American Options in the Heston Model with Stochastic Interest Rate and Its Generalizations

Svetlana Boyarchenko and Sergei LevendorskiĬ

Applied Mathematical Finance, 2013, vol. 20, issue 1, 26-49

Abstract: We consider the Heston model with the stochastic interest rate of Cox--Ingersoll--Ross (CIR) type and more general models with stochastic volatility and interest rates depending on two CIR-factors; the price, volatility and interest rate may correlate. 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 L�vy 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.

Date: 2013
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DOI: 10.1080/1350486X.2012.655935

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