Lower Bound Approximation to Basket Option Values for Local Volatility Jump-Diffusion Models

TL;DR

This paper introduces a fast, accurate approximation method for lower bounds of European basket call options under local volatility jump-diffusion models, using asymptotic expansion techniques.

Contribution

It provides a novel, easily computed approximation for basket option prices in complex models, with a closed-form solution for time-independent volatility.

Findings

The approximation is faster than Monte Carlo methods.

It achieves comparable accuracy to existing methods.

Numerical tests validate the method's efficiency and precision.

Abstract

In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European basket call prices. If the local volatility function is time independent then there is a closed-form expression for the approximation. Numerical tests show that the suggested approximation is fast and accurate in comparison with the Monte Carlo and other approximation methods in the literature.