Drift Approximations in a Forward-Rate-Based LIBOR Market Model

In a market model of forward interest rates, a specification of the volatility structure of the forward rates uniquely determines their instantaneous drifts via the no-arbitrage condition. The resulting drifts are state-dependent and are sufficiently complicated that an explicit solution to the forward rate stochastic differential equations cannot be obtained. The lack of an analytic solution could be a major obstacle when pricing derivatives using Monte Carlo if it implied that the market could only be accurately evolved using small time steps. In this paper we use a predictor-corrector method to approximate the solutions to the forward rate SDEs and demonstrate that the market can be accurately evolved as far as twenty years in one step.