McKean’s Method applied to American Call Options on Jump-Diffusion Processes
In this paper we derive the implicit integral equation for the price of an American call option in the case where the underlying asset follows a jump-diffusion process. We extend McKean's incomplete Fourier transform approach to solve the free boundary problem under Merton's framework, with the distribution for the jump size remaining unspecified. We show how our results are consistent with those of Gukhal (2001), who derived the same integral equation using the Geske-Johnson discretisation approach. The paper also derives some results concerning the limit for the free boundary at expiry, and presents an iterative numerical algorithm for solving the linked integral equation system for the American call's price and early exercise boundary. This scheme is applied to Merton's jump-diffusion model, where the jumps are log-normally distributed.
(This abstract was borrowed from another version of this item.)
To our knowledge, this item is not available for
download. To find whether it is available, there are three
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
|Date of creation:||01 Aug 2003|
|Date of revision:|
|Contact details of provider:|| Web page: http://comp-econ.org/|
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Mulinacci, Sabrina, 1996. "An approximation of American option prices in a jump-diffusion model," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 1-17, March.
- Carl Chiarella & Andrew Ziogas, 2002.
"Evaluation of American Strangles,"
Computing in Economics and Finance 2002
28, Society for Computational Economics.
- Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
- Amin, Kaushik I, 1993. " Jump Diffusion Option Valuation in Discrete Time," Journal of Finance, American Finance Association, vol. 48(5), pages 1833-63, December.
- Peter Carr & Robert Jarrow & Ravi Myneni, 1992. "Alternative Characterizations Of American Put Options," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 87-106.
- Ball, Clifford A & Torous, Walter N, 1985. " On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-73, March.
- Jarrow, Robert A & Rosenfeld, Eric R, 1984. "Jump Risks and the Intertemporal Capital Asset Pricing Model," The Journal of Business, University of Chicago Press, vol. 57(3), pages 337-51, July.
- S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
- Merton, Robert C., 1976.
"Option pricing when underlying stock returns are discontinuous,"
Journal of Financial Economics,
Elsevier, vol. 3(1-2), pages 125-144.
- Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Chandrasekhar Reddy Gukhal, 2001. "Analytical Valuation of American Options on Jump-Diffusion Processes," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 97-115.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-72.
- Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
- Carl Chiarella & Boda Kang & Gunter H. Meyer, 2014. "Introduction," World Scientific Book Chapters, in: The Numerical Solution of the American Option Pricing Problem Finite Difference and Transform Approaches, chapter 1, pages 1-2 World Scientific Publishing Co. Pte. Ltd..
When requesting a correction, please mention this item's handle: RePEc:sce:scecf3:39. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.