An n-dimensional Markov-functional interest rate model

Linus Kaisajuntti and Joanne Kennedy

Abstract

ABSTRACT

This paper develops an n-dimensional Markov-functional interest rate model, ie, a model driven by an n-dimensional state process and constructed using Markov functional techniques. It is shown that this model is very similar to an n-factor LIBOR market model, thus allowing intuition from the LIBOR market model to be transferred to the Markov functional model. This generalizes the results of Bennett and Kennedy from one-dimensional to n-dimensional driving state processes. The model is suitable for pricing certain types of exotic interest rate derivative products, such as targeted accrual redemption notes, on LIBORs or constant maturity swap spreads. For these products, the n-dimensional Markov-functional model may be used as a benchmark model, allowing for powerful and flexible control of both correlations between different rates and skews/smiles in implied volatilities.