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Cerrato, Mario, Lo, Chia Chun and Skindilias, Konstantinos (2011) Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diffusions. Centre for EMEA Banking, Finance and Economics Working Paper Series, 2011 (28). pp. 1-22.
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 Kologorov-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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