A Parametric n-Dimensional Markov-Functional Model in the Terminal Measure

Abstract

This paper develops and tests an n-dimensional Markov-functional interest rate model in the terminal measure based on parametric functional forms of exponential type. The parametric functional forms enable analytical expressions for forward discount bonds and forward LIBORs at all times and allows for calibration of the model to caplet prices given by a displaced diffusion Black model. The analytical expressions of the model provides a theoretical tool for understanding the structure of standard Markov-functional models as well as comparisons with the LIBOR market model.

In particular it is shown that for 'typical' market data the model is close enough to the LIBOR market model to be able to calibrate using the LIBOR market model calibration setup and machinery. This provides further information about the similarities (as well as some of the differences) between Markov-functional and LIBOR market models.

The parametric n-dimensional Markov-functional model may be used for products that require high-dimensional models for appropriate pricing and risk management. Compared with an n-factor LIBOR market model it has the virtue of being (much) faster for certain types of products.

Keywords: Interest rate derivatives, Markov-functional models, LIBOR market models, multi-dimensional, terminal measure