The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines

Carl Chiarella, Boda Kang, Gunter H. Meyer and Andrew Ziogas
Additional contact information
Gunter H. Meyer: School of Mathematics, Georgia Institute of Technology, Atlanta
Andrew Ziogas: Integral Energy, Australia

No 219, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston (1993), and by a Poisson jump process of the type originally introduced by Merton (1976). We develop a method of lines algorithm to evaluate the price as well as the delta and gamma of the option, thereby extending the method developed by Meyer (1998) for the case of jump-diffusion dynamics. The accuracy of the method is tested against two numerical methods that directly solve the integro-partial differential pricing equation. The first is an extension to the jump-diffusion situation of the componentwise splitting method of Ikonen & Toivanen (2007). The second method is a Crank-Nicolson scheme that is solved using projected successive over relaxation which is taken as the benchmark. The relative efficiency of these methods for computing the American call option price, delta, gamma and free boundary is analysed. If one seeks an algorithm that gives not only the price but also the delta and gamma to the same level of accuracy for a given computational effort then the method of lines seems to perform best amongst the methods considered.

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: 43 pages
Date: 2008-03-01
New Economics Papers: this item is included in nep-bec and nep-ore
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Citations: View citations in EconPapers (31)

Published as: Chiarella, C., Kang, B., Meyer, G. H. and Ziogas, A., 2009, "The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines", International Journal of Theoretical and Applied Finance, 12(3), 393-425.

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Related works:
Journal Article: THE EVALUATION OF AMERICAN OPTION PRICES UNDER STOCHASTIC VOLATILITY AND JUMP-DIFFUSION DYNAMICS USING THE METHOD OF LINES (2009)
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