(A) study of the pricing and hedging of long-term foreign currency options with stochastic volatility

Abstract

This paper investigates the consequences of stochastic volatility upon the pricing and hedging of long-term foreign currency options. The traditional method of pricing such options uses a constant volatility option model with an implicit volatility derived from a traded short-term option. I find that the traditional method leads to small pricing errors for shor-term options, but does a poor job in pricing long-term options. I show that allowing volatility to be stochastic results in a much better fit in estimating the derivatives of the option``s value with respect to the exchange rate (delta) and the volatility (vega). The improvements in the calculation of these derivatives, which are used in forming the replicating portfolio, lead to better performance in hedging strategies.