Adaptive continuous time Markov chain approximation model to general jump-diffusions
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:||Jun 2011|
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"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, 2008. "Simulation-based Estimation of Contingent-claims Prices," Finance Working Papers 22473, East Asian Bureau of Economic Research.
- 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.
- Takamizawa, Hideyuki, 2006.
"Is Nonlinear Drift Implied by the Short-End of the Term Structure?,"
2006-08, Graduate School of Economics, Hitotsubashi University.
- 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.
- 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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- 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.
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