Adaptive continuous time Markov chain approximation model to general jump-diffusions
AbstractWe 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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Bibliographic InfoPaper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 2011_16.
Date of creation: Jun 2011
Date of revision:
Markov Chains; Diffusion Approximation; Transition Density; Jump-Diffusion Approximation; Option Pricing;
Find related papers by JEL classification:
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- 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.
- Konstantinos Kalogeropoulos & Gareth O. Roberts & Petros Dellaportas, 2007.
"Inference for stochastic volatility models using time change transformations,"
- Kalogeropoulos, Konstantinos & Roberts, Gareth O. & Dellaportas, Petros, 2007. "Inference for stochastic volatility model using time change transformations," MPRA Paper 5697, University Library of Munich, Germany.
- Peter C.B.Phillips & Jun Yu, .
"Simulation-based Estimation of Contingent Claims Prices,"
CoFie-05-2008, Sim Kee Boon Institute for Financial Economics.
- 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.
- 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.
- 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.
- 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.
- Merton, Robert C., 1975.
"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
- 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.
- 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.
- Igor Halperin & Andrey Itkin, 2013. "USLV: Unspanned Stochastic Local Volatility Model," Papers 1301.4442, arXiv.org, revised Mar 2013.
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