Moment Matching Method for Pricing Spread Options with Mean-Variance Mixture L\'evy Motions

TL;DR

This paper extends the moment matching method to derive semi-closed form formulas for pricing spread options under exponential Lévy models with mean-variance mixture, providing accurate prices with a new approach.

Contribution

It introduces a novel semi-closed form pricing formula for spread options under mean-variance mixture Lévy models, differing from Fourier inversion methods.

Findings

Formulas produce accurate spread option prices

Method simplifies computation compared to Fourier inversion

Applicable to exponential Lévy models with mixing distributions

Abstract

The paper Borovkova et al. [4] uses moment matching method to obtain closed form formulas for spread and basket call option prices under log normal models. In this note, we also use moment matching method to obtain semi-closed form formulas for the price of spread options under exponential L\'evy models with mean-variance mixture. Unlike the semi-closed form formulas in Caldana and Fusai [5], where spread prices were expressed by using Fourier inversion formula for general price dynamics, our formula expresses spread prices in terms of the mixing distribution. Numerical tests show that our formulas give accurate spread prices also