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 the existing calibration strategies by the incorporation of spread option implied correlation information. The correlation structure implied by constant maturity swap (CMS) spread options observed in the present-day market motivates us to extend the 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 to match 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 the pricing of a callable swap on CMS spread using the parameterizations compared before.