  In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models
driven by fractional Brownian motions. By using support arguments we prove that
the resulting model is arbitrage free under proportional transaction costs in
the same spirit of Guasoni [Math. Finance 16 (2006) 569-582]. In particular, we
obtain a drift condition which is similar in nature to the classical HJM
no-arbitrage drift restriction. The second part of this paper deals with
consistency problems related to the fractional HJM dynamics. We give a fairly
complete characterization of finite-dimensional invariant manifolds for HJM
models with fractional Brownian motion by means of Nagumo-type conditions. As
an application, we investigate consistency of Nelson-Siegel family with respect
to Ho-Lee and Hull-White models. It turns out that similar to the Brownian case
such a family does not go well with the fractional HJM dynamics with
deterministic volatility. In fact, there is no nontrivial fractional interest
rate model consistent with the Nelson-Siegel family.
