On the Dynamics of the Forward Interest Rate Curve and the Evaluation of Interest Rate Derivatives and their Sensitivities

Abstract

We present an overview of in project developed new techniques in computing key quantities of financial markets. Our approach is generic in the sense that the techniques apply essentially in the general frame work of markets which are described by systems of stochastic differential equations. We exemplify our methods in the LIBOR market model which is a standard interest rate market model widely used in practice and has its name from the daily quoted London interbank offered rates. The LIBOR market model has been developed in recent years beyond the classical framework in the direction of incomplete market models (with stochastic volatility and with jumps). Particular challenges are the high dimensionality (up to 20–40 factors), the calibration, and related problems of derivative prices evaluation and computation of sensitivities. We show how advanced Monte-Carlo techniques can be combined with analytic results about transition densities in order to obtain highly efficient and accurate numerical schemes for computing some of the key quantities in financial markets, especially hedging parameters.