Libor L(t, T) is one of the primary interest rate instruments in the capital markets, the other being Euribor. The term Libor will be used generically for all interest rates on fixed deposits. The Libor Market Model (LMM) is defined in the framework of quantum finance and leads to a key generalization: the Libors, for different future times, are imperfectly correlated. A major difference between a forward interest rates' model and the LMM lies in the fact that the LMM is calibrated directly from the observed market values for L(t, T). The short distance Wilson expansion of the Gaussian quantum field A(t, x) driving the Libors yields a derivation of the Libor drift term that incorporates imperfect correlations of the different Libors. The logarithm of Libor ϕ(t, x) is defined and leads to a quantum field theory of Libor. The Lagrangian and Feynman path integral are obtained for the log Libor quantum field ϕ(t, x).

Introduction

Interest rates can be modeled using either the zero coupon bonds B(t, T) or the simple interest Libor L(t, T). Both these approaches are, in principle, equivalent but are quite different from an empirical, computational, and analytical point of view.

One can take the view that there exists a single set of underlying forward interest rates f(t, x) that can be used for modeling both L(t, T) and B(t, T). The HJM approach, in fact, takes this view and the HJM's quantum finance generalization goes a long way in accurately modeling interest rate instruments.