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...

The "Vorticity Redistribution Method" developed in this report is a numerical method to handle partial differential equations arising out of modeling diffusion processes. The redistribution method is essentially based on the evolution of integral invariants of a partial differential equation....

The drift or the mean-reversion level of short-rate models under jump-diffusion is derived to fit the initial term-structure of zero-coupon bond. In particular, the drift is obtained for Hull-White and Cox-Ingersoll-Ross short-rate models. The purpose of obtaining the drift is for the...

The nonsteady drift of the Cox-Ingersoll-Ross model is obtained by noticing that the affine term-structures for small volatility is a perturbation of the Hull-White affine term-structure. Fast mean reversion ensures that a first-order perturbation expansion is sufficient when the volatility is...

The regular perturbation approach to nonsteady drift of the Cox-Ingersoll-Ross model even under time-varying mean-reversion produces a closed system of higher-order forward-rate derivatives. This closure yields a second-order ordinary differential equation for the nonsteady drift