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

14 Pages Posted: 5 Feb 2013

See all articles by Joerg Kienitz

Joerg Kienitz

University of Wuppertal - Applied Mathematics; University of Cape Town (UCT); Quaternion Risk Management

Date Written: February 4, 2013

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 di erent 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

Suggested Citation

Kienitz, Joerg, Libor Market Model with Stochastic Basis - Calibration Using OIS Yield and Money Market Basis Spreads (February 4, 2013). Available at SSRN: https://ssrn.com/abstract=2211175 or http://dx.doi.org/10.2139/ssrn.2211175

Joerg Kienitz (Contact Author)

University of Wuppertal - Applied Mathematics ( email )

Gaußstraße 20
42097 Wuppertal
Germany

University of Cape Town (UCT) ( email )

Private Bag X3
Rondebosch, Western Cape 7701
South Africa

Quaternion Risk Management ( email )

54 Fitzwilliam Square North
Dublin, D02X308
Ireland

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