On the Calibration of the LIBOR Market Model

This thesis presents a study of LIBOR1 market model calibration. In particular, the study builds on the prevailing calibration methodologies in an attempt to find a method that simultaneously recovers implied volatility and forward rate correlations structures from market prices of plain vanilla options. In order to ensure that complex derivative pricing and hedging requirements are jointly addressed, the study extends the performance analysis of calibration methods from a static level of goodness-of-fit with market prices test, to a dynamic level of approximation to next period’s LIBOR dynamics when tested on a series of market prices. Among the methodologies considered, the results show that for caplets, full calibration results in least pricing error when tested on an intra-day pricing prediction, and generates a stable evolution of day-to-day implied volatility. For swaptions, analytic approximation provides better estimate on an intra-day pricing but Monte Carlo simulation with parametrized correlations matrix provides a stable evolution of volatility and correlation (or covariance). This approach for swaptions calibration outperforms the other methods used despite the modifications made in volatility and initial thetas 2 specifications. All together, the results suggest that the Monte Carlo method with parametrized correlations appear to be superior as it provides smooth evolution of covariance of forward rates that is desired in complex derivative pricing and hedging. 1LIBOR stands from London Interbank Offer Rate. LIBOR has become a standard term for the quoted interest rate at which a particular bank is willing to make a large wholesale deposit. 2Parameters for the correlations matrix based on Rebonato’s volatility specification expressed in spherical coordinates