Abstracts

We see that the classical Hull and White formula with stochastic volatility can be decomposed into the Black-Scholes formula plus other terms. We calculate the decomposition using three different methods: classical Itô calculus, functional Itô calculus and Malliavin calculus. We notice that solving the problem using classical Itô calculus is equivalent to use the functional Itô calculus. All the three methods are applied in the case that the price follows a more generic stochastic differential equation than the ones studied in others papers. In addition, we give an expression to the derivative of the implied volatility.