Forecasting volatility and option pricing for exchange-rate dynamics : a comparison of models

This paper explores the applicability of static and dynamic models to capture the stylized facts of exchange-rate dynamics. The static models (mixture of distributions, compound Poisson process, generalized Student distribution) are compatible with leptokurtosis and can be characterized as scale-compounded distributions. The dynamic models (GARCH, GARCH-t, EGARCH, Markov-switching model), on the other hand, are compatible with both leptokurtosis and heteroskedasticity. In a comparison of the candidate models, it is found that the dynamic models do indeed achieve a better fit to the data than the static models. However, in forecasting experiments the dynamic models can outperform a 'naive' model of constant variances only with respect to unbiasedness but not with respect to precision. Furthermore, the paper examines the implications of the static and dynamic models for the pricing of foreign-currency options by simple simulations. Static models show significang option-price effect only when the maturity is short. GARCH and EGARCH models, on the other hand, imply options prices which are higher than Black-Scholes prices for the full range of moneyness. Only the Markov-switching model is compatible with the observed 'smile effects' on option markets.