Efficient Analytical Cascade Calibration of the LIBOR Market Model with Endogenous Interpolation

Abstract

The LIBOR Market Model (LMM) is rapidly becoming the industry standard approach for pricing interest rate derivatives like caps and swaptions. But while fast and exact calibration of model parameters to market cap quotes is possible, the problem is much more complicated for swaptions. The Cascade Calibration Algorithm (CCA) offers a solution, but implementing it can present serious numerical difficulties. Brigo and Morini explore how these can arise, and how they can be corrected by reducing the rank of the correlation matrix, for specific correlation structures. Numerical problems also arise when the data are not complete across maturities and swap lengths, which requires missing values to be introduced by interpolation. A new algorithm, the Endogenous Interpolation Cascade Calibration Algorithm, is presented to deal with this situation. The article shows that it is fast and accurate, and that it eliminates the numerical problems suffered by the CCA.