American Option Pricing Using Particle Filtering Under Stochastic Volatility Correlated Jump Model

A particle filter based method to price American option under partial observation framework is introduced. Assuming the underlying price process is driven by unobservable latent factors, the pricing methodology should contain inference on latent factors in addition to the original least-squares Monte Carlo approach of Longstaff and Schwartz. Sequential Monte Carlo is a widely applied technique to provide such inference. Applications on stochastic volatility models has been introduced by Rambharat, who assume that volatility is a latent stochastic process, and capture information about it using particle filter based “summary vectors”. This paper investigates this particle filter based pricing methodology, with an extension to a stochastic volatility jump model, stochastic volatility correlated jump model (SVCJ), and auxiliary particle filter (APF) introduced first by Pitt and Shephard. In the APF algorithm of SVCJ model, it also provides a modification version to enhance the performance in the resampling step. A detailed implementation and numerical examples of the algorithm are provided. The algorithm is also applied to empirical data.