Stochastic models of exchange-rate dynamics and their implications for the pricing of foreign-currency options
The aim of this study is to find a suitable approach to model econometrically exchange-rate dynamics. In the first chapter, I examine the empirical properties of four exchange rates. The data used are daily, weekly, monthly and quarterly exchange rates of the German mark, the British pound, the Swiss franc, and the Japanese yen against the U.S. dollar from July 1974 to December 1987.1 study the moment properties and time-series properties of these exchange rates and find in daily and weekly data leptokurtosis and heteroskedasticity. On the other hand, the hypotheses of no serial correlation, of a constant mean of zero, and of a symmetric distribution cannot be rejected. The fact that the daily and weekly data are not strictly equi-distant does not have a strong impact on these empirical regularities. In chapter 2, static distributional models (mixture of distributions, compound Poisson process, Student distribution, and stable Paretian distributions) are estimated. Chi-squared goodness-of-fit tests reject these models. Direct inferential evidence against stable distributions is found by estimating the characteristic exponent by FFT and by estimating the exponent of regularly varying tails. In chapter 3, dynamic models of heteroskedasticity (ARCH and Markov-switching models) are introduced. Quite satisfactory results are obtained for the EGARCH model and the Markov-switching model whereas the ARCH, GARCH and GARCH-t models are in conflict with stationarity conditions for the variance. Chapter 4 compares the static and dynamic models with respect to goodness-of-fit and forecasting performance. With respect to goodness-of-fit criteria, the dynamic models appear to be superior to the static models. Furthermore, the dynamic models outperform a naive model of constant variance with respect to unbiasedness but not with respect to precision. Chapter 5 studies the option-price implications of the static and dynamic models. The spot-rate effects of static models are rather small and they disappear, as expected, under temporal aggregation. GARCH and EGARCH models, on the other hand, imply higher option prices compared to Black-Scholes option prices along the whole spectrum of moneyness. Only the Markov-switching model is compatible with observed smile effects.