An efficient pricing algorithm for American options with double stochastic volatilities and double jumps. (September 2018)

• Record Type: Journal Article
• Authors: Zhang, Sumei
• Is Part Of: Journal of algorithms & computational technology. Volume 13(2019)
• Publication Date: 2018-09
• Subjects: American options -- Bermudan options -- double exponential jumps -- double Heston model -- Richardson extrapolation -- COS method; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1177/1748301818797064
• Languages: English
• ISSNs: 1748-3018

Abstract

The purpose of the paper is to provide an efficient pricing algorithm for American options with stochastic volatilities and jumps. This paper extends the double Heston model with double exponential jumps and derives the characteristic function of the model by Feynman–Kac theorem. With the obtained characteristic function, this paper also extends the Fourier-cosine expansion method for pricing Bermudan options to the model. Based on the COS method, this paper approximates American options by using Richardson extrapolation schemes on a series of Bermudan options and provides a pricing algorithm for American put options. Numerical results show that the proposed pricing algorithm is efficient, especially for short-term American put options.