American Options in Regime-Switching Lévy Models With Non-Semibounded Stochastic Interest Rates
6 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. 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: Suggested Citation