A Coherent Approach to Interest Rate Modelling
Dr Dorje Brody, Blackett Laboratory, Imperial College

The conditional variance representation for the state price density leads to a natural characterisation of the entire class of positive interest HJM models valid over all time horizons. Making use of this representation, we introduce here a special class of interest rate models called ''coherent term structures'', in terms of which all other admissible models can be built up in a tractable manner by linear superposition. Specifically, we derive simple analytic formulae for the bond price system, the volatility structure, the short rate, and the risk premium associated with an arbitrary admissible term structure model. Extensions to the foreign exchange market and general asset systems are also discussed.