A Monte Carlo approach to value exchange options using a single stochastic factor

Abstract

This article describes an important sampling regarding modification of the Monte Carlo method in order to minimise the variance of simulations. In a particular way,we propose a generalisation of the antithetic method and a new a-sampling of stratified procedure with a ≠ 1/2 to value exchange options using a single stochastic factor. As is well known, exchange options give the holder the right to exchange one risky asset V for another risky asset D and therefore, when an exchange option is valued, we generally are exposed to two sources of uncertainity. The reduction of the bi-dimensionality of valuation problem to a single stochastic factor implies a new stratification procedure to improve the Monte Carlo method. We also provide a set of numerical experiments to verify the accuracy derived by a-sampling.