Basket Options Valuation for a Local Volatility Jump-Diffusion Model with the Asymptotic Expansion Method

TL;DR

This paper introduces an asymptotic expansion method for efficiently valuing basket options under a correlated local volatility jump-diffusion model, providing a fast and accurate alternative to Monte Carlo simulations.

Contribution

It develops a novel asymptotic expansion approach to approximate basket options prices in complex jump-diffusion models with local volatility.

Findings

Method is faster than Monte Carlo simulations.

Approximations are highly accurate in numerical tests.

Applicable to general stochastic processes with jumps.

Abstract

In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expansion method to approximate the conditional expectation of the stochastic variance associated with the basket value process. The numerical tests show that the suggested method is fast and accurate in comparison with the Monte Carlo and other methods in most cases.