Diffusion Approximations of the Geometric Markov Renewal Processes and Option Price Formulas
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2010-12-19
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Abstract
We consider the geometric Markov renewal processes as a model for a securitymarket and study this processes in a diffusion approximation scheme. Weak convergenceanalysis and rates of convergence of ergodic geometric Markov renewal processes in diffusionscheme are presented. We present European call option pricing formulas in the case ofergodic, double-averaged, and merged diffusion geometric Markov renewal processes.
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Anatoliy Swishchuk and M. Shafiqul Islam, “Diffusion Approximations of the Geometric Markov Renewal Processes and Option Price Formulas,” International Journal of Stochastic Analysis, vol. 2010, Article ID 347105, 21 pages, 2010. doi:10.1155/2010/347105