Correlation Analysis in the LIBOR and Swap Market Model

In the general framework that is offered by the market model, each LIBOR interest rate is a lognormal martingale under its own probability measure. The advantage is that the approach is consistent with the way cap, floor and swaption volatilities are quoted. The joint distribution of several LIBOR or swap rates under a common probability measure is somehow more complicated because it requires the specification of a drift term structure and the specification of a correlation term structure. In this paper, the correlation between the LIBORs is represented by a function of the LIBOR maturities. The form of this function is inspired by the stochastic string theory that was recently introduced in finance for the modelling of yield curves. The function is fitted to the volatilities of the LIBOR and swap rates so that it is consistent with market observations and does not rely on statistical analysis of any historical data.