Sequential Monte Carlo Methods for Option Pricing

TL;DR

This paper reviews and develops sequential Monte Carlo methods tailored for option pricing, highlighting their advantages in complex models and demonstrating improvements in estimating arithmetic Asian options under stochastic volatility.

Contribution

It provides an up-to-date review of SMC methods for option pricing and shows how these methods can enhance existing approaches, especially for complex stochastic volatility models.

Findings

SMC methods improve estimation accuracy for Asian options.

Enhanced strategies for complex stochastic volatility models.

Review of SMC applicability in option pricing literature.

Abstract

In the following paper we provide a review and development of sequential Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of related probability measures. These approaches have been used, successfully, for a wide class of applications in engineering, statistics, physics and operations research. SMC methods are highly suited to many option pricing problems and sensitivity/Greek calculations due to the nature of the sequential simulation. However, it is seldom the case that such ideas are explicitly used in the option pricing literature. This article provides an up-to date review of SMC methods, which are appropriate for option pricing. In addition, it is illustrated how a number of existing approaches for option pricing can be enhanced via SMC. Specifically, when pricing the arithmetic Asian option w.r.t a complex stochastic volatility model, it is shown that SMC methods provide additional strategies to improve estimation.