Representation and Numerical Approximation of American Option Prices under Heston Stochastic Volatility Dynamics

Thomas Adolfsson, Carl Chiarella, Andrew Ziogas and Jonathan Ziveyi
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Thomas Adolfsson: Finance Discipline Group, UTS Business School, University of Technology Sydney
Andrew Ziogas: Lloyds Banking
Jonathan Ziveyi: Risk and Actuarial Studies, Australian School of Business, University of New South Wales

No 327, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: In this paper we consider the evaluation of American call options on dividend paying stocks in the case where the underlying asset price evolves according to Heston’s (1993) stochastic volatility model. We solve the Kolmogorov partial differential equation associated with the driving stochastic processes using a combination of Fourier and Laplace transforms and so obtain the joint transition probability density function for the underlying processes. We then use Duhamel’s principle to obtain the expression for the American option price, which depends upon the unknown early exercise surface. By evaluating the pricing equation along the free surface boundary, we obtain the corresponding integral equation for the early exercise surface. An algorithm is proposed for solving the integral equation system, based upon numerical integration techniques for Volterra integral equations. The method is used to explore the impact of stochastic volatility on the price and free boundary of American call options.

Keywords: American options; stochastic volatility; Volterra integral equations; free boundary problem (search for similar items in EconPapers)
JEL-codes: C61 D11 (search for similar items in EconPapers)
Pages: 86 pages
Date: 2013-03-01
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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