American Options in Lévy Models with Stochastic Interest Rates

31 Pages Posted: 20 Sep 2007

See all articles by Svetlana Boyarchenko

Svetlana Boyarchenko

University of Texas at Austin - Department of Economics

Sergei Levendorskii

Calico Science Consulting

Date Written: September 17, 2007

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 Lévy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. An explicit algorithm for the case of positive stochastic interest rates driven by a process of the Ornstein-Uhlenbeck type is derived. Efficiency of the method is illustrated with numerical examples.

Keywords: optimal stopping, American options, regime switching, Lévy processes, stochastic interest rate models, quadratic term structure models

JEL Classification: D81, C61, G31

Suggested Citation

Boyarchenko, Svetlana I. and Levendorskii, Sergei Z., American Options in Lévy Models with Stochastic Interest Rates (September 17, 2007). Available at SSRN: https://ssrn.com/abstract=1015409 or http://dx.doi.org/10.2139/ssrn.1015409

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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