On Single and Multiple Currency Multifactor LIBOR Market Models: Application to Currency Options

Werner Hrlimann

Abstract: In the mainstream Gaussian setting of log-normal forward rates, a comprehensive specification of single and multiple currency multifactor LIBOR market models is undertaken. It includes an in-depth presentation of important old and new results on correlation matrices. The evaluation of Greeks is done with the LRM algorithm. To illustrate, a Monte-Carlo simulation of European currency option prices and deltas for a cross currency multifactor LIBOR market model is tested against known analytical asymptotic expansion formulas. Concluding with a non-Gaussian copula outlook, we show the existence of single currency two-factor LIBOR market models of arbitrary dimension with arbitrary margins.

Keywords: LIBOR market model, forward rates, correlation matrix, Greeks, currency option, universal copula, linear circular copula