An Analysis of American Options Under Heston Stochastic Volatility and Jump-Diffusion Dynamics

Gerald Cheang, Carl Chiarella and Andrew Ziogas
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Gerald Cheang: Division of Banking and Finance, Nanyang Business School,Nanyang Technological University
Andrew Ziogas: Bank of Scotland Treasury, Australia

No 256, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square root process as used by Heston (1993), and by a Poisson jump process as introduced by Merton (1976). Probability arguments are invoked to find a representation of the solution in terms of expectations over the joint distribution of the underlying process. A combination of Fourier transform in the log stock price and Laplace transform in the volatility is then applied to find the transition probability density function of the underlying process. It turns out that the price is given by an integral dependent upon the early exercise surface, for which a corresponding integral equation is obtained. The solution generalises in an intuitive way the structure of the solution to the corresponding European option pricing problem in the case of a call option and constant interest rates obtained by Scott (1997).

Keywords: American options; stochastic volatility; jump-diffusion processes; Volterra integral equations; free boundary problem; method of lines (search for similar items in EconPapers)
JEL-codes: C61 D11 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2009-08-01
New Economics Papers: this item is included in nep-ore
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Citations: View citations in EconPapers (4)

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