Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions
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).
|Date of creation:||2011|
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- Kalogeropoulos, Konstantinos & Roberts, Gareth O. & Dellaportas, Petros, 2007.
"Inference for stochastic volatility model using time change transformations,"
5697, University Library of Munich, Germany.
- 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.
- Konstantinos Kalogeropoulos & Gareth O. Roberts & Petros Dellaportas, 2007. "Inference for stochastic volatility models using time change transformations," Papers 0711.1594, arXiv.org.
- S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
- Peter C. B. Phillips & Jun Yu, 2009. "Simulation-Based Estimation of Contingent-Claims Prices," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3669-3705, September.
- Peter C.B. Phillips & Jun Yu, 2007. "Simulation-based Estimation of Contingent-claims Prices," Cowles Foundation Discussion Papers 1596, Cowles Foundation for Research in Economics, Yale University.
- Peter C. B. Phillips & Jun Yu, 2008. "Simulation-based Estimation of Contingent-claims Prices," Finance Working Papers 22473, East Asian Bureau of Economic Research.
- 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.
- Takamizawa, Hideyuki, 2006. "Is Nonlinear Drift Implied by the Short-End of the Term Structure?," Discussion Papers 2006-08, Graduate School of Economics, Hitotsubashi University.
- 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.
- 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.
- John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
- 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.
- 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 637-654, May-June.
- 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.
- 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.
- 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.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
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