The lognormal distribution assumption for the term structure of interest is the most natural way to exclude negative spot and forward rates. However, imposing this assumption on the continuously compounded interest rate has a serious drawback: rates explode and expected rollover returns are...

The lognormal distribution assumption for the term structure of interest is the most natural way to exclude negative spot and forward rates ... The purpose of this paper is to show that the problem with lognormal models result from modelling the wrong rate, namely the continuously compounded...

A term structure model with lognormal type volatility structure is proposed. The Heath, Jarrow and Morton (HJM) framework, coupled with the theory of stochastic evolution equations in infinite dimensions, is used to show that the resulting rates are well defined (they do not explode) and remain...