LIBOR Market Models with Stochastic Basis

Abstract

We extend the LIBOR market model to accommodate the new market practice of using different forward and discount curves in the pricing of interest-rate derivatives. Our extension is based on modeling the joint evolution of forward rates belonging to the discount curve and corresponding spreads with FRA rates. We start by considering general stochastic-volatility dynamics and show how to address both the caplet and swaption pricing problems in general. We then consider specific examples, including a model for the simultaneous evolution of different rate and spread tenors. We conclude the article with an example of calibration to real market data. A reduced version of this article can be downloaded at: http://ssrn.com/abstract=1583081

Keywords: LIBOR market model, stochastic basis, forward curves, discount curve, OIS rates, FRAs, swaps, caps, swaptions, measure changes, stochastic volatility, multiple tenors, closed form formulas

JEL Classification: E45, G13