Quasi-Monte Carlo methods for derivatives on realised variance of an index under the benchmark approach

Abstract

We apply quasi-Monte Carlo methods to the pricing of derivatives on realised variance of an index under the benchmark approach. The resulting integration problem is shown to depend on the joint density of the realised variance of the index and t he terminal value of the index. Employing a transformation mapping for this joint density to the unit square reduces the difficulty of the resulting integration problem. The quasi-Monte Carlo methods compare favourably to Monte Carlo methods when applied to the given problem