American Options in Regime-Switching Lévy Models With Non-Semibounded Stochastic Interest Rates

6 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. Contrary to the earlier version of the method, the interest rate may assume non-positive values. As applications, explicit algorithms for Vasicek and Black's models with jumps are derived. Numerical examples show that the option prices in these two models are very close.

Keywords: optimal stopping, American options, regime switching, Lévy processes, stochastic interest rate models, Vasicek model, Black's model, Ornstein-Uhlenbeck driven models, affine term structure models

JEL Classification: D81, C61, G31

Suggested Citation

Boyarchenko, Svetlana I. and Levendorskii, Sergei Z., American Options in Regime-Switching Lévy Models With Non-Semibounded Stochastic Interest Rates (September 17, 2007). Available at SSRN: https://ssrn.com/abstract=1015410 or http://dx.doi.org/10.2139/ssrn.1015410

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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