates, Stn , for a given value of the volatility, σ S , and the time series of option prices, Ctn (as well as the other parameters 18 Strictly speaking, we employ portfolios of option prices. 19 The estimation approach used here is based on a suggestion made by Duan (1994). An example of the application considering corporate debt can be found in Duan, Gauthier, Simonato, and Zaanoun (2003), and an example of valuing bank deposits in Duan and Simonato (2002).

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in Eq. (11), i.e. the peg rate (strike price), S ∗ , the domestic and foreign riskless interest rate, r and r f , and the time to maturity, T −t). No pricing error occurs in this calculation. For any observation date tn , we find a unique solution by solving Eq. (11) for the exchange rate Stn — the only remaining unknown quantity. For a given time series of observed option prices Ctn and the parameters of the option pricing formula, we can calculate a time series of exact values of the true exchange rates Stn . This can be done for each possible value of the volatility σ S without estimation errors. To estimate the volatility parameter, we apply an iterative approach using the maximum likelihood function as a selection criterion. We include an arbitrary (and constant) value for the volatility and calculate the corresponding time series of exchange rates, Stn, for given option values Ctn . This is done for a range of possible volatility values. To find the best estimator, we calculate the value of the likelihood function for each volatility value. We choose the estimator of the volatility that yields the highest value of the likelihood function, i.e., that best fits the model’s assumptions. The likelihood function also depends on the assumptions of the model. Instead of absolute values of the true exchange rate, we consider its log-changes, which are assumed to be independently identically normally distributed for equidistant time intervals. Thus, the likelihood function corresponding to the normal distribution should be used. The likelihood function, however, has to be modified, since the true exchange rates, and hence their changes, are unobservable. Thus, instead of the likelihood function of these unobservable quantities, we use the likelihood function of the observable option values formulated in terms of growth rates of the true exchange rate. The log likelihood function used here is given by (see Duan, 1994): √ L L F = − ln( 2π ) − ln(σˆ s,(1t) ) −

N −1 X n=0 N −1 X

1 2



stn − µˆ s,N ,(1t) σˆ s,(1t)

∂Ctn − ln ∂ Stn n=0 

 −

N −1 X

2

mean, µˆ s,N ,(1t) , and the standard deviation, σˆ s,(1t) , of the time series are required. Furthermore, we need the values of the partial derivative of Ctn with respect to Stn : √ ∂Ct = N (d1 + σ S T − t), ∂ St

ln Stn .

(14)

The true exchange rates, Stn, their growth rates, stn, the

(15)

where the variables are the same as those in Eq. (11). The standard deviation of the time series σs,(1t) can be determined using Eq. (10) and the given value of the volatility parameter of the stochastic process σ S , which is used to estimate the respective time series of the state variable: √ σˆ s,(1t) = σ S 1t. (16) Since the growth rates of the exchange rates are independently identically normally distributed, the mean can be determined by the estimated growth rates: µˆ s,N ,(1t) =

−1 1 NX st . N n=0 n

(17)

By maximizing the likelihood function, we minimize the (standardized) residuals, i.e., the differences between the growth rates, stn , of the exchange rates (derived from ADR prices using the option pricing formula (11)) and the mean, µˆ s,N ,(1t) , of the time series of these growth rates (see the third term in Eq. (14)). In other words, we obtain the estimator of the volatility by searching for the empirical distribution of growth rates that best fits the assumed normal distribution, i.e., the volatility for which the assumptions of the model are fulfilled best. The maximum value for the likelihood function indicates the best estimator for the volatility of a given time series of option prices Ctn. Applying this optimal volatility estimator in Eq. (11) yields our optimal estimate of true exchange rates, Stn. The corresponding drift estimator can be derived from the mean estimated by the log-changes (see Eq. (17)). Using Eq. (10), the exchange rate drift is given by: µˆ S =

n=0

869

µˆ ∗s,N ,(1t) 1t

+

σˆ S2 . 2

(18)

As was explained above, our estimation approach relies purely on the assumptions of the theoretical model. It is thus less restrictive than alternative ap-

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proaches, such as the Kalman filter,20 which require additional assumptions. In the following, we discuss the application of our estimation approach. 4. Empirical application 4.1. First example of an empirical application: Venezuela 1995/1996 4.1.1. Options-based estimation of the true exchange rate and the currency crisis probability We first apply our options-based approach to forecasting the Venezuelan currency crisis which began on April 22, 1996. Two necessary conditions for the application are fulfilled: the existence of both markettraded ADRs on “original” Venezuelan stocks and capital controls which prevented arbitrage between ADR stocks in the US and their corresponding “original” stocks in Venezuela. For our empirical applications, we create an equally weighted option portfolio including the i different stock pairs. The reason for employing a portfolio rather than i different stocks is to smooth temporary divergences of individual option prices from their equilibrium level. The stock pairs included are presented in Table 1. Based on a daily time series of option portfolio prices, Ctn , we apply the maximum likelihood approach described in the last section to derive the corresponding time series of estimated true exchange rates Stn and their stochastic parameters µ S and σ S simultaneously. In addition to the option prices, the peg exchange rate, S ∗ , the time to maturity, T − t, and the riskless interest rates r and r f , are needed. As is common practice, we use the country’s term structure (maturity of one year), which we take from Datastream, to infer the riskless interest rates r and r f . 20 See Harvey (1989). In the basic version, the Kalman filter assumes a linear relationship between unknown and observable variables. Since our model equation (see Eq. (9)) is a nonlinear function, a linear approximation is required (resulting in the socalled extended Kalman filter), which is, however, a potential source of errors. The Kalman filter also assumes that noise and uncertainty are Gaussian by nature, which is important for the results. The errors which arise when the model equation is used to calculate the latent quantities from observable quantities are assumed to be independently identically normally distributed. Furthermore, these errors and the error terms in the stochastic process of the latent variable are assumed to be independent.

Table 1 Venezuelan ADR portfolio. ADR stock

ADR level

Stock exchange of ADR stock

Industry

Conversion ratio (ADR: underlying)

Mantex

I

OTC

Sivensa

I

OTC

Sudamtex de Venezuelaa

I

OTC

Personal 1:15 goods Industrial 1:98 metals Textiles 1:200

a Sudamtex ADR was delisted in April 20, 2007.

We consider a time span starting on December 12, 1995, the date the Venezuelan government fixed the exchange rate at 290 bolivars per US dollar — the strike price S ∗ of our call option contract. Furthermore, capital controls were in place to defend the peg. The controls ended on April 19, 1996, the maturity date of our option contract. The time series thus begins with a maturity of 94 days and reduces by one day each day thereafter. Using the estimation approach outlined in Section 3, we obtain a volatility estimator of 0.45. The drift estimator corresponding to the estimated time series of true exchange rates is 1.30. The dashed line in Fig. 2 represents the daily time series of the true exchange rates, St , as estimated by the option approach. During the whole period, the estimated true exchange rate is above the peg exchange rate, represented by the solid line.21 This means that market participants considered the bolivar to be overvalued at the fixed rate. Over time, the overvaluation increases. At its peak, the estimated true exchange rate is 538 bolivars per US dollar. This corresponds to the time pattern of the option value (see Fig. 5). The option value rises, although the time to maturity – and thus the time value of the option – decreases. The estimated values of the true exchange rate reflect the impending devaluation which actually occurred when the capital controls were lifted on April 22, 1996. On this first day of floating, the observed market exchange rate was 499 bolivars per US dollar. This exaggeration was alleviated over the 21 The thin solid line shows the current estimation of the actual exchange rate derived using the future approach, as discussed in Section 4.1.3.

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871

Fig. 2. Estimated and observed exchange rates for Venezuela.

Fig. 3. Devaluation probability for Venezuela.

next few days, as the observed exchange rate dropped to between 463 and 471 bolivars per US dollar. Our options-based framework forecasts the bolivar’s floating exchange rate quite well, as the estimated exchange rate for the last day of capital controls (April 19, 1996) was 461 — pretty close to the observed values. The values for St displayed by the dashed line in Fig. 2 show the ADR market participants’ estimations of the true exchange rate for each day of prognosis, t. Using these values, the drift µ S , and Eq. (13), we can create exchange rate forecasts E t [ST ] for the day the

capital controls were lifted. Fig. 6 displays the results. The x-coordinates represent the day of prognosis, t. The dashed line shows the respective true exchange rate E t [ST ] forecasts on day t for day T . Like the daily exchange rates, the forecast values are close to the actual rates observed when the controls were lifted. By employing Eq. (12) and using the parameters for drift and volatility, as well as the estimated true exchange rates St , we can calculate the devaluation probabilities for the day T when capital control was lifted, Pt,T , for each day t in the observation period. The results are shown in Fig. 3. The day of prognosis is

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displayed on the x-axis, and the corresponding dot on the curve shows the devaluation probability estimated for this specific day. The devaluation probability is quite high, around 95%, right from the beginning. Later, it rises even further, so that by mid-February a currency crisis appears imminent, with a probability of almost 100%. 4.1.2. Tests and robustness checks Our approach relies on the assumption that the true exchange rate follows a stochastic Ito process, as described by Eq. (9), which implies that the growth rates are independently identically normally distributed (see Eq. (10)). Dating back to Mandelbrot (1963), this assumption has been discussed intensively in the literature for several types of securities. To analyze the validity of this assumption, the distribution of the growth rates is tested for normality on the one hand, and on the other, the time series of growth rates are tested for dependencies (see, e.g., Akgiray, 1989). We follow this approach and analyze the properties of the growth rate of the exchange rate estimated by the option approach. The results are reported in Tables 3 and 4. The distribution of the growth rates estimated for Venezuela is skewed only slightly, at −0.33, and the kurtosis of 3.6 is remarkably close to 3, the kurtosis of a normal distribution. Thus, the Jarque–Bera test does not reject the hypothesis that the growth rates are normally distributed. The test statistic is 3.52, and the p-value is 0.197. We further test for dependencies in the time series. We search not only for linear dependencies, measured by autocorrelations of the growth rates, but also for dependencies of higher orders. As has been proposed in the literature (see, e.g., Akgiray, 1989), we consider autocorrelations of squared residuals, computed as differences between the actual growth rates and the expected growth rate (this follows from our assumption that the expected growth rate is given by the mean). We include this analysis to test for constant volatility. Since the squared residuals give an indication of the instantaneous variance, testing for correlations in time series of squared residuals is a common approach to identifying the changing volatilities and volatility clustering often observed in financial time series. As Table 4 shows, we did not find evidence for dependencies within the time series for either growth rates or squared residuals. All in all,

our tests thus provide no evidence that the assumption of an Ito process is not valid for Venezuela.22 Still, the question arises as to how robust the results are with respect to estimation errors, which may result because the model assumptions are not perfectly fulfilled. Stability of the parameters is important, on the one hand, since constant parameters are one of the model’s and the estimation procedure’s fundamental assumptions. On the other hand, stability is important for out-of-sample forecasts of crises. If the parameters are indeed constant and the estimation approach works well, we obtain the same estimators for the parameters (and the corresponding exchange rates) for every sub-sample. In reality, the parameters may change because the structure of the time series changes. In the following, we consider results obtained from outof-sample forecasts to analyze the stability of the estimates of the parameters. Fig. 2 indicates that the true exchange rates estimated in the first half of the observation period grew faster than in the second half. This would imply different drift parameters for different sub-samples. To analyze whether the drift and volatility are indeed different for different sub-samples and how this affects the results, we split our sample in two sub-samples. The first half of our series (the estimation period) is used to estimate the parameters. For the second half of the series (the forecast period), we perform out-ofsample forecasts. The volatility estimated for the first half of the time series is 0.43, which is only slightly lower than the 0.45 obtained for the whole series. This indicates that the assumption of constant volatility seems to be valid. The drift, however, changes over time: the drift rate for the first half of the time series is 1.52, which is higher than the drift of 1.30 estimated for the whole series. Nevertheless, the differences in the current value of the underlying at the observation date, i.e. the estimates of the true exchange rate, St , are very small.23 The small differences in the estimates of 22 The assumptions match reality much better in our example than in many other applications of option pricing theory. For example, it is a well-known fact that even in the standard case – options on stocks – the distribution of the growth rates of the underlying stocks displays high excess kurtosis, and there are (higher order) dependencies in the time series (volatility clustering). 23 We do not display the values in Fig. 2 because the resulting curve is virtually equal to the one resulting from the estimation

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the current value of the true exchange rate occur because the volatility is almost equal for the two subsamples. In contrast to the volatility, the drift does not enter the option pricing formula (see Eq. (11)). It therefore does not influence the exchange rate directly, and differences in the drift do not directly affect the estimation of the current value of the true exchange rate, St . The expected value of the true exchange rate, E t [ST ], however, does directly depend on the drift (see Eq. (13)). To analyze the influence of the drift on the expected future exchange rate, we provide out-of-sample predictions for the second half of the time series. This means that we use the estimators for the drift derived for the first half of the time series to calculate the true value of the exchange rate expected at day T (when the capital controls are lifted) for every day in the forecast period. We insert the drift into Eq. (13), together with the current value of the true exchange rate estimated for day t when the forecast is made. These are the values for St discussed above. They are themselves estimated by inserting the option values observed in the forecast period and the volatility estimated from the first half of the time series into the option pricing formula. Fig. 7 displays the resulting out-of-sample forecasts (the thin dashed line), together with the in-sample forecasts discussed above (the bold dashed line in Figs. 6 and 7). Regardless of the differences in the drift, the outof-sample estimates differ only slightly from the insample forecasts. (We changed the scale of the y-axis in Fig. 7 to make the differences visible.) The out-ofsample forecasts of the exchange rates are higher than the in-sample forecasts because of the higher drift. In addition, the out-of-sample estimates of the crisis probability are also above the in-sample estimates. This is because the estimated drift is higher for the first sub-sample, but the current estimation of the true exchange rate, St , and the volatility estimator are fairly similar for the two samples. Since, however, the crisis probability estimated with the in-sample approach for the forecast period (the second half of the time series) is virtually 100%, the actual differences

of the whole sample. For December 12, 1995, the first day in the observation period and the day with the greatest difference between the two estimates (due to the longest time to maturity), we obtain an exchange rate of 294 bolivars per US dollar instead of 292.

873

between the two estimates of the crisis probability are virtually zero. Overall, the results for Venezuela obtained for different sub-samples are quite similar. 4.1.3. Estimation results for the futures-based actual exchange rates The thin solid line in Fig. 2 shows the current estimates (on day t) of the actual exchange rate expected for the day when capital controls are lifted, which are derived by interpreting the ADR portfolio as a future on the actual value of the currency. As was explained in Section 2.4, these values differ from the estimates of the true exchange rate since they reflect the possibility that the peg will be maintained. Thus, they must be higher than or at least equal to the options-based true exchange rates. In the Venezuelan example, however, the differences are rather small, since the call option is “deep in the money,” i.e. the true value of the exchange rate (the underlying) is much higher than the pegged rate (the strike price). Thus, the probability of devaluation is also very high (see the discussion above). This means that the probability that the peg will be maintained is very low. In addition, the time value of the option is rather small, since there is a short time to maturity and a relatively low volatility. In situations where the time value of the option is greater and the crisis probability is lower than in the example considered here, we would expect to observe greater differences between the estimates of the actual and the true exchange rate. 4.2. Second example of an empirical application: The Argentine crisis 2001/2002 4.2.1. Options-based estimation of the true exchange rate and the currency crisis probability From the results presented in the last section, our options-based framework seems to produce reasonable forecasts. However, since the Venezuelan exchange rate was pegged, its “true” value was unobservable, and we therefore had no benchmark with which to assess the accuracy of our estimations. The currency crisis in Argentina in 2002 presents a different picture.24 The Argentine currency board 24 See Stiglitz (2002), de la Torre, Levy Yeyati, and Schmukler (2003), and Dominguez and Tesar (2007) for excellent analyse of the timeline and causes of the Argentine crisis.

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Table 2 Argentine ADR portfolio. ADR stock

ADR level

Stock exchange of ADR stock

Industry

Conversion ratio (ADR : underlying)

BBVA Banco Frances S.A. Cresud S.A.C.I.F. Y A. Financiero Galicia S.A. Irsa Inversiones S.A. Metrogas S.A. Perez Companca Telecom Argentina S.A. Telefonica de Argentina S.A. Transportadora de Gas del Sur S.A. YPF S.A.

III II II II II II III II III III

NYSE NASDAQ NASDAQ NYSE NYSE NYSE NYSE NYSE NYSE NYSE

Banks Food producers Banks Real estate Gas, Water, Multiutility Oil & gas producers Fixed line telecom Fixed line telecom Oil & gas service Oil & Gas Producers

1:3 1:10 1:10 1:10 1:10 1:10 1:5 1:10 1:5 1:1

a Today: Petrobras Energia Participaciones.

Fig. 4. Estimated and observed exchange rates for Argentina.

collapsed on January 11, 2002.25 Capital controls, known as Corralito, were in place from December 3, 2001, to December 2, 2002, and prevented ADR arbitrage. These circumstances give us the opportunity to compare the exchange rates estimated using our approach with observable market exchange rates that have floated since January 11, 2002, and thus have not been affected by central bank interventions attempting to maintain a peg. The time span used in our analysis begins on January 11, 2002, and ends with the lifting 25 Schmukler and Serv´en (2002) show that significant currency risk was perceived during the whole life span of Argentina’s currency board.

of capital controls on December 2, 2002. Thus, the initial time to maturity is 231 trading days, and reduces by one day each day thereafter. The strike price of the option is 1, since the peg exchange rate was fixed at 1 Argentine peso per US dollar. As in the Venezuelan case, we use an equally weighted portfolio of option prices. Table 2 presents the Argentine option portfolio.26 The data are taken from Datastream. The time series of option values is displayed in Fig. 8. We again estimate Argentine exchange rates, Stn, and stochastic parameters, µs 26 We exclude the stocks Alto Palermo, APSA, Nortel Inversiones and Siderca due to heavy illiquid trading in 2002.

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875

Fig. 5. Option value for Venezuela.

and σs, based on the time series of portfolio option prices, Ctn. Fig. 4 displays the results. The dashed lines show the values of the true exchange rate estimated by interpreting the ADR portfolio as an option. The bold dashed line relies on in-sample estimation with data observed after January 11, 2002, whereas the thin dashed line shows the results of out-of-sample estimation with data observed before January 11 (which are discussed in Section 4.2.3). The thin solid line shows the current estimation of the actual value of the exchange rate on day T estimated by interpreting the ADR portfolio as a currency future (see Section 4.2.4). The bold solid line displays the observed exchange rates, i.e. the floating rate after the breakdown of the currency board. Although the estimated exchange rates tend to be slightly higher than the observed exchange rates, the values are fairly similar. On average, the deviation between the true exchange rate estimated by the option approach and the exchange rate observed after floating is 6.0%.27 This finding implies that our approach produces reasonable results, as the exchange rates estimated using the options-based framework are similar to the true exchange rates that market conditions without central bank intervention produce. 27 To calculate the average, we use absolute values of the errors to avoid positive and negative deviations cancelling each other out.

The same holds true for the parameters of the stochastic process. By estimating the drift for the (log-changes of) exchange rates using our estimation approach, we get a value of 1.16. When using the observed exchange rates and the respective mean estimator, we obtain a drift of 1.18. The volatility estimator derived from our approach is 0.58. Estimating the volatility by applying the standard deviation estimator to the time series of observed exchange rates yields a value of 0.55.28 Although the devaluation happened at the beginning of our observation period, we can forecast the exchange rate value E t [ST ] that ADR market participants expected for the day the capital controls were lifted (December 2, 2002) by using the data calculated up to that point.29 This is done for each day of the time span. Fig. 9 displays the results. The dashed line shows the exchange rate forecasts using our approach, i.e. the estimated true exchange rates shown in Fig. 4 by the bold dashed line and the drift parameter (1.16) for this time series. Since exchange rates for Argentina are observable (see the bold solid line in Fig. 4), we can also use these to predict future values. In doing so, we utilize the drift parameter (1.18) estimated for 28 The parameters estimated for the period before January 11, 2002, are discussed in Section 4.2.3. 29 It should be mentioned that we can forecast exchange rate values for any other day in the future by employing Eq. (13) and replacing T with the respective forecast horizon.

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Fig. 6. Expected exchange rate, E t [ST ], and exchange rate after float for Venezuela.

Fig. 7. Out-of-sample (and in-sample) forecasts of the expected exchange rate, E t [ST ], and exchange rate after float for Venezuela.

this time series. The solid line in Fig. 9 shows the results for the exchange rate forecasts based on observed exchange rates. At the beginning of the observation period, the forecasted exchange rates overestimate the exchange rate for December 2, 2002. This holds true for both the forecasts based on estimated data and the forecasts based on observed data. However, for shorter forecast periods, the predicted values converge to the actual value for December 2, 2002. For the sake of completeness, we also estimate the devaluation probability. Although the Argentine peg

had already been abandoned by the time of prognosis, the exercise is still worthwhile, since devaluation, i.e. an exchange rate higher than the peg rate, on the date of maturity T (the day capital controls were lifted), is not 100% certain. Theoretically, the exchange rate could appreciate to its previous peg level after the crisis outbreak. However, since the estimated exchange rates for any day t are much higher than the fixed exchange rate, and since the drift is positive, we obtain values for the probability of devaluation close to one, regardless of the time of prognosis

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Fig. 8. Option values for Argentina.

Fig. 9. Expected exchange rates, E t [ST ], for Argentina.

and the forecast interval. Using actual exchange rates produces the same result. 4.2.2. Tests and robustness checks In the following, we discuss the stability of the estimated parameters and the results of the out-ofsample forecasts. Here, we discuss the results of outof-sample estimations for the time after January 11, 2002 – after the breakdown of the currency board – when we can observe prices for the floating currency. In Section 4.2.3, we provide, in addition, the results

obtained when pre-crisis data are used to forecast the currency crisis of January 2002 and to estimate the true exchange rates after the breakdown of the currency board.30 As in the case of Venezuela, we derive out-ofsample forecasts for the period after the breakdown of the currency board by splitting the time series into two halves and using the first half to estimate the 30 By the term “pre-crisis” we mean the time before January 11, 2002, when the currency board broke down.

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parameters estimated for Argentina may be due to the fact that our time sample covers the period after the currency board’s collapse, rather than the pre-crisis period, as with Venezuela. As the findings discussed so far show, the time series properties of the growth rates for Argentina contradict the assumption of an Ito process with constant parameters. The assumption of normality is rejected by the Jarque–Bera test at the usual levels, particularly because the kurtosis is so high (8.5), while the skewness is relatively low (−0.16). There are also dependencies of a higher order within the time series: the growth rates are not autocorrelated, but the squared residuals are (which is an indication of volatility clustering). Although the estimates of the parameters for the two periods differ, the estimates of the true exchange rate St derived using the parameters estimated using the first half of the sample are very similar to the exchange rate values derived using the parameters estimated for the entire sample. The value for January 11, 2002 – the first date of the observation period and the date with the greatest difference between the exchange rates estimated for the two samples, due to the longer time to maturity – is 1.48 instead of 1.55.

Table 3 Characteristics of the distribution of exchange rate growth rates.

No. of observations Skewness Kurtosis Jarque–Bera p-value

Venezuela

Argentina

93 −0.311 3.671 3.252 0.197

230 −0.169 8.58 299.971 0

parameters. The estimation of the volatility for the first half of the time series, 0.76, is higher than the estimate for the whole sample, 0.58. This difference may be an indication that uncertainty about the true value of a currency is higher directly after the breakdown of the currency board, since uncertainty about the consequences of the currency crisis was high during this time. The annualized drift of 2.14 estimated for the first half of the time series is also considerably higher than that for the entire period (1.16). That the drift is higher shortly after the crisis than in the later period may mean that market participants’ perceptions of the true value of the currency deteriorate rapidly following the currency board’s collapse. This may account for the consequences of the feedback effects of the crisis. Thus, the changes in the time series

Table 4 Correlogram and tests of autocorrelation of growth rates and squared residuals for Venezuela.

Lag

Venezuela Growth rates ACC PACC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

0.04 −0.13 −0.02 −0.01 −0.11 0.02 −0.02 0.07 0.06 0.03 −0.11 −0.01 −0.04 0.07 0.06 −0.01 0.00 0.07

0.04 −0.13 0.00 −0.03 −0.11 0.03 −0.05 0.08 0.04 0.03 −0.09 0.00 −0.05 0.08 0.06 −0.02 0.01 0.05

PV

Squared residuals ACC PACC

0.68 0.43 0.63 0.79 0.73 0.82 0.89 0.90 0.93 0.95 0.93 0.96 0.97 0.97 0.98 0.99 0.99 0.99

0.00 0.02 −0.06 0.03 −0.03 0.04 −0.06 0.00 −0.02 −0.12 −0.03 −0.11 −0.01 −0.02 −0.07 −0.06 0.21 0.00

0.00 0.02 −0.06 0.03 −0.02 0.04 −0.05 −0.01 −0.01 −0.13 −0.03 −0.12 −0.02 −0.02 −0.09 −0.06 0.20 −0.01

PV

Argentina Growth rates ACC PACC

PV

Squared residuals ACC PACC

PV

0.98 0.99 0.98 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.99 1.00

−0.02 0.03 −0.04 −0.10 −0.11 0.04 0.09 −0.04 −0.05 0.02 0.04 −0.06 0.10 0.04 −0.05 −0.02 −0.09 0.00

0.75 0.89 0.91 0.57 0.33 0.40 0.32 0.39 0.42 0.51 0.56 0.57 0.43 0.49 0.51 0.57 0.51 0.58

0.32 0.21 0.31 −0.03 −0.02 −0.03 0.02 0.10 0.04 0.01 0.04 0.00 −0.01 0.04 0.11 0.06 0.08 0.10

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

−0.02 0.02 −0.04 −0.10 −0.11 0.04 0.09 −0.05 −0.09 0.02 0.08 −0.06 0.07 0.04 −0.03 −0.01 −0.09 0.01

0.32 0.12 0.24 −0.23 −0.02 −0.07 0.16 0.10 −0.01 −0.11 −0.01 0.03 0.05 0.05 0.09 −0.05 0.03 0.02

Note: ACC means autocorrelation coefficient, PACC means partial autocorrelation coefficient, and PV is the p-values of the Ljung–Box Q test.

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Thus, displaying this time series in Fig. 4 would yield virtually the same curve as for the estimates for the entire sample. The similarity between the exchange rate estimates occurs, to a certain extent, because the drift has no direct influence on the exchange rate estimation, as was explained in the Venezuelan example. Unlike Venezuela, however, the volatility estimates for Argentina also differ considerably. Although the volatility influences the exchange rate estimates directly, since it enters the option pricing formula, which describes the relationship between observed option prices Ct and estimated true exchange rates St , these differences in the volatility have only minor effects on the results. This is because the option’s time to maturity is rather short. A short time to maturity is typical of the situations considered here, where capital controls are installed for a short time to defend a currency peg in times of financial turmoil. With respect to changes in the estimates of the parameters, our approach produces robust estimates of the true value of the exchange rate for these situations. As with Venezuela, we produce out-of-sample forecasts of the crisis probability and the expected exchange rate on the day when capital controls are lifted. We use the estimates of the parameters derived in the first half of the time series (the estimation period) for the second half of the time series (the forecast period). As with the in-sample forecast for Argentina, the crisis probability is virtually 100%. The values are even (marginally) higher, since the drift estimated for the first half of the time series is higher. The exchange rates forecasted for the day when capital controls are lifted are higher than those obtained for the in-sample period (see Fig. 10, which displays the results of both the out-of-sample forecasts and the in-sample forecasts relying on the estimates for the entire sample period). Since the drift obtained for the first half of the time series exceeds the drift for the whole time series, the exchange rate forecasts exceed the values observed for the end of the forecast period. At the beginning of the forecast period the differences are greater, whereas towards the end of the forecast period the forecasts are close to the values observed on day T . This is because for short forecast periods, the drift µ S only influences the expected values (see Eq. (13)) slightly, relative to the current value, St . As was explained above, the estimation of the current value of the true exchange rate obtained

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by our approach for the chosen estimation period produces reasonable results, and ones which are relatively robust to the estimation period chosen. For longer time periods, forecasting the drift is rather problematic. The problem is not specific to the option approach used here, however. Forecasting exchange rates over extended time periods is in general a rather difficult task. Indeed, forecasting future exchange rates based on observed exchange rates rather than estimated exchange rates yields an even higher bias. This is illustrated in Fig. 10: the thin solid line tracks the out-of-sample forecasts based on observed exchange rates that are obtained by estimating the drift in the first half of the sample using the mean estimator. The resulting drift of the observed exchange rates is 2.30. For practical purposes, decision-makers may be more interested in the current value of the true exchange rate, or short-term rather than long-term predictions.31 4.2.3. Pre-crisis estimation So far, we have considered the period after the collapse of the currency board on January 11, 2002. This enabled us to compare our exchange rate estimations with observable values. The question arises, however, as to how well the Argentine crisis could be forecasted using ADR market data. Unlike the example of Venezuela, the estimation for the pre-crisis period is somewhat problematic. Since the time series between the introduction of capital controls on December 3, 2001, and the collapse of the currency board on January 11, 2002, is very short, there are only a limited number of observations available. Outliers therefore have a strong impact on the estimation results, which is a relatively minor problem for longer time series. Between December 19 and December 20, there is a jump in the prices of the ADR portfolio, since the option value increases by more than 75% (from 0.22 to 0.39), which equals an annual (continuous) growth rate of about 14,300%. Furthermore, we observe a considerable change in the structure within in the pre-crisis series: there 31 If the Argentine government had opted to realign its currency instead of allowing it to float at a date prior to lifting the capital controls on December 2, 2002, for example, the best (realigned) peg rate would have been the current value of the true exchange rate, St , at this date, and not its value expected for December 2 (on December 2, the current value and the expected value are equal anyway).

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Fig. 10. Out-of-sample (and in-sample) forecasts of the expected exchange rate, E t [ST ], and the exchange rate after float for Argentina.

are considerable differences between the drift and volatility estimated before and after December 20 (even if we do not take this date into consideration). This is because immediately after the introduction of capital controls we observe very high growth rates of ADR spreads (starting from virtually zero, which implies a very small denominator) and extreme variations, resulting in a very high volatility. After December 20, the growth rate and variation of ADR spreads are considerably lower than for the first period. Because of these extreme changes in the time series pattern, an estimation that includes the whole precrisis period would lead to the misspecification of the parameters. We therefore limit the estimation period to December 20, 2001, to January 10, 2002. Since this leaves only 17 observations, the results must be interpreted with caution; nevertheless, they provide interesting additional information. The estimated volatility of 0.92 for the pre-crisis period is considerably higher than the values of 0.76 and 0.58 obtained for the first half of the crisis period (forecast period) and the entire crisis period, respectively. This may reflect greater uncertainty about the true exchange rate before market values of the exchange rate are observable. Because of the exchange rate’s rapid growth over the 17 days in the pre-crisis estimation period, the annualized drift is µ S = 4.8. Thus, the estimated drift for the period shortly before the collapse of the currency board is

much higher than the values of 2.14 and 1.16 estimated for the forecast and complete observation periods, respectively. This may be because we overestimate the parameters due to the problems related to the small number of observations mentioned above. This may also indicate, however, that market participants’ perceptions of the true value of the exchange rate deteriorated rapidly in the first weeks after capital controls were imposed, and, thus, they correctly anticipated the currency board’s collapse and the exchange rate that was actually observed after floating. The dashed line in Fig. 11 shows the exchange rate forecast for January 11, 2002, based on the pre-crisis forecast sample of December 20, 2001, to January 10, 2002. With the exception of a short drop at the end of the year, the expected exchange rate is well above the pegged rate. From early January onward, it converges to the exchange rate observed after floating. In the last days before the crisis, the expected rate nearly equals the floating rate. Fig. 12 displays the probability that the true exchange rate at January 11, 2002, will be above the pegged rate. This probability is above 50% for the entire period, and from early January onward it is virtually 100%. The thin dashed line in Fig. 4 shows the exchange rates St estimated for each day when we apply the volatility of 0.92 (estimated for the pre-crisis period, together with option prices observed at dates after January 11, 2002). The values are slightly lower than

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Fig. 11. Expected true exchange rates estimated with the option approach and estimates of the actual exchange rates obtained by the futures approach for Argentina in the pre-crisis period.

Fig. 12. Devaluation probability for Argentina in the period before January 11, 2002.

the estimates obtained using the in-sample parameters (the bold dashed line), due to the higher volatility (see Eq. (11)). On average, the differences in the observed rate are 6.1% (compared to 6.0% obtained for the in-sample estimates). Again, the similarity between the exchange rate estimates demonstrates the robustness of our approach with respect to changes in the estimated volatility. Although we must be cautious in our assessment of the pre-crisis estimation results because of the short

time series used in the estimation of the parameters, the robustness check shows that our approach produces reasonable and robust results for Argentina, and not solely because the actual market values of the currency were already observable. Overall, the estimation approach provides reasonable out-ofsample results for both Argentina and Venezuela. On the whole, the differences between the observed exchange rate and our estimates and forecasts derived using the option approach for different samples

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are rather small. The results are robust, regardless of whether we perform in-sample or out-of-sample forecasts and whether we consider data observed before or after the collapse of the currency board. We therefore conclude that our approach of using ADR market data to estimate currency crisis risk and the true values of the exchange rate provides reasonable results for both Argentina and Venezuela. 4.2.4. Estimation results for the futures-based actual exchange rates So far we have discussed estimates of the true value of the currency derived using the option approach. We now turn to the current estimates of the actual exchange rate, which are derived by interpreting the ADR portfolio as a future on the actual value of the currency (instead of as an option on its true value). The thin solid line in Fig. 4 shows the results of the future approach. As in the case of Venezuela, the difference to the results of the option approach is small. The option’s time value is somewhat higher for Argentina because of the longer time to maturity, but the option is “deeper in the money” than in Venezuela, and the crisis probability is even higher. In fact, the crisis had already happened in Argentina at the beginning of the observation period. Thus, from a theoretical perspective, the actual exchange rate estimated using the future approach and the true exchange rate estimated using the option approach should be equal, both to each other and to the observed exchange rate. The differences between the estimates of the actual and true exchange rates can, however, be interpreted as consequences of the possibility that the Argentine government could fix the currency (at a level where it is undervalued, i.e. St < S ∗ ) again at or before the date when capital controls end. As for the option approach discussed above, the estimates of the exchange rate derived using the future approach deviate only slightly from the observed rate. The average deviation between the estimated actual exchange rate and the observed exchange rate is 7.4%. Fig. 11 displays the pre-crisis estimation of the current value of the actual exchange rate derived using the future approach (shown by the thin solid line). We can see that it is higher than the forecasted true exchange rate, and partly exceeds the value observed directly after the float. All in all, the differences

between the observed exchange rate and that obtained using the future approach are rather small.

5. Conclusion We present and apply a framework which enables us to derive detailed information on currency crisis risk from ADR stock market data. On the one hand, we derive the probability of a currency crisis. On the other, we forecast the expected magnitude of devaluation by estimating the true value of the currency. To do this, we adapt option pricing theory to the problem of currency crisis forecasting by interpreting price differences between ADR stocks and their “original” stocks as a call option which can be used to hedge proceeds against possible devaluation losses. We also derive current estimates of the exchange rate that will actually prevail when the capital controls are lifted by interpreting the ADR portfolio as a currency future. Based on ADR market data, we estimate the parameters required to determine the probability and magnitude of devaluation by using a maximum likelihood approach. This approach exploits the features of the option pricing model, and, unlike other estimation approaches, requires no additional assumptions. In particular, this framework enables us to estimate the true value of a country’s exchange rate — which is otherwise not known when the currency is pegged and foreign exchange market data are not available. Since capital controls are often imposed to maintain a currency peg, the true exchange rate is an unknown quantity. For an example where a currency peg and capital controls existed simultaneously and where ADR market data are available, we consider the situation in Venezuela in 1995/1996. We obtain devaluation probabilities of around 95% and almost 100%, respectively, for four and two months prior to the outbreak of the Venezuelan currency crisis on April 22, 1996. With respect to the magnitude of the devaluation, we find that the expected exchange rates are very close to the initial floating values. Whereas in the Venezuelan case (1996) the true value of the currency is unknown, during the Argentine capital control period (2002) it is known. Shortly after capital controls were imposed, the Argentine peg

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collapsed. In this case, we find that the difference between the exchange rate value estimated using our framework and the actual market exchange rate is quite small, indicating reasonable results. Several robustness checks for our examples demonstrate that the results are relatively robust to moderate changes in the parameters. In the future, international firms and investors, as well as governments, could apply our approach to obtain a better assessment of devaluation risk and potential devaluation losses. Investors in international markets could detect profit opportunities from cross market arbitrage, which could emerge if other assets, like forward exchange rates or differentials between domestic and foreign interest rates, reflect a different expected exchange rate to the one derived from call option prices. Most importantly, however, our approach can help governments make the right decisions with respect to exchange rate policy. An increasing likelihood and estimated magnitude of a devaluation could be a wake-up call for policymakers to strengthen the value of their currencies. If the government is not able or willing to do this – and if letting the currency float is undesirable – it can realign the peg rate. In this case, the government can use our approach to identify the magnitude of devaluation the market demands, and in so doing sustain the peg arrangement and avoid a currency crisis.

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Melvin, M. (2003). A stock market boom during a financial crisis? ADRs and capital outflows in Argentina. Economics Letters, 81, 129–136. Merton, R. C. (1973). A rational theory of option pricing. Bell Journal of Economics and Management Science, 4, 141–183. Merton, R. C. (1974). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29, 449–470. Merton, R. C. (1977). An analytic derivation of the cost of deposit insurance and loan guarantees. Journal of Banking and Finance, 1, 3–11. Schmukler, S. L., & Serv´en, L. (2002). Pricing currency risk under currency boards. Journal of Development Economics, 69, 367–391. Stiglitz, J. E. (2002). Argentina, shortchanged. Why the nation that followed the rules fell to pieces. Washington Post, May 12. Vasicek, O. A. (1977). An equilibrium characterisation of the term structure. Journal of Financial Economics, 5, 177–188. Dominik Maltritz studied business and physics at the University of Goettingen (Germany). He received his doctoral degree in economics from Dresden University of Technology (Germany), where he currently works as a researcher at the Chair for Monetary Economics. His research interests include monetary economics, international economics, and financial markets. His research focuses on forecasting international financial crises, modeling dependencies between different types of crisis, the determinants of country default risk, the application of structural credit risk models, the determinants of foreign direct investment, option pricing theory, American Depository Receipts, and forecasting takeover prices. Stefan Eichler graduated from Dresden University of Technology in 2006, having received the award for the best graduate student in economics. Currently, he is a doctoral candidate at the Chair for Monetary Economics at Dresden University of Technology. His fields of interest include open economy macroeconomics and international finance. His research focuses on forecasting financial crises, and in particular currency crises, as well as forecasting takeover bids, exchange rate theory, and twin crises, especially the interaction between currency crises and stock markets.