About this Journal Submit a Manuscript Table of Contents
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 761637, 17 pages
http://dx.doi.org/10.1155/2012/761637
Research Article

A Fast Fourier Transform Technique for Pricing European Options with Stochastic Volatility and Jump Risk

1School of Science, Xi'an Jiaotong University, Xi'an 710049, China
2School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
3Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA

Received 7 April 2011; Revised 15 October 2011; Accepted 31 October 2011

Academic Editor: M. D. S. Aliyu

Copyright © 2012 Su-mei Zhang and Li-he Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Black and M. S. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economy, vol. 81, no. 3, pp. 637–654, 1973.
  2. R. C. Merton, “Option pricing when underlying stock returns are discontinuous,” Journal of Financial Economics, vol. 3, no. 1-2, pp. 125–144, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. R. Cont, “Empirical properties of asset returns: stylized facts and statistical issues,” Quantitative Finance, vol. 1, no. 2, pp. 223–236, 2001. View at Publisher · View at Google Scholar
  4. R. Cont, J. da Fonseca, and V. Durrleman, “Stochastic models of implied volatility surfaces,” Economic Notes, vol. 31, no. 2, pp. 361–377, 2002. View at Publisher · View at Google Scholar · View at Scopus
  5. E. Eberlein and U. Keller, “Hyperbolic distributions in finance,” Bernoulli, vol. 1, no. 3, pp. 281–299, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. D. B. Madan, P. P. Carr, and E. C. Chang, “The variance gamma process and option pricing,” European Finance Review, vol. 2, no. 1, pp. 79–105, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. D. Duffie, J. Pan, and K. Singleton, “Transform analysis and asset pricing for affine jump-diffusions,” Econometrica, vol. 68, no. 6, pp. 1343–1376, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. L. H. Steven, “A closed-form solution for options with stochastic volatility with applications to bond and currency options,” Review of Financial Studies, vol. 6, no. 2, pp. 327–343, 1993. View at Publisher · View at Google Scholar
  9. D. S. Bates, “Jumps and stochastic volatility: exchange rate processes implicit in deutsche mark options,” Review of Financial Studies, vol. 9, no. 1, pp. 69–107, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. J. Keppo, X. Meng, S. Shive, and M. Sullivan, “Modelling and hedging options under stochastic pricing parameters,” in Proceedings of the Industrial and Operations Engineering, University of Michigan at Ann Arbor, 2003. View at Publisher · View at Google Scholar
  11. S. G. Kou, “A jump-diffusion model for option pricing,” Management Science, vol. 48, no. 8, pp. 1086–1101, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. S. G. Kou and H. Wang, “Option pricing under a double exponential jump diffusion model,” Management Science, vol. 50, no. 9, pp. 1178–1192, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. J. R. Birge and V. Linetsky, Handbooks in Operations Research and Management Science, vol. 15, North-Holland, 2008.
  14. G. Bakshi, C. Cao, and Z. Chen, “Pricing and hedging long-term options,” Journal of Econometrics, vol. 94, no. 1-2, pp. 277–318, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. T. W. Epps, Pricing Derivative Securities, World Scientific, Singapore, 2nd edition, 2007.
  16. P. P. Carr and D. B. Madan, “Option valuation using the fast Fourier transform,” Journal of Computational Finance, vol. 2, no. 4, pp. 61–73, 1999.
  17. P. P. Carr and L. Wu, “Time-changed Lévy processes and option pricing,” Journal of Financial Economics, vol. 71, no. 1, pp. 113–141, 2004. View at Publisher · View at Google Scholar · View at Scopus
  18. T. R. Hurd and Z. Zhou, “A Fourier transform method for spread option pricing,” SIAM Journal on Financial Mathematics, vol. 1, pp. 142–157, 2010. View at Publisher · View at Google Scholar
  19. M. Schmelzle, “Option pricing formulae using Fourier transform: theory and application,” 2010, http://pfadintegral.com.
  20. V. Naik and M. Lee, “General equilibrium pricing of options on the market portfolio with discontinuous returns,” Review of Financial Studies, vol. 3, no. 4, pp. 493–521, 1990. View at Publisher · View at Google Scholar
  21. A. R. Hall and A. Inoue, “The large sample behaviour of the generalized method of moments estimator in misspecified models,” Journal of Econometrics, vol. 114, no. 2, pp. 361–394, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus