Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions
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 Scottish Institute for Research in Economics (SIRE) in its series SIRE Discussion Papers with number 2011-53.
Date of creation: 2011
Date of revision:
Markov Chains; Di ffusion Approximation; Transition Density; Jump-Diffusion; Approximation; Option Pricing;
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