This paper uses a rich new data set of option prices on the dollar-mark, dollar-yen, and key EMS cross-rates to extract the entire risk-neutral probability density function (pdf) over horizons of one and three months. We compare three alternative smoothing methods--cubic splines, an implied binomial tree (trimmed and untrimmed), and a mixture of lognormals--for transforming option data into the pdf. Despite their methodological ifferences, the three approaches lead to a similar pdf distinct from the lognormal benchmark, and usually characterized by skewness and leptokurtosis. We then document a striking positive correlation between skewness in these pdfs and the spot rate. The stronger a currency the more expectations are skewed towards a further appreciation of that currency. We interpret this finding as a rejection that these exchange rates evolve as a martingale, or that they follow a credible target zone, explicit or implicit. Instead, this this positive correlation is consistent with target zones with endogenous realignment risk. We discuss two interpretations of our results on skewness: when a currency is stronger, the actual probability of further large appreciation is higher, or because of risk, such states are valued more highly.

This volume is a collection of classical and recent empirical studies of currency options and their implications for issues of exchange rate economics, such as exchange rate risk premium, volatility, market expectations, and credibility of exchange rate regimes. It contains applications on how to extract useful information from option market data for financial forecasting policy purposes. The subjects are discussed in a self-contained, user-friendly format, with introductory chapters on currency option theory and currency option markets.The book can be used as supplementary reading for graduate finance and international economics courses, as training material for central bank and regulatory authorities, or as a reference book for financial analysts.

Chapter 1: Historically, the currency derivative pricing literature and the macroeconomics literature on FX determination have progressed separately. In this Chapter I argue the joint study of these two strands of literature and give an overview of FX option pricing concepts and terminology crucial for this interdisciplinary study. I also explain the three sources of information about market expectations and perception of risk that can be extracted from FX option prices and review empirical methods for extracting option-implied densities of future exchange rates. As an illustration, I conclude the Chapter by investigating time series dynamics of option-implied measures of FX risk vis-a-vis market events and US government policy actions during the period January 2007 to December 2008. Chapter 2: This Chapter proposes using foreign exchange (FX) options with different strike prices and maturities to capture both FX expectations and risks. We show that exchange rate movements, which are notoriously difficult to model empirically, are well-explained by the term structures of forward premia and options-based measures of FX expectations and risk. Although this finding is to be expected, expectations and risk have been largely ignored in empirical exchange rate modeling. Using daily options data for six major currency pairs, we first show that the cross section options-implied standard deviation, skewness and kurtosis consistently explain not only the conditional mean but also the entire conditional distribution of subsequent currency excess returns for horizons ranging from one week to twelve months. This robust empirical pattern is consistent with a representative expected utility maximizing investor who, in addition to caring about the mean and variance, also cares about the skewness and kurtosis of the return distribution. Our results highlight the importance of expectations and risk in explaining exchange rate dynamics and suggest that the perennial problems faced by the empirical exchange rate literature are most likely due to overly restrictive auxiliary assumptions inherent in prevailing testing methods. Chapter 3: Standard ordinary least squares (OLS)-based tests of the uncovered interest parity (UIP) condition often make strong auxiliary assumptions beyond the joint hypotheses of rational expectations and risk-neutrality. This paper proposes using prices of foreign exchange (FX) option with different strike prices to test the time-varying risk premia explanation of the UIP puzzle. The options-based testing framework rests on the theoretical result that the forward exchange rate is the theoretical first moment of the option-implied distribution of future spot exchange rate. The framework allows us to test a more general version of FX market efficiency, which is the hypothesis that the option-implied risk-neutral distribution is an unbiased predictor of the future realized distribution of future spot rate. For five currency pairs, I do not reject the null hypothesis of UIP using the options-based approach.

Abstract: Using high-frequency data on Deutschemark and Yen returns against the dollar, we construct model-free estimates of daily exchange rate volatility and correlation, covering an entire decade. In addition to being model-free, our estimates are also approximately free of measurement error under general conditions, which we delineate. Hence, for all practical purposes, we can treat the exchange rate volatilities and correlations as observed rather than latent. We do so, and we characterize their joint distribution, both unconditionally and conditionally. Noteworthy results include a simple normality-inducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and highly.