Pricing Currency Options in the Presence of Time-Varying Volatility and Nonnormalities

A new framework is developed for pricing currency options where the distribution of exchange rate returns exhibits time-varying volatility and nonnormalities. A forward looking volatility structure is adopted whereby volatility is expressed as a function of currency returns over the life of the contract. Time-to-maturity e¤ects as well as levels e¤ects in volatility are also considered. Both skewness and fat-tails in currency returns are priced using a range of nonnormal risk neutral probability distributions. A special feature of the approach is that an analytical solution for the option price is obtained up to a one-dimensional integral in the real plane. This enables option prices to be computed e¢ ciently and accurately, which is in contrast to existing methods that rely on Monte Carlo numerical procedures to price options in the presence of nonnormal returns and time-varying moments. The proposed modelling framework is applied to pricing European currency call options for the UK pound written on the US dollar using daily data over the period October 1997 to September 1998. The results show that the new approach yields, in general, more accurate within-sample …t and outof-sample prediction of observed currency option prices, when compared with a range of competing option price models. The results also demonstrate that skewness has important implications for constructing hedged portfolios and managing risk. Key words: Option pricing; skewness; fat-tails; time-varying volatility; generalised Student t; lognormal mixture; semi-nonparametric. JEL classi…cation: C13, G13 (a) Department of Economics, University of Melbourne, Victoria, Australia. (b) Department of Econometrics and Business Statistics, Monash University, Victoria, Australia.