The Intertemporal Relationship Between the Currency Spot Market and the Currency Option Market

This study examines the lead/lag relationship between currency option and currency spot markets for the Deutsche mark and the Japanese yen. Using intraday currency option transactions data for the year 1989 and applying a European type currency option pricing model, pair data series of the implied and the observed exchange rates are compiled. Causality tests are then employed to test the causal relation between the observed and the implied exchange rate changes. The results indicate that the currency spot market leads the currency option market by about ninety minutes.     

Spot and forward volatility in foreign exchange

This paper investigates the empirical relation between spot and forward implied volatility in foreign exchange. We formulate and test the forward volatility unbiasedness hypothesis, which may be viewed as the volatility analogue to the extensively researched hypothesis of unbiasedness in forward exchange rates. Using a new dataset of spot implied volatility quoted on over-the-counter currency options, we compute the forward implied volatility that corresponds to the delivery price of a forward contract on future spot implied volatility. This contract is known as a forward volatility agreement. We find strong evidence that forward implied volatility is a systematically biased predictor that overestimates movements in future spot implied volatility. This bias in forward volatility generates high economic value to an investor exploiting predictability in the returns to volatility speculation and indicates the presence of predictable volatility term premiums in foreign exchange.     

Dynamics of foreign exchange implied volatility and implied correlation surfaces

The prices of currency options expressed in terms of their implied volatilities and the implied correlations between foreign exchange rates at a given point in time depend on option delta and time to maturity. Implied volatilities and implied correlations likewise may thus be represented as a surface. It is well known that these surfaces exhibit both skew/smile features and term structure effects and their shapes fluctuate substantially over time. Using implied volatilities on three currency pairs as well as historical implied correlation values between them, we study the nature of these fluctuations by applying a Karhunen-Loève decomposition that is a generalization of a principal component analysis. We demonstrate that the largest share in the dynamics of these surfaces' fluctuations may be explained by exactly the same three factors, providing evidence of strong interdependences between implied correlation and implied volatility of global currency pairs.     

Efficiency tests with overlapping data: an application to the currency options market

This paper presents the results of an empirical study into the efficiency of the currency options market. The methodology derives from a simple model often applied to the spot and forward markets for foreign exchange. It relates the historic volatility of the underlying asset to the implied volatility of an option on the underlying at a specified prior time and then proceeds to test obvious hypotheses about the values of the coefficients. The study uses panel regression to address the problem of overlapping data which leads to dependence between observations. It also uses volatility data directly quoted on the market in order to avoid the biases which may occur when ‘backing out’ volatility from specific option pricing models. In general, the evidence rejects the hypothesis that the currency option market is efficient. This suggests that implied volatility is not the best predictor of future exchange rate volatility and should not be used without modification: the models presented in this paper could be a way of producing revised forecasts.     

An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates

This paper proposes an asymptotic expansion scheme of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas for the density functions of the underlying assets and for pricing currency options based on a third order asymptotic expansion scheme; we do not model a foreign exchange rate’s variance such as in Heston [(1993) The Review of Financial studies, 6, 327–343], but its volatility that follows a general time-inhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. Finally, numerical examples are provided and the pricing formula are applied to the calibration of volatility surfaces in the JPY/USD option market.     

Biases in option prices : Evidence from the foreign currency option market

This paper examines a European call model of option pricing over a data set which does not suffer from the early exercise problems that have plagued earlier studies of call options on common stocks. We specifically examine a data set of American call prices on spot foreign exchange for which it is plausible to apply an adjusted version of the Garman-Kohlhagen (1983) and Grabbe (1983) European call option model. We make adjustments for interest rate risk and find that the model is nearly unbiased in the valuation of foreign currency options. We conclude that the Geske-Roll (1984) conjecture about dividend uncertainty creating biases in stock option prices holds analogously in the foreign currency option market. Interest rate differential risk (analogous to risky dividends) thus appears to be an important element in the valuation of foreign currency options.     

THE VALUATION OF CURRENCY OPTIONS FOR ALTERNATE STOCHASTIC PROCESSES

This paper compares the ability of four valuation models — the Pure Diffusion model of Black-Scholes-Merton, the Absolute Diffusion and Pure Jump models of Cox-Ross, and the mixed Jump-Diffusion model of Merton — to explain the observed behavior of market prices of foreign currency options. The empirical tests are based on a comparison of the pattern of implied volatilities obtained from option market prices and the Black-Scholes-Merton model with those expected theoretically if exchange rates follow the four stochastic processes specified above. The results of the comparison show that the pattern of implied volatilities is most consistent with the mixed Jump-Diffusion model.     

Theory and evidence on the dynamic interactions between sovereign credit default swaps and currency options

Using sovereign CDS spreads and currency option data for Mexico and Brazil, we document that CDS spreads covary with both the currency option implied volatility and the slope of the implied volatility curve in moneyness. We propose a joint valuation framework, in which currency return variance and sovereign default intensity follow a bivariate diffusion with contemporaneous correlation. Estimation shows that default intensity is much more persistent than currency return variance. The market price estimates on the two risk factors also explain the well-documented evidence that historical average default probabilities are lower than those implied from credit spreads.     

FOREIGN EXCHANGE AND CROSS-BORDER VALUATION

Should a corporate financial manager analyze a cross-border investment proposal from the perspective of the foreign currency or the home currency? The conventional wisdom among economists is that it doesn't matter–the valuation of an asset should be the same in one currency as in another, given the spot FX rate. This assertion implies that it is irrelevant whether we analyze an overseas investment's NPV in the home currency or the foreign currency, as long as we use consistent cross-border conversions.
But what happens if managers' foreign exchange forecasts differ from the efficient markets forecast that is implicit in interest rates? In that case, as this article demonstrates through a series of examples, managers' FX forecasts can affect their investment, hedging, and financing decisions.     

International market response to announcements of US macroeconomic data

This paper presents empirical evidence relating the announcement effects of US money supply and inflation (CPI and PPI) to Eurocurrency interest rates and the foreign currency markets (both spot and forward) for seven industrial countries over the period 1977–1982. The results indicate that unanticipated components of announced changes in money supply have a significant positive effect on Eurocurrency interest rates and a negative effect (implying dollar appreciation) on the spot exchange rates. Unanticipated changes in PPI have a positive significant effect on interest rates, a small surprisingly negative impact on spot exchange rates, and a positive effect on gold prices. The CPI has no effect on either market.     

Dynamic Volatility Trading Strategies in the Currency Option Market

The conditional volatility of foreign exchange rates can be predicted using GARCH models or implied volatility extracted from currency options. This paper investigates whether these predictions are economically meaningful in trading strategies that are designed only to trade volatility risk. First, this article provides new evidence on the issue of information content of implied volatility and GARCH volatility in forecasting future variance. In an artificial world without transaction costs both delta-neutral and straddle trading stratgies lead to significant positive profits, regardless of which volatility prediction method is used. Specifically, the agent using the Implied Stochastic Volatility Regression method (ISVR) earns larger profits than the agent using the GARCH method. Second, it suggests that the currency options market is informationally efficient. After accounting for transaction costs, which are assumed to equal one percent of option prices, observed profits are not significantly differentfrom zero in most trading strategies. Finally, these strategies offered returns have higher Sharpe ratio and lower correlation with several major asset classes. Consequently, hedge funds and institutional investors who are seeking alternative “marketneutral” investment methods can use volatility trading to improvethe risk-return profile of their portfolio through diversification. This revised version was published online in November 2006 with corrections to the Cover Date.     

Valuation of quanto options in a Markovian regime-switching market: A Markov-modulated Gaussian HJM model

We consider the valuation of European quanto call options in an incomplete market where the domestic and foreign forward interest rates are allowed to exhibit regime shifts under the Heath–Jarrow–Morton (HJM) framework, and the foreign price dynamics is exogenously driven by a regime switching jump-diffusion model with Markov-modulated Poisson processes. We derive closed-form solutions for four different types of quanto call options, which include: options struck in a foreign currency, a foreign equity call struck in domestic currency, a foreign equity call option with a guaranteed exchange rate, and an equity-linked foreign exchange-rate call.     

Confidence building on Euro convergence: Evidence from currency options

We study the evolution of investor confidence in 1992-1998 over the chance of individual currencies to converge to the Euro, using data on currency option prices. Convergence risk, which may reflect uncertainty over policy commitment as well as exogenous fundamentals, induces a level of implied volatility in excess of actual volatility. This volatility wedge should gradually decrease as confidence grows over time as convergence policy is maintained, and the risk of a reversal is progressively resolved. Empirically, we indeed find a positive volatility wedge which declines over time only for currencies involved in the Euro convergence process. The wedge and other convergence risk measures are correlated with both exogenous fundamentals and proxies for policy commitment uncertainty. We also find that the wedge responds to policy shocks in an asymmetric fashion, suggesting that policy risk is resolved at different rates after negative and positive shocks. Finally, we estimate a regime-switching model of convergence uncertainty, using data on interest rates, currency rates, and currency option prices. The results confirm the time-varying and asymmetric nature of convergence risk, and indicate that investors demand a risk premium for convergence risk.     

Equilibrium Valuation of Foreign Exchange Claims

This article studies the equilibrium valuation of foreign exchange contingent claims. Within a continuous-time Lucas (1982) two-country model, exchange rates, interest rates and, in particular, factor risk prices are all endogenously and jointly determined. This guarantees the internal consistency of these price processes with a general equilibrium. In the same model, closed-form valuation formulas are presented for currency options and currency futures options. Common to these formulas is that stochastic volatility and stochastic interest rates are admitted. Hedge ratios and other comparative statics are also provided analytically. It is shown that most existing currency option models are included as special cases.     

The Accuracy of Density Forecasts from Foreign Exchange Options

Financial decision makers often consider the information incurrency option valuations when making assessments about futureexchange rates. The purpose of this article is to systematicallyassess the quality of option-based volatility and density forecasts.We use a unique dataset consisting of more than 10 years ofdaily data on over-the-counter (OTC) currency option prices.We find that the OTC implied volatilities provide largely unbiasedand fairly accurate forecasts of one-month- and three-month-aheadrealized volatility. Furthermore, we find that the one-monthoption implied density forecasts are well calibrated for thecenter of the distribution, but we find evidence of misspecificationin the tail density forecasts.     

Segmentation and time-of-day patterns in foreign exchange markets

This paper sheds light on a puzzling pattern in spot foreign exchange markets: domestic currencies appreciate (depreciate) systematically during foreign (domestic) working hours. This phenomenon spans many years and several exchange rates, and overrides calendar effects. We argue that it is mainly due to liquidity and inventory patterns that emerge from the combination of two factors: domestic agents tend to be net buyers of foreign currency and to trade mostly in their country’s working hours. The prevalence of domestic (foreign) traders demanding the counterpart currency during domestic (foreign) working hours implies sell-price (buy-price) pressure on the domestic currency during domestic (foreign) working hours.     

Option volume,strike distribution,and foreign exchange rate movements

Using Deutschmark currency option data from the Philadelphia Stock Exchange and British pound option data from the Chicago Mercantile Exchange, this article examines the signaling quality of option volume measures on movements in the underlying spot exchange rates. The concept of a volume-weighted strike distribution is proposed. It is demonstrated that measures using the strike distribution are inherently better predictors of both direction and volatility of the exchange rate movements as compared to their more traditional counterparts used in practice, such as the put-call ratio.      

Expectations Hypothesis of the Term Structure of Implied Volatility: Evidence from Foreign Currency and Stock Index Options

Using a stochastic volatility option pricing model, we showthat the implied volatilities of at-the-money options are notnecessarily unbiased and that the fixed interval time-seriescan produce misleading results. Our results do not support theexpectations hypothesis: long-term volatilities rise relativeto short-term volatilities, but the increases are not matchedas predicted by the expectations hypothesis. In addition, anincrease in the current long-term volatility relative to thecurrent short-term volatility is followed by a subsequent decline.The results are similar for both foreign currency and the S&P500 stock index options.     

An equilibrium approach to pricing foreign currency options

The paper presents a modified version of the Garman-Kohlhagen formula for pricing European currency options. The equilibrium approach deviates from the no-arbitrage approach by allowing domestic and foreign interest rates and their dynamics to be determined endogenously in the model. By using the relations between exchange rate dynamics and the dynamics of interest rates, I provide a new characterisation of the relevant volatilities for European currency option pricing, which only depends on parameters describing the variability of the log-exchange rate. The implications of the model for the valuation of American currency options and optimal exercise strategies are examined by applying numerical methods.     

Predicting Volatility in the Foreign Exchange Market

Measures of volatility implied in option prices are widely believed to be the best available volatility forecasts. In this article, we examine the information content and predictive power of implied standard deviations (ISDs) derived from Chicago Mercantile Exchange options on foreign currency futures. The article finds that statistical time-series models, even when given the advantage of “ex post” parameter estimates, are outperformed by ISDs. ISDs, however, also appear to be biased volatility forecasts. Using simulations to investigate the robustness of these results, the article finds that measurement errors and statistical problems can substantially distort inferences. Even accounting for these, however, ISDs appear to be too variable relative to future volatility.