The forward Kolmogorov ( Fokker-Planck ) partial differential equation for the transition density under forward measure is developed to value european option under stochastic interest rate and local volatility. The advantage of this approach is that the density needs to be computed just once out...

European option under local volatility and Cox-Ingersoll-Ross model of short rate is computed from one-dimensional partial differential equations: the Black-Scholes equation for option price and the forward Kolmogorov equation for probability transition density. Both the computations are...