A universal lattice

When valuing derivative contracts with lattice methods, one often needs different lattice structures for different stochastic processes, different parameter values, or even different time intervals to obtain positive probabilities. In view of this stability problem, in this paper, we derive a trinomial lattice structure that can be universally applied to any diffusion process for any set of parameter values at any given time interval. It is particularly useful to the processes that cannot be transformed into constant diffusion. This lattice structure is unique in that it does not require branches to recombine but allows the lattice to freely evolve within the prespecified state space. This is in spirit similar to the implicit finite difference method. We demonstrate that this lattice model is easy to follow and program. The universal lattice is applied to time and state dependent processes that have recently become popular in pricing interest rate derivatives. Numerical examples are provided to demonstrate the mechanism of the model.