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We use a power series expansion method to get an analytic approximation value for the quanto option price under the Hull and White stochastic volatility model, which turns out to be accurate enough by comparing with the simulation prices using Monte Carlo method. A quanto is a type of financial derivative whose pay-out currency differs from the natural denomination of its underlying financial variable. Its main purpose is to provide exposure to a foreign asset without taking the corresponding exchange rate risk. A quanto option is a foreign currency stock option whose payoff is converted into a domestic currency at maturity at a predetermined foreign exchange rate. The profit of quanto option is worked out a particular currency, but the pay-out of the quanto option is made by cash settlement of fixed exchange rate for another currency. Stochastic volatility models are frequently used in pricing various kinds of European options. The most famous and popular stochastic volatility models include the Hull and White (6), the Stein and Stein (7), the Heston (5) ones. Their main purpose is to resolve a shortcoming that the Black-Scholes' constant volatility model which cannot explain long-observed features of the implied volatility surface such as volatility smiles and skews. For that reason, in valuing a quanto option it is natural to consider a stochastic volatility model. Despite its importance, very little research has been done on pricing a quanto option using a stochastic volatility model primarily due to the sophisticated stochastic process for underlying assets and volatilities as well as the difficulty of finding analytic form of a quanto option price. To mention some of the related previous work, Ball and Roma (4) examined alternative methods for pricing options when the underlying security volatility is stochastic.

PRICING OF QUANTO OPTION UNDER THE HULL AND WHITE STOCHASTIC VOLATILITY MODEL