American Options in the Heston Model With Stochastic Interest Rate

22 Pages Posted: 20 Nov 2007

See all articles by Svetlana Boyarchenko

Svetlana Boyarchenko

University of Texas at Austin - Department of Economics

Sergei Levendorskii

Calico Science Consulting

Date Written: November 19, 2007

Abstract

We consider the Heston model with the stochastic interest rate of the CIR type and more general models with stochastic volatility and interest rates depending on two CIR - factors. 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 arising in the time - discretization of a Markov - modulated Levy model. Options in this sequence are solved using an iteration method based on the Wiener - Hopf factorization. Typical shapes of the early exercise boundary are shown, and good agreement of option prices with prices calculated with the Longstaff - Schwartz method and Medvedev - Scaillet asymptotic method is demonstrated.

Keywords: Optimal stopping, American options, regime switching,stochastic volatility models, Heston model,stochastic interest rate, CIR process

JEL Classification: D81, C61, G31

Suggested Citation

Boyarchenko, Svetlana I. and Levendorskii, Sergei Z., American Options in the Heston Model With Stochastic Interest Rate (November 19, 2007). ; EFA 2008 Athens Meetings Paper. Available at SSRN: https://ssrn.com/abstract=1031282 or http://dx.doi.org/10.2139/ssrn.1031282

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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