Calibration of LIBOR Market Model: Comparison between the Separated and the Approximate Approach

This paper empirically analyzes and compares two methods of calibration for the Libor Market Models, developed by Brace, Gatarek and Musiela (1997) using data on EUR swaptions and historical EUR yield curves. The first method of calibration proposed by Dariusz Gatarek is the separated approach, which gives good results but is computationally intensive. The second method of calibration – proposed by Ricardo Rebonato and Peter Jackel - uses an approximation for the instantaneous volatility and correlation functions of European swaptions in a forward rate based Brace-Gatarek-Musiela framework which enables us to calculate prices for swaptions without the need for Monte Carlo simulations. The method generates appropriate results in a fraction of a second. To this end we show that using an approximation for the volatility and correlation function can lead to an accurate calibration by optimizing the parameters of the two volatility and correlation functions.