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

Song Bin (), Liang Enqi () and Liu Bing ()
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Song Bin: Investment Department, School of Management Science and Engineering, Central University of Finance and Economics, Beijing, 100081, China
Liang Enqi: Derivatives Trading Department, China Securities Co., Ltd., Beijing, 100010, China
Liu Bing: Investment Department, School of Management Science and Engineering, Central University of Finance and Economics, Beijing, 100081, China

Journal of Systems Science and Information, 2014, vol. 2, issue 6, 505-519

Abstract: 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.

Keywords: American options; sequential Monte Carlo; particle filter; latent variable; stochastic volatility jump; auxiliary particle filter (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:jossai:v:2:y:2014:i:6:p:505-519:n:2

DOI: 10.1515/JSSI-2014-0505

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