Option pricing in the multidimensional Black-Scholes market with Vasicek interest rates

Abstract

An explicit state-price deflator for the multidimensional Black-Scholes market with Vasicek stochastic interest rates is constructed. It is applied to obtain extensions of the Margrabe and Black-Scholes option pricing formulas. These formulas, which are validated in a multiple risk economy with stochastic interest rates, remain invariant under changing market prices of risk. Some comments including related research round up the exposé.