Implementation of a One-Factor Markov-Functional Interest Rate Model

Abstract

The interest rate market has been expanding immensely for thirty years, both in term of volumes and diversity of traded contracts. The growing complexity of derivatives has implied a need for sophisticated models in order to price and hedge these products. Three main approaches can be distinguished in interest rates modeling. Short-rate models model the dynamics of the term structure of interest rates by specifying the dynamics of a single rate (the spot rate or the instantaneous spot rate) from which the whole term structure at any point in time can be calculated. The prices of derivatives in these models are quite involved functions of the underlying process which is being modeled. This fact makes these models difficult to calibrate. However the short rate process is easy to follow and hence implementation is straightforward.Unlike short rate models the class of Market Models is formulated in terms of market rates which are directly related to tradable assets. Thus they exhibit better calibration properties than short rate models. However they are high dimensional by construction and tedious to implement.In 1999, Hunt, Kennedy and Pelsser introduced the class of Markov-Functional Models (MFM) aiming at developing models which could match as many market prices as Market Models while maintaining the efficiency of short rate models in calculating derivative prices.After a general overview of the two dominant paradigms in section III, this report will focus on the class of Markov-functional models. Section IV presents the general framework. Then several issues related to the implementation of a one-factor MFM model are analyzed in section V. Finally we will display in section VI some numerical results of the simulations of this one-factor model.