The Pricing Of Exchange Option

Exchange option is a bind of agrement, it makes the people who own the option having the power that exchange a bind of asset by another bind of asset at maturity T. W.Margrabe (1976) deried an pricing formula for exchange option when the assets value follow Geometric Brownian Motion and the volatility of the assets value and the interest rate are constant. Yao Xiaoyi (2002). Qian Xiaosong (2004) deried an analytical formula of exchange option under Jump-diffusion process and the volatility is constant. In this paper, by using change of numeriaire, change of probility measure and Charcteristic function property, we have deried the closed-form solution of the exchange option under the combination of a stochastic volatility process and a Jump process.