Calibration of the Libor Market Model Using Correlations Implied by CMS Spread Options

This work discusses the calibration of instantaneous Libor correlations in the Libor market model. We extend existing calibration strategies by incorporation of spread option implied correlation information. The correlation structure implied by CMS spread options observed in the present-day's market motivates us to extend existing parameterizations of ratio correlations by a new three parameter approach. For the first time, this paper presents an extensive empirical study of different parameterizations and their capability of matching market correlations. We can show that our approach leads to stable calibrations and gives a satisfactory fit to the market. We conclude our investigation with a pricing of a callable swap on cms spread using the parameterizations compared before