Journal Article

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

Brigo, Damiano, Morini, Massimo

2006

Overview

This article presents a new method for the analytical calibration of the LIBOR Market Model. We start from the swaptions cascade calibration algorithm (CCA) introduced by Brigo and Mercurio. The CCA is very fast, leads to the perfect recovery of market quotes, and induces a direct correspondence between market volatilities and model parameters. However, tests in the previous literature are affected by numerical problems. This leads us to perform first an analysis of the effects of different correlation structures on calibration, isolating key features that impact the regularity of the outputs, and hence detecting a range of cases leading to regular results. Then we study the link between the remaining irregularities and the use in calibration of artificial data computed via interpolation between market quotations, and introduce a new calibration algorithm. This algorithm, called Endogenous Interpolation CCA, maintains all positive characteristics of cascade calibration but is based only on directly quoted market data. Empirical results show this new algorithm to be robust and efficient, a remarkable improvement over the basic CCA. Regular and financially significant calibration outputs and diagnostic structures are now normally obtained across general market situations and model parameterizations. Finally, we use Monte Carlo simulation to investigate the reliability of the approximation underlying cascade calibration and consider the joint calibration including caps. [PUBLICATION ABSTRACT]

• Publisher: Pageant Media
• Subject: Algorithms / Calibration / Interpolation / LIBOR / Monte Carlo simulation / Studies / Swap arrangements