A Markov Chain Approximation for American Option Pricing in Tempered Stable-GARCH Models

Frontiers in Applied Mathematics and Statistics

Zhang, Lihua¹  Kim, Young S. A.²  Shi, Xiang³ 

[1] Business School of Administration, Zhejiang University of Technology, Hangzhou, China;College of Business, Stony Brook University, Stony Brook, NY, USA;Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY, USA

关键词: Tempered stable distribution;    GARCH;    American options;    Markov chain;    Minimal entropy;   

DOI  :  10.3389/fams.2015.00013

学科分类：数学（综合）

来源: Frontiers

【 摘 要 】

This paper considers the American option pricing problem under the stochastic volatility models. In particular, we introduce the GARCH model with two heavy-tailed distributions: classical tempered stable (CTS) and normal tempered stable (NTS) distribution. Then we apply the Markov chain approach to compute the prices of American style options under these two models. Minimal entropy provides a convenient way to construct equivalent martingale measure (EMM) and allows us to overcome the difficulties in incorporating the Markov chain approximation. The convergence of the approximation is also proved. Both numerical and empirical results are analyzed to show the advantages and drawbacks of our approach.

【 授权许可】

CC BY