A perturbative moment approach to option pricing

TL;DR

This paper introduces a perturbative moment expansion method for option pricing, approximating complex distributions with simpler ones by matching moments, enabling efficient numerical solutions for various exotic options.

Contribution

The paper presents a novel perturbative moment expansion approach that improves numerical option pricing by matching moments around a base distribution, applicable to path-dependent options.

Findings

Provides accurate numerical solutions for Asian, reverse cliquet, and barrier options.

Demonstrates efficiency over traditional methods through comparative analysis.

Offers a flexible framework for pricing complex derivatives.

Abstract

In this paper we present a new methodology for option pricing. The main idea consists to represent a generic probability distribution function (PDF) via a perturbative expansion around a given, simpler, PDF (typically a gaussian function) by matching moments of increasing order. Because, as shown in literature, the pricing of path dependent European options can be often reduced to recursive (or nested) one-dimensional integral calculations, the above perturbative moment expansion (PME) leads very quickly to excellent numerical solutions. In this paper, we present the basic ideas of the method and the relative applications to a variety of contracts, mainly: asian, reverse cliquet and barrier options. A comparison with other numerical techniques is also presented.