ABSTRACT
In the previous chapter we introduced the geometric Markov renewal processes (GMRP) as a model for a security market and we considered its approximations in the form of averaged, merged, and double averaged geometric Markov renewal processes. In this chapter we study the geometric Markov renewal processes in a diffusion approximation scheme. Weak convergence analysis and rates of convergence of ergodic geometric Markov renewal processes in diffusion schemes are presented. We present European call option pricing formulas in the case of ergodic, double averaged, and merged diffusion geometric Markov renewal processes.
