An Empirically Efficient Analytical Cascade Calibration of the LIBOR Market Model Based Only on Directly Quoted Swaptions Data

Abstract

This work focuses on the swaptions automatic cascade calibration algorithm (CCA) for the LIBOR Market Model (LMM) flrst appeared in Brigo and Mercurio (2001). This method induces a direct analytical correspondence between market swaption volatilities and LMM parameters, and allows for a perfect recovery of market quoted swaption volatilities if a common industry swaptions approximation is used. We present explicitly an extension of the CCA to calibrate the entire swaption matrix rather than its upper triangular part. Then, while previous tests on earlier data showed the appearance of numerical problems, we present here difierent calibration cases leading to acceptable results. We analyze the characteristics of the conflgurations used and concentrate on the efiects of difierent exogenous instantaneous historical or parametric correlation matrices. We also investigate the in∞uence of manipulations in input swaptions data for missing quotes, and devise a new algorithm maintaining all the positive characteristics of the CCA while relying only on directly quoted market data. Empirical results on a larger range of market situations and instantaneous covariance assumptions show this algorithm to be more robust and e‐cient than the previous version. Calibrated ae parameters are in general regular and flnancially satisfactory, as conflrmed by the analysis of various diagnostics implied structures. Finally we Monte Carlo investigate the reliability of the underlying LMM swaption analytical approximation in the new context, and present some possibilities to include information coming from the semi-annual tenor cap market.