One-dimensional Markov-functional models driven by a non-Gaussian driver

Jaka Gogala and Joanne Kennedy

Abstract

The class of Markov-functional models (MFMs) provides a framework that can be used to define interest-rate models of finite dimension calibrated to any arbitrage-free formula for caplet or swaption prices. Because of their computational efficiency, one-factor MFMs are of particular interest. So far, the literature has focused on mod- els driven by a Gaussian process. The aim of this paper is to move away from this Gaussian assumption and to provide new algorithms that can be used to implement an MFM driven by a more general class of one-dimensional diffusion processes. We provide additional insight into the role of the driving process by presenting a simple copula-based criterion that can be used to distinguish between models. Finally, we offer further insight into the dynamics of one-dimensional MFMs by relating them to separable local-volatility Libor market models and demonstrate this with a practical example.