Option Pricing under Stochastic Interest Rates

This paper considers the pricing problem of European options. We will generalize the jump-diffusion option pricing formula by incorporating stochastic interest rates. Under the hypothesis of underlying asset price being driven by a jump-diffusion process that is a kind of special renewal process discussed the option pricing when interest rate is random variable, the formula of European options for dividend paying securities is deduced. Hence the results in R.C.Merton are generalized.