American Options in Lévy Models with Stochastic Interest Rates
31 Pages Posted: 20 Sep 2007
Date Written: September 17, 2007
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
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