Spread option and exchange option with stochastic interest rates

In this work, we consider the issue of pricing exchange options and spread options with stochastic interest rates. We provide the closed form solution for the exchange option price when interest rate is stochastic. Our result holds when interest rate is modeled with a stochastic term structure of general form, which includes Vasicek model, CIR term structure, and other well-known term structure models as special cases. In particular, we have discussed the possibility of using our closed form solution as a control variate in pricing spread options with stochastic interest rate.