Correlating Market Models

Abstract

One of the key features differentiating methods of calibrating the lognormal LIBOR Market Model (LMM) to observed at-the-money option prices is the way in which these methods handle correlation between forward rates of different maturities. On the basis of the Pedersen (1998) calibration algorithm, we pursue the question of whether there is sufficient information contained in swaption prices to calibrate correlation, and what this means for the pricing of exotic derivatives off a calibrated LMM.

After briefly summarising the calibration method, we review the different concepts of correlation relevant to the LMM. The potential inconsistency between historical and implied correlation is found not to be an issue. We analyse the sensitivity of swaption prices and the calibrated volatility levels to correlations, and also study the trade-off between fitting correlations and fitting a calendar-time dependence of volatility. Subsequently, we discuss the effects of calibration ambiguity on derivatives priced off the calibrated model.

Keywords: LIBOR Market Models, interest rate term structure, model calibration, swaptions, correlation, implied volatility

JEL Classification: G13, E43