Libor Market Model with Stochastic Basis - Calibration Using OIS Yield and Money Market Basis Spreads

Abstract

Usually a Libor Market model with a stochastic basis as specied for instance by Mercurio, F. (2009) lacks of a suitable calibration since there are not enough market quotes available. To this end we suggest to take a low parametric model which essentially is calibrated to the current OIS curve. Then, for the forwards we use a Libor Market model for which enough quoted instruments such as caps, swaptions, CMS or CMS spread options are available. The dependency of the OIS curve and the Libor model is given by the money market basis spread.

The idea for taking a low factor model for the OIS dynamic is presented in Mercurio, F. and Xie, Z. (2012). But they also propose to use a low factor model for the forwards. In this note we combine a low factor dynamic for the OIS zero coupon bonds with the framework presented in Mercurio, F. (2009) for a multi-curve Libor Market model by a somewhat dierent modelling approach.

We show how to obtain all model parameters and for the rst time an example of a calibration of a multi-curve Libor Market model using the current market quotes.

Keywords: OIS, zero bond dynamics, multi-curve, Libor Market model, forward, cap, swap, swaption, basis spread

JEL Classification: C00, C13, C51, C63