Valuing Exchange Options Under an Ornstein-Uhlenbeck Covariance Model

TL;DR

This paper introduces an efficient approximation method for pricing exchange options under a complex Ornstein-Uhlenbeck covariance model with jump processes, outperforming Monte Carlo in speed while maintaining accuracy.

Contribution

It develops a novel Taylor and spline expansion approach for pricing exchange options under a stochastic jump covariance model, improving computational efficiency.

Findings

The proposed method is faster than Monte Carlo simulations.

It maintains comparable accuracy to Monte Carlo methods.

The approach effectively handles jump processes in covariance modeling.

Abstract

In this paper we study the pricing of exchange options under a dynamic described by stochastic correlation with random jumps. In particular, we consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise Process driven by Inverse Gaussian subordinators. We use expansion in terms of Taylor polynomials and cubic splines to approximately compute the price of the derivative contract. Our findings show that this approach provides an efficient way to compute the price when compared with a Monte Carlo method while maintaining an equivalent degree of accuracy with the latter.