An efficient option pricing method based on Fourier-cosine expansions was presented by Fang and Oosterlee for European options in 2008, and later, this method was also used by them to price early-exercise options and barrier options respectively, in 2009. In this paper, this method is applied to price discretely American barrier options in which the monitored dates are 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 and efficiently for different exponential Lévy asset models.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
A D Andricopoulos, M Widdicks, P D Duck, P D Newton. Universal option valuation using quadrature methods, J Financ Econ, 2003, 67: 447–471.
O E Barndorff-Nielsen. Normal inverse Gaussian distributions and stochastic volatility modelling, Scand J Statist, 1997, 24(1): 1–13.
D S Bates. Jumps and stochastic volatility: exchange rate processes implicit in Deutsch mark options, Rev Financ Stud, 1996, 9: 69–107.
F Black, M Scholes. The pricing of options and corporate liabilities, J Polit Econ, 1973, 81(3): 637–654.
P Carr, H Geman, D B Madan, M Yor. The fine structure of asset returns: An empirical investigation, J Bus, 2002, 75(2): 305–332.
P Carr, D Madan. Option valuation using the fast Fourier transform, J Comput Financ, 1999, 2: 61–73.
R Cont, P Tankov. Financial Modelling with Jump Processes, Chapman & Hall/CRC Press, 2003.
C Dean, J F Lawless, G E Willmot. A mixed Poisson-Inverse-Gaussian regression model, Canad J Statist, 1989, 17(2): 171–181.
D Ding, S C U. Efficient option pricing methods based on Fourier series expansions, JMath Res Exposition, 2010, 31: 12–22.
F Fang, C W Oosterlee. A novel pricing method for European option based on Fourier-cosine series expansions, SIAM J Sci Comput, 2008, 31: 826–848.
F Fang, C W Oosterlee. Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions, Numer Math, 2009, 114: 27–62.
L Feng, V Linetsky. Pricing discretely monitored barrier options and defaultable bonds in Lévy process models: a fast Hilbert transform approach, Math Financ, 2008, 18: 337–384.
B Gao, J Huang, M Subrahmanyam. The valuation of American barrier options using the decomposition technique, J Econ Dyn Control, 2000, 24: 1783–1827.
S L Heston. A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev Financ Stud, 1993, 6: 327–343.
S G Kou. A jump-diffusion model for option pricing, Manage Sci, 2002, 48: 1086–1101.
R Lord, F Fang, F Bervoets, C W Oosterlee. A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes, SIAM J Sci Comput, 2008, 30: 1678–1705.
D B Madan, P Carr, E Chang. The variance gamma process and option pricing, Eur Financ Rev, 1998, 2: 79–105.
C R Merton. Option pricing when underlying stock returns are discontinuous. J Financ Econ, 1976, 3: 125–144.
The work was partially supported by the research grants (UL020/08-Y4/MAT/JXQ01/FST and MYRG136(Y1-L2)-FST11-DD) from University of Macau.
About this article
Cite this article
Ding, D., Huang, N. & Zhao, J. An efficient algorithm for Bermudan barrier option pricing. Appl. Math. J. Chin. Univ. 27, 49–58 (2012). https://doi.org/10.1007/s11766-012-2516-5
MR Subject Classification
- American barrier option
- Bermudan option
- Fourier transform
- Fourier-cosine expansion