BFS 2002

Contributed Talk

A general proof of the Dybvig-Ingersoll-Ross-Theorem: Long forward rates can never fall

Irene Klein, Friedrich Hubalek, Josef Teichmann

It is an interesting question to analyse the stochastic nature of long term rates in interest rate markets. In Dybvig-Ingersoll-Ross 1996 the authors show that long forward and zero coupon rates can never fall. In their proof they implicitly use an ``ergodicity'' assumption, which is economically reasonable, but does not hold in any arbitrage-free interest rate model. We prove without any additional assumption that long forward rates can never fall, if they exist.