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
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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