An Accurate FFT-Based Algorithm for Bermudan Barrier Option Pricing

Deng Ding, Zuoqiu Weng, Jingya Zhao

Bank of Ningbo, Shenzhen Branch, Shenzhen, China.
Department of Mathematics, University of Macau, Macao, China.

DOI: 10.4236/iim.2012.43014                

Abstract

An efficient and accurate numerical method, which is called the CONV method, was proposed by Lord et al in [1] to price Bermudan options. In this paper, this method is applied to price Bermudan barrier options in which the monitored dates may be many times more than the exercise dates. The corresponding algorithm is presented to practical option pricing. Numerical experiments show that this algorithm works very well for different exponential Lévy asset models.

Keywords

Fast Fourier Transform (FFT); Bermudan Barrier Option; CONV Method.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	P. Carr, H. Geman, D. B. Madan and M. Yor, “The Fine Structure of Asset Returns: An Empirical Investigation,” Journal of Business, Vol. 75, No. 2, 2002, pp. 305-332. doi:10.1086/338705
[2]	R. Lord, F. Fang, F. Bervoets and C.W. Oosterlee, “A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options under Lévy Processes,” SIAM Journal on Scientific Computing, Vol. 30, No. 4, 2008, pp. 1678-1705. doi:10.1137/070683878
[3]	P. Carr and D. Madan, “Option Valuation Using the Fast Fourier Transform,” Journal of Computational Finanace, Vol. 2, No. 4, 1999, pp. 61-73.
[4]	R. Cont and P. Tankov, “Financial Modelling with Jump Processes,” Chapman & Hall/CRC Press, 2003. doi:10.1201/9780203485217
[5]	C. Dean, J. F. Lawless and G. E. Willmot, “A Mixed Poisson- Inverse-Gaussian Regression Model,” The Canadian Journal of Statistics /La Revue Canadienne de Statistique, Vol. 17, No. 2, 1989, pp. 171-181.
[6]	D. Ding and S. C. U, “An Accurate and Stable FFT- Based Method for Pricing Options under Exp-Levy Processes,” In: J. W. Z. Lu, et al., Eds., The Proceedings of ISCM II- EPMSC XII, American Institute of Physics, New York, 2010, pp. 741-746.
[7]	L. Feng and V. Linetsky, “Pricing Discretely Monitored Barrier Options and Defaultable Bonds in Lévy Process Models: A Fast Hilbert Transform Approach,” Mathematical Finance, Vol. 18, No. 3, 2008, pp. 337-384. doi:10.1111/j.1467-9965.2008.00338.x
[8]	F. Fang and C. W. Oosterlee, “Pricing Early-Exercise and Discrete Barrier Options by Fourier-Cosine Series Expansions,” Numerische Mathematik, Vol. 114, No. 1 2009, pp. 27-62. doi:10.1007/s00211-009-0252-4
[9]	D. Ding and S. C. U, “Efficient option pricing methods based on Fourier series expansions,” Journal of Mathematical Research & Exposition, Vol. 31, No. 1, 2011, pp. 12-22.
[10]	D. Ding, N. Huang and J. Zhao, “An Efficient Algorithm for Bermudan Barrier Option Pricing,” Applied Mathematics—A Journal of Chinese Universities, Series B, Vol. 27, No. 1, 2012, pp. 49-58. doi:10.1007/s11766-012-2516-5