Efficient Techniques for Simulation of Interest Rate Models Involving Non-Linear Stochastic Differential Equations

This paper examines methods to reduce systematic and random errors in simulations of interest rate models based on non-solvable, non-linear stochastic differential equations (SDEs). The paper illustrates how application of high-order Ito-Taylor discretization schemes in combination with appropriate variance reduction techniques can yield very significant improvements in speed and accuracy. Besides discussing and testing several traditional approaches to variance reduction, we consider the more recent techniques of Girsanov measure transformation and quasi-random sequences. Using the Cox, Ingersoll, and Ross square-root diffusion model as a specific example, we find that applying a secondor third-order discretization scheme in combination with a probability measure transformation and the antithetic variate method yields the best results overall. Although quite effective in problems of low dimension, quasi-random sequences suffer from certain fundamental problems that limit their usefulness in the applications considered here.