One-Dimensional Markov-Functional Models Driven by Non-Gaussian Markov Processes

Abstract

The class of Markov-functional models provide 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 Markov-functional models are of particular interest. So far the literature has been focused on models 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 a Markov-functional model 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 Markov-functional models by relating them to separable local-volatility LIBOR market models and demonstrate this with a practical example.