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

Abstract

This article 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 provide a theoretical tool for understanding the structure of standard Markov-functional models (MFMs) as well as comparisons with the LIBOR market model (LMM). In particular, it is shown that for ‘typical’ market data the model is close enough to the LMM to be able to calibrate using the LMM calibration set-up and machinery. This provides further information about the similarities (as well as some of the differences) between MFM and LMM. The parametric n-dimensional MFM may be used for products that require high-dimensional models for appropriate pricing and risk management. When compared with an n-factor LMM, it has the virtue of being (much) faster for certain types of products.