European option pricing when the interest rate is stochastic

In this paper, we investigate the European option pricing when the riskfree interest rate is stochastic. We consider two cases: (1)the riskfree rate follows a diffusion process and the underlying state process is a Markov chain; (2)the riskree rate follows a jump process. Riskfree interest rate is assumed to be observable but the state process is not. Filtering techniques will be employed to estimate the state process and the option pricing is calculated by simulation. Such approach also takes care of the volatility part of the asset price process.