An Improved Finite Difference Approach to Fitting the Initial Term Structure

This paper describes an alternative discretization strategy for mean-reverting models which permits the use of implicit finite difference methods along lines developed for explicit methods by Hull and White (1990a). This provides significant benefits in terms of stability, convergence, and flexibility. A technique for fitting the initial term structure is developed which is similar to that proposed by Uhrig and Walter (1996), but much more efficient computationally. The approach is illustrated with applications to three common single factor models and two factor stochastic volatility extensions of these models.