Term-Structure Models: a Review

Abstract

Introduction 1.1 Justification for Another Review of Interest-Rate Models The topic of term-structure modelling for derivatives pricing has been covered in recent years, at least in book form (see, eg, [Rebonato (1998)], [James and Webber (2000)], [Hughston (2000)], [Brigo and Mercurio (2001)]). One obvious justification for updating these works is that the modelling of interest rates is still rapidly evolving. There are, however, deeper reasons why a fresh examination of the current state of research in this area deserves attention. The first is that recently a qualitatively new dimension has been added to the modelling complexity, because of the appearance of pronounced and complex smiles in the implied volatility surfaces of caplets and swaptions. Sure enough, smiles of sorts were produced by some of the early modelling approaches (eg, by the [Hull and White (1993)] model), but these were at the time obtained as an 'afterthought', and by and large regarded as an unpleasant fea

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