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Pricing Currency Options Under Stochastic Volatility

This paper investigates the relative pricing performance between constant volatility and stochastic volatility pricing models, based on a comprehensive sample of options on four currencies, including the British pound, Deutsche mark, Japanese yen and Swiss franc, traded frequently in the Philadelphia Stock Exchange (PHLX) from 1994 to 2001. The results show that the model of Heston (1993) outperforms the model of Garman and Kohlhagen (1983) in terms of sum of squared pricing errors for all currency options. Furthermore, the adjustment speed toward the long-run mean volatility in the currency market is faster than that in the stock market. It may be attributed to the larger momentum effect in the stock. We also find that the stock market exhibits larger implied skewness than the currency market. This may be due to stronger 'trend effect' in the stock market, especially involved in the bear market.