BFS 2002

Contributed Talk

On the Error in the Monte Carlo Pricing of Some Familiar European Path-Dependent Options

Per Hörfelt

This talk studies the relative error in the crude Monte Carlo pricing of some familiar European path- dependent multi asset options. For the crude Monte Carlo method, it is well-known that the convergence rate $O(n^{-1/2})$, where $n$ is the number of simu- lations, is independent of the dimension of the integral. We show that for a large class of pricing problems in the multi-asset Black-Scholes market also the constant in $O(n^{-1/2})$ is independent of the dimension. The main tool to prove this result is the isoperimetric inequality for Wiener measure.