This thesis presents a study of LIBOR 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 (London Interbank Offer Rate) 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 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.
MSc in Finance
Finance and Financial Management | Portfolio and Security Analysis
LIM, Kian Guan
DEMELINDA, U Lagunzad.
On the Calibration of the Libor Market Model. (2007). Dissertations and Theses Collection (Open Access).
Available at: http://ink.library.smu.edu.sg/etd_coll/33