Black-Scholes formulas without the normality assumption: Applications to stochastic volatility and stochastic interest rate

Abstract

We provide explicit, simple price formulas for the European options under stochastic volatility and stochastic interest rate. The formulas are as simple as the classical Black-Scholes formula. Moreover, the formulas do not require the normality of the returns. We do not need to know the distribution of the returns/price.