Arbitrage with fixed costs and interest rate models

In this paper, we start by considering market models with fixed costs; in such a context, we characterize the absence of arbitrage opportunity and we provide pricing rules. We then apply these results to extend some classical interest rate and option pricing models. In particular, we prove that the quite surprising result obtained by Dybvig-Ingersoll-Ross $\left( 1996\right) $, which asserts that, under the assumption of absence of arbitrage, long zero-coupon rates can never fall, is no longer true in models with fixed costs. Models where the long rate follows a diffusion process as in Brennan-Schwartz $\left( 1979\right) $ are no more to be rejected for arbitrage considerations.