LIBOR market models in practice

Abstract

In this paper, LIBOR market models with a number of factors ranging from 1 to 10 are studied. The emphasis throughout is on the application for term structure modeling and (exotic) securities pricing rather than on technical issues. The study falls into two parts. In the first part, the models are calibrated to cap and swaption prices for several major markets and it is observed - perhaps contrary to expectations - that the overall market fit is independent of the number of factors. Closer investigation shows that the number of factors affects the implicit calendar time dependence of the volatility function: models with a high number of factors allow a more stationary volatility function than do models with few factors. In the second part of the study, the implications for exotics pricing of the number of factors in the model are investigated. As expected in view of the findings regarding the time dependence of the volatility function, a very strong sensitivity of exotics prices to the number of factors is found. This finding has far-reaching implications for derivatives pricing in practice.