A LIBOR Market Model 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 OIS curve and corresponding spreads with FRA rates for different tenors.

We consider stochastic-volatility dynamics and address the related caplet and swaption pricing problems. We conclude the article with an example of calibration to real market data.

An extended version of this article can be downloaded at: http://ssrn.com/abstract=1563685

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