Pricing Currency Options Under Stochastic Volatility

underlying return and its volatility, although they do consider the phenomenon ofleptokurtosis of the return process. Fleming (1998) and Guo (1996) argued that theimplied variance extracted from the model of Hull and White (1987) is dominant butstill a biased estimator in terms of out-of-sample forecasting performance in thestock-index and foreign currency options markets.Stein and Stein (1991) offered the stock price distribution evaluated by an inverseFourier series transformation based on the no correlation between the underlying returnand its volatility, and obtained a closed-form formula for the European options.Specifically, Hull and White (1987), Scott (1987), Wiggins (1987) and Stein and Stein(1991) contributed the consideration of the kurtosis by modeling the volatility to astochastic process, but left the skewness of the underlying returns to be not incorporatedin the models.Heston (1993) argued that the correlation between the underlying asset return andits volatility affected both the skewness and the leptokurtosis of the distribution ofunderlying returns. This correlation is important in explaining for the skewness thataffects the pricing of in-the-money options. With the zero correlation, the stochasticvolatility is only related to the kurtosis that influences the pricing of near-the-moneyand far-from-the-money options, thus it can induce the pricing errors in options. Bates(1996) offered an empirical study based on the closed form solution of Heston (1993),with a diffusion-jump process. By estimating the parameters in the volatility process onthe Deutsche mark options, Bates (1996) found that the stochastic volatility couldexplain the implicit leptokurtosis only by considering the jump risk. Guo (1998)empirically studied the parameters on the risk-neutral variance process and the marketprice of variance risk implied in the PHLX currency options, based on the model ofHeston (1993). Guo found that the market price of variance risk was nonzero, time4