Dual Swap and Swaption Formulae in the Normal and Lognormal Models

Abstract

When the Gaussian HJM model is recast in terms of simple forwards, it becomes dual to the LogNormal Forward model in the sense that for almost every formula in one model there is a similar formula in the other which can be obtained by simple transformation or substitution. INTRODUCTION The Gaussian Heath Jarrow Morton (HJM) (see references 2,3 and 4) and LogNormal Forward (see references 1,5 and 6) models are dual in the sense that for almost every formula in one model there is a similar formula in the other which can be obtained by simple transformation or substitution. That is important from both pedagogical and implementation points of view. A common problem in coming to grips with the LogNormal Forward model is understanding the role of the forward measures. But when the widely accepted Gaussian HJM model is recast in terms of simple forwards, it too, just like the lognormal model, is a play on forward measures. So intuition developed on the normal model, can be articulated to th..