A partial differential equation formulation is developed to value an european option under stochastic interest rate and local volatility. The partial differential equation is one dimensional under forward measure.The formulation follows the usual techniques based on replication or the martingale...

A one-dimensional partial differential-difference equation (pdde) under forward measure is developed to value European option under jump-diffusion, stochastic interest rate and local volatility. The corresponding forward Kolmogorov partial differential-difference equation for transition...

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...