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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 761637, 17 pages
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.
- 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.
- R. C. Merton, “Option pricing when underlying stock returns are discontinuous,” Journal of Financial Economics, vol. 3, no. 1-2, pp. 125–144, 1976.
- R. Cont, “Empirical properties of asset returns: stylized facts and statistical issues,” Quantitative Finance, vol. 1, no. 2, pp. 223–236, 2001.
- R. Cont, J. da Fonseca, and V. Durrleman, “Stochastic models of implied volatility surfaces,” Economic Notes, vol. 31, no. 2, pp. 361–377, 2002.
- E. Eberlein and U. Keller, “Hyperbolic distributions in finance,” Bernoulli, vol. 1, no. 3, pp. 281–299, 1995.
- 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.
- 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.
- 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.
- 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.
- 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.
- S. G. Kou, “A jump-diffusion model for option pricing,” Management Science, vol. 48, no. 8, pp. 1086–1101, 2002.
- 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.
- J. R. Birge and V. Linetsky, Handbooks in Operations Research and Management Science, vol. 15, North-Holland, 2008.
- 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.
- T. W. Epps, Pricing Derivative Securities, World Scientific, Singapore, 2nd edition, 2007.
- 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.
- 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.
- 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.
- M. Schmelzle, “Option pricing formulae using Fourier transform: theory and application,” 2010, http://pfadintegral.com.
- 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.
- 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.