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Diffusion Approximations of the Geometric Markov Renewal Processes and Option Price Formulas

Anatoliy Swishchuk and M. Shafiqul Islam

International Journal of Stochastic Analysis, 2010, vol. 2010, 1-21


We consider the geometric Markov renewal processes as a model for a security market and study this processes in a diffusion approximation scheme. Weak convergence analysis and rates of convergence of ergodic geometric Markov renewal processes in diffusion scheme are presented. We present European call option pricing formulas in the case of ergodic, double-averaged, and merged diffusion geometric Markov renewal processes.

Date: 2010
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DOI: 10.1155/2010/347105

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