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http://dx.doi.org/10.7737/MSFE.2013.19.2.037

Valuation of European and American Option Prices Under the Levy Processes with a Markov Chain Approximation  

Han, Gyu-Sik (Division of Business Administration, Chonbuk National University)
Publication Information
Management Science and Financial Engineering / v.19, no.2, 2013 , pp. 37-42 More about this Journal
Abstract
This paper suggests a numerical method for valuation of European and American options under the two L$\acute{e}$vy Processes, Normal Inverse Gaussian Model and the Variance Gamma model. The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the existing numerical method, the lattice-based method.
Keywords
Markov Chain; Normal Inverse Gaussian model; Variance Gamma Model; European Option; American Option;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Amin, K., "Jump-diffusion Option Valuation in Discrete Time," Journal of Finance 48 (1993), 1833-1863.   DOI   ScienceOn
2 Barndorff-Nielsen, O. E., "Normal Inverse Gaussian Distribution and Stochastic Volatility Modelling," Scandinavian Journal of Statistics 24 (1997), 1-13.   DOI   ScienceOn
3 Black, F. and M. Scholes, "The Pricing of Options and Corporate Liabilities," Journal of Political Economy 81 (1973), 637-659.   DOI   ScienceOn
4 Carr, P., H. Geman, D. B. Madan, and M. Yor, "Stochastic Volatility for Levy Processes," Mathematical Finance 13 (2003), 345-382.   DOI   ScienceOn
5 Carr, P. and D. B. Madan, "Option Valuation using the fast Fourier Transform," Journal of Computational Finance 2 (1999), 61-73.   DOI
6 Cont, R. and E. Voltchkova, "Integro-Differential Equations for Option Prices in Exponential Levy Models," Finance Stochastics 9 (2005), 299-325.   DOI
7 Cox, J. C., S. A. Ross, and M. Rubinstein, "Option Pricing: A Simplified Approach," Journal of Financial Economics 3 (1979), 125-144.
8 Duan, J. C. and J.-G. Simonato, "American Option Pricing under GARCH by a Markov Chain Approximation," Journal of Economic Dynamics and Control 25 (2001), 1689-1718.   DOI   ScienceOn
9 Eberlein, E., U. Keller, and K. Prause, "New Insights into Smile, Mispricing and Value at Risk," Journal of Business 71 (1998), 371-406.   DOI   ScienceOn
10 Fu, M. C., S. B. Laprise, D. B. Madan, Y. SU, and R. WU, "Pricing American Options: A Comparison of Monte Carlo Simulation Approaches," Journal of Computational Finance 2 (2001), 62-73.
11 Geman, H., D. B. Madan, and M. Yor, "Time Changes for Levy Processes," Mathematical Finance 11 (2001), 79-96.   DOI   ScienceOn
12 Glasserman, P., Monte Carlo Methods in Financial Engineering, Springer, New York, 2003.
13 Han, G. S., "Valuation of American Option Prices Under the Double Exponential Jump Diffusion Model with a Markov Chain Approximation," Journal of the Korean Institute of Industrial Engineer 38 (2012), 249-253.   과학기술학회마을   DOI   ScienceOn
14 Madan, D. B. and E. Seneta, "The Variance Gamma (VG) Model for Share Market Returns," Journal of Business 63 (1990), 511-524.   DOI   ScienceOn
15 Hirsa, A. and D. B. Madan, "Pricing American Options under Variance Gamma," Journal of Computational Finance 7 (2004), 63-80.
16 Kellezi, E. and N. Webber, "Valuing Bermudan Options When Asset Returns Are Levy Processes," Quantitative Finance 4 (2004), 87-100.   DOI   ScienceOn
17 Kou, S. G., "A Jump-diffusion Model for Option Pricing," Management Science 48 (2002), 1086-1101.   DOI   ScienceOn
18 Madan, D. B. and F. Milne, "Option Pricing with VG Martingale Components," Mathematical Finance 1 (1991), 39-56.   DOI
19 Madan, D. B., P. Carr, and E. Chang, "The Variance Gamma Process and Option Pricing," European Finance Review 2 (1998), 79-105.   DOI   ScienceOn
20 Maller, R., D. H. Solomon, and A. Szimayer, "A Multinomial Approximation for American Option Prices in Levy Process Models," Mathematical Finance 16 (2006), 613-633.   DOI   ScienceOn
21 Matache, A.-M., P. A. Nitsche, and C. Schwab, "Wavelet Galerkin Pricing of American Options on Levy Driven Assets," Quantitative Finance 5 (2005), 403-424.   DOI   ScienceOn
22 Merton, R. C., "Option Pricing When the Underlying Process for Stock Returns is Discontinuous," Journal of Financial Economics 3 (1976), 124-144.
23 Mulinacci, S., "An Approximation of American Option Prices in a Jump-Diffusion Model," Stochastic Processes Application 62 (1996), 1-17.   DOI   ScienceOn
24 Simonato, J.-G., "Computing American Option Prices in the Lognormal Jump-diffusion Framework with a Markov Chain," Finance Research Letters 8 (2011), 220-226.   DOI   ScienceOn