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

45 Pages Posted: 2 Jun 2004

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Massimo Morini

Banca IMI; Bocconi University

Date Written: January 2005

Abstract

This work focuses on the swaptions automatic cascade calibration algorithm (CCA) for the LIBOR Market Model (LMM) first 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 different calibration cases leading to acceptable results. We analyze the characteristics of the configurations used and concentrate on the effects of different exogenous instantaneous historical or parametric correlation matrices.

We also investigate the influence 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 efficient than the previous version. Calibrated parameters are in general regular and financially satisfactory, as confirmed 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.

Keywords: Libor Market Model, swaptions, calibration, cascade calibration

JEL Classification: G13

Suggested Citation

Brigo, Damiano and Morini, Massimo, An Empirically Efficient Analytical Cascade Calibration of the Libor Market Model Based Only on Directly Quoted Swaptions Data (January 2005). Available at SSRN: https://ssrn.com/abstract=552581 or http://dx.doi.org/10.2139/ssrn.552581

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

Massimo Morini (Contact Author)

Banca IMI ( email )

Corso Matteotti 6
20121 Milano, 20100
Italy

Bocconi University ( email )

Via Sarfatti, 25
Milan, MI 20136
Italy

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