An FFT-network for Lévy option pricing
This paper develops a simple network approach to American exotic option valuation under Lévy processes using the fast Fourier transform (FFT). The forward shooting grid (FSG) technique of the lattice approach is then generalized to expand the FFT-network to accommodate path-dependent variables. This network pricing approach is applicable to all Lévy processes for which the characteristic function is readily available. In other words, the log-value of the underlying asset can follow finite-activity or infinite-activity Lévy processes. With the powerful computation of FFT, the proposed network has a negligible additional computational burden compared to the binomial tree approach. The early exercise policy and option values in the continuation region are determined in a way very similar to that of the lattice approach. Numerical examples using American-style barrier, lookback, and Asian options demonstrate that the FFT-network is accurate and efficient.
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- Chung, San-Lin & Shih, Pai-Ta, 2009. "Static hedging and pricing American options," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 2140-2149, November.
- Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(02), pages 153-164, June.
- Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
- Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
- Wong, Hoi Ying & Lo, Yu Wai, 2009. "Option pricing with mean reversion and stochastic volatility," European Journal of Operational Research, Elsevier, vol. 197(1), pages 179-187, August.
- Hilliard, Jimmy E. & Schwartz, Adam, 2005. "Pricing European and American Derivatives under a Jump-Diffusion Process: A Bivariate Tree Approach," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(03), pages 671-691, September.
- Chung, San-Lin & Hung, Mao-Wei & Wang, Jr-Yan, 2010. "Tight bounds on American option prices," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 77-89, January.
- Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1689-1718, November.
- 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.
- Jérôme Barraquand & Thierry Pudet, 1996. "Pricing Of American Path-Dependent Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 17-51.
- Alfredo Ibáñez, 2003. "Robust Pricing of the American Put Option: A Note on Richardson Extrapolation and the Early Exercise Premium," Management Science, INFORMS, vol. 49(9), pages 1210-1228, September.
- Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
- Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA. Full references (including those not matched with items on IDEAS)
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