AUTHOR=Shi Xiang , Zhang Lihua , Kim Young S. A. 

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

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=1

YEAR=2016

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2015.00013

DOI=10.3389/fams.2015.00013

ISSN=2297-4687

ABSTRACT=<p>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.</p>