HJM Interest Rate Models with Fractional Brownian Motions

In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. We consider the term structure of interest rates as given by a stochastic partial differential equation driven by a cilindrical fractional white noise. We obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. By using support arguments we prove that the resulting model is arbitrage-free under proportional transaction costs.