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
Boda Kang: School of Finance and Economics, University of Technology, Sydney, Australia
Gunter H. Meyer: School of Mathematics, Georgia Institute of Technology, Atlanta, USA
Andrew Ziogas: Integral Energy, Australia

International Journal of Theoretical and Applied Finance (IJTAF), 2009, vol. 12, issue 03, 393-425

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 [18], and by a Poisson jump process of the type originally introduced by Merton [25]. 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 [26] 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 and Toivanen [21]. The second method is a Crank-Nicolson scheme that is solved using projected successive over relaxation and which is taken as the benchmark for the price. 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)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (42)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219024909005270
Access to full text is restricted to subscribers

Related works:
Working Paper: The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines (2008)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:12:y:2009:i:03:n:s0219024909005270

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219024909005270

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().