American Options in Levy Models with Stochastic Volatility
36 Pages Posted: 20 Nov 2007 Last revised: 12 May 2008
Date Written: May 10, 2008
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 the sequence are solved using an iteration method based on the Wiener-Hopf factorization. As an application, an explicit algorithm for the case of a Levy process with the intensity coefficient driven by the square root process with embedded jumps is derived. Numerical examples corroborate the general result about a gap between strike and early exercise boundary at expiry, in a neighborhood of r=0, in the presence of jumps.
Keywords: optimal stopping, American options, regime switching, Levy processes, stochastic volatility models, Heston model, Bates model
JEL Classification: D81, C61, G31
Suggested Citation: Suggested Citation