American Options in Levy Models With Stochastic Interest Rate of CIR-Type
37 Pages Posted: 27 Nov 2007
Date Written: November 26, 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 Levy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. As an application, an explicit algorithm for the case of interest rate driven by the square root process with embedded jumps is derived. Numerical examples show that fairly accurate results can be obtained in reasonable time. It is shown that the shape of the early exercise boundary strongly depends on the sign of the leverage parameter.
Keywords: optimal stopping, American options, regime switching, Levy processes, stochastic interest rate, CIR model
JEL Classification: D81, C61, G31
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