Displaced Diffusion Libor Market Model
Document ID: 2010-1638
Published on: 5th January 2010
Author: David Roseburgh
The Barrie & Hibbert iESG allows users to model the term structure of nominal interest rates using the Libor Market Model (LMM) which gives great scope for accurate calibration to derivative prices as observed in the market. However, when using this model in a market-consistent framework it is possible to observe cases of extremely high interest rates (exploding rates), which some ESG users find undesirable.
The Displaced Diffusion Libor Market Model is a common extension to the standard lognormal Libor Market Model, where the forward rate distribution is shifted by some constant. In this paper we’ll show that if we choose the displacement carefully, DDLMM is actually exactly equivalent to the Gaussian case of the ubiquitous Heath Jarrow Morton model, in which all continuously compounded rates are normally distributed- giving us a model which allows for extremely accurate calibration while reducing (or indeed eliminating) the occurrence of exploding rates.
