American Options in Levy Models with Stochastic Volatility

36 Pages Posted: 20 Nov 2007 Last revised: 12 May 2008

See all articles by Svetlana Boyarchenko

Svetlana Boyarchenko

University of Texas at Austin - Department of Economics

Sergei Levendorskii

Calico Science Consulting

Date Written: May 10, 2008

Abstract

A general numerical method for pricing American options in regime switching jump diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Levy model. Options in the sequence are solved using an iteration method based on the Wiener-Hopf factorization. As an application, an explicit algorithm for the case of a Levy process with the intensity coefficient driven by the square root process with embedded jumps is derived. Numerical examples corroborate the general result about a gap between strike and early exercise boundary at expiry, in a neighborhood of r=0, in the presence of jumps.

Keywords: optimal stopping, American options, regime switching, Levy processes, stochastic volatility models, Heston model, Bates model

JEL Classification: D81, C61, G31

Suggested Citation

Boyarchenko, Svetlana I. and Levendorskii, Sergei Z., American Options in Levy Models with Stochastic Volatility (May 10, 2008). Available at SSRN: https://ssrn.com/abstract=1031280 or http://dx.doi.org/10.2139/ssrn.1031280

Svetlana I. Boyarchenko

University of Texas at Austin - Department of Economics ( email )

Austin, TX 78712
United States

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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