Sequential Monte Carlo Methods for Option Pricing

In the following paper, we provide a review and development of sequential Monte Carlo (SMC) methods ([17, 18, 24]) 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 and physics (e.g. [18, 24]). 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, and illustrates how a number of existing approaches for option pricing can be enhanced via SMC. It is also shown, when pricing the arithmetic asian option, w.r.t a complex stochastic volatility model, that SMC methods provide additional strategies to improve estimation.