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Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

  • Cerrato, Mario
  • Lo, Chia Chun
  • Skindilias, Konstantinos
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    We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

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    Paper provided by Scottish Institute for Research in Economics (SIRE) in its series SIRE Discussion Papers with number 2011-53.

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    Date of creation: 2011
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    Handle: RePEc:edn:sirdps:286
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    1. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    2. Osnat Stramer & Matthew Bognar & Paul Schneider, 2010. "Bayesian Inference for Discretely Sampled Markov Processes with Closed-Form Likelihood Expansions," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(4), pages 450-480, Fall.
    3. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
    4. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    5. Konstantinos Kalogeropoulos & Gareth O. Roberts & Petros Dellaportas, 2010. "Inference for stochastic volatility models using time change transformations," LSE Research Online Documents on Economics 31421, London School of Economics and Political Science, LSE Library.
    6. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    7. Peter C. B. Phillips & Jun Yu, 2008. "Simulation-based Estimation of Contingent-claims Prices," Finance Working Papers 22473, East Asian Bureau of Economic Research.
    8. Hideyuki Takamizawa, 2008. "Is Nonlinear Drift Implied by the Short End of the Term Structure?," Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 311-346, January.
    9. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    10. 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.
    11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    12. Erik Lindström, 2007. "Estimating parameters in diffusion processes using an approximate maximum likelihood approach," Annals of Operations Research, Springer, vol. 151(1), pages 269-288, April.
    13. Bakshi, Gurdip & Ju, Nengjiu & Ou-Yang, Hui, 2006. "Estimation of continuous-time models with an application to equity volatility dynamics," Journal of Financial Economics, Elsevier, vol. 82(1), pages 227-249, October.
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