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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 651573, 11 pages
A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model
Institute of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang 315100, China
Received 30 September 2012; Revised 15 December 2012; Accepted 17 December 2012
Academic Editor: M. Ruiz Galan
Copyright © 2013 Jian Huang et al. 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. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economy, vol. 81, no. 3, pp. 637–654, 1973.
- R. Cont and P. Tankov, Financial Modelling with Jump Processes, Chapman & Hall/CRC Press, Boca Raton, Fla, USA, 2004.
- S. Heston, “A closed-form solution for options with stochastic volatility with applications to bond and currency options,” Reviews of Financial Studies, vol. 6, no. 2, pp. 327–343, 1993.
- J. Hull and A. White, “The pricing of options on assets with stochastic volatilities,” Journal of Finance, vol. 42, no. 2, pp. 281–300, 1987.
- R. C. Merton, “Option pricing when underlying stock return are discontinuous,” Journal of Financial Economics, vol. 3, no. 1-2, pp. 125–144, 1976.
- S. G. Kou, “A jump-diffusion model for option pricing,” Management Science, vol. 48, no. 8, pp. 1086–1101, 2002.
- K. Amin, “Jump diffusion option valuation in discrete time,” Journal of Finance, vol. 48, no. 5, pp. 1883–1863, 1993.
- X. L. Zhang, “Numerical analysis of American option pricing in a jump-diffusion model,” Mathematics of Operations Research, vol. 22, no. 3, pp. 668–690, 1997.
- R. Cont and E. Voltchkova, “A finite difference scheme for option pricing in jump diffusion and exponential Lévy models,” SIAM Journal on Numerical Analysis, vol. 43, no. 4, pp. 1596–1626, 2005.
- L. Andersen and J. Andreasen, “Jump-diffusion processes: volatility smile fitting and numerical methods for option pricing,” Review of Derivatives Research, vol. 4, no. 3, pp. 231–262, 2000.
- A. Almendral and C. W. Oosterlee, “Numerical valuation of options with jumps in the underlying,” Applied Numerical Mathematics, vol. 53, no. 1, pp. 1–18, 2005.
- Y. d'Halluin, P. A. Forsyth, and G. Labahn, “A penalty method for American options with jump diffusion processes,” Numerische Mathematik, vol. 97, no. 2, pp. 321–352, 2004.
- Y. d'Halluin, P. A. Forsyth, and K. R. Vetzal, “Robust numerical methods for contingent claims under jump diffusion processes,” IMA Journal of Numerical Analysis, vol. 25, no. 1, pp. 87–112, 2005.
- S. Salmi and J. Toivanen, “An iterative method for pricing American options under jump-diffusion models,” Applied Numerical Mathematics, vol. 61, no. 7, pp. 821–831, 2011.
- J. Toivanen, “Numerical valuation of European and American options under Kou's jump-diffusion model,” SIAM Journal on Scientific Computing, vol. 30, no. 4, pp. 1949–1970, 2008.
- J. Toivanen, “A high-order front-tracking finite difference method for pricing American options under jump-diffusion models,” Journal of Computational Finance, vol. 13, no. 3, pp. 61–79, 2010.
- K. Zhang and S. Wang, “Pricing options under jump diffusion processes with fitted finite volume method,” Applied Mathematics and Computation, vol. 201, no. 1-2, pp. 398–413, 2008.
- K. Zhang and S. Wang, “A computational scheme for options under jump diffusion processes,” International Journal of Numerical Analysis and Modeling, vol. 6, no. 1, pp. 110–123, 2009.
- P. Wilmott, J. Dewynne, and S. Howison, Option Pricing: Mathematical Models and Computation, Oxford Financial Press, Oxford, UK, 1993.
- Z. Cen and A. Le, “A robust and accurate finite difference method for a generalized Black-Scholes equation,” Journal of Computational and Applied Mathematics, vol. 235, no. 13, pp. 3728–2733, 2011.
- S. Wang, “A novel fitted finite volume method for the Black-Scholes equation governing option pricing,” IMA Journal of Numerical Analysis, vol. 24, no. 4, pp. 699–720, 2004.
- L. Angermann and S. Wang, “Convergence of a fitted finite volume method for the penalized Black-Scholes equation governing European and American option pricing,” Numerische Mathematik, vol. 106, no. 1, pp. 1–40, 2007.
- R. Zvan, P. A. Forsyth, and K. R. Vetzal, “Penalty methods for American options with stochastic volatility,” Journal of Computational and Applied Mathematics, vol. 91, no. 2, pp. 199–218, 1998.
- B. F. Nielsen, O. Skavhaug, and A. Tveito, “Penalty and front-fixing methods for the numerical solution of American option problems,” Journal of Computational Finance, vol. 5, pp. 69–97, 2002.
- Z. Cen, A. Le, and A. Xu, “A second-order difference scheme for the penalized Black-Scholes equation governing American put option pricing,” Computational Economics, vol. 40, no. 1, pp. 49–62, 2012.
- K. Zhang and S. Wang, “Convergence property of an interior penalty approach to pricing American option,” Journal of Industrial and Management Optimization, vol. 7, no. 2, pp. 435–447, 2011.
- R. Kangro and R. Nicolaides, “Far field boundary conditions for Black-Scholes equations,” SIAM Journal on Numerical Analysis, vol. 38, no. 4, pp. 1357–1368, 2000.
- D. B. Madan and E. Seneta, “The variance gamma (V.G.) model for share market returns,” Journal of Business, vol. 63, no. 4, pp. 511–524, 1990.
- 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, pp. 305–332, 2002.
- A. Almendral and C. W. Oosterlee, “On American options under the variance gamma process,” Applied Mathematical Finance, vol. 14, no. 2, pp. 131–152, 2007.
- D. B. Madan, P. Carr, and E. C. Chang, “The variance Gamma process and option pricing,” European Finance Review, vol. 2, no. 1, pp. 79–105, 1998.
- R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, USA, 1962.
- R. B. Kellogg and A. Tsan, “Analysis of some difference approximations for a singular perturbation problem without turning points,” Mathematics of Computation, vol. 32, no. 144, pp. 1025–1039, 1978.
- M. Giles and R. Carter, “Convergence analysis of Crank-Nicolson and Rannacher time marching,” Journal of Computational Finance, vol. 9, no. 4, pp. 89–112, 2006.
- A. Q. M. Khaliq, D. A. Voss, and K. Kazmi, “Adaptive -methods for pricing American options,” Journal of Computational and Applied Mathematics, vol. 222, no. 1, pp. 210–227, 2008.
- D. M. Pooley, K. R. Vetzal, and P. A. Forsyth, “Convergence remedies for non-smooth payoffs in option pricing,” Journal of Computational Finance, vol. 6, no. 4, pp. 25–40, 2003.
- S. Wang, X. Q. Yang, and K. L. Teo, “Power penalty method for a linear complementarity problem arising from American option valuation,” Journal of Optimization Theory and Applications, vol. 129, no. 2, pp. 227–254, 2006.