Arbitrage with fixed costs and interest rate models

Clotilde Napp (1, 2) , Elyès Jouini (3)

1 DRM - Dauphine Recherches en Management
2 CREST - Centre de Recherche en Économie et Statistique
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We study securities market models with fixed costs. We first characterize the absence of arbitrage opportunities and provide fair pricing rules. We then apply these results to extend some popular interest rate and option pricing models that present arbitrage opportunities in the absence of fixed costs. In particular, we prove that the quite striking result obtained by Dybvig, Ingersoll, and Ross (1996), 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, even arbitrarily small fixed costs. For instance, models in which the long-term rate follows a diffusion process are arbitrage-free in the presence of fixed costs (including arbitrarily small fixed costs). We also rationalize models with partially absorbing or reflecting barriers on the price processes. We propose a version of the Cox, Ingersoll, and Ross (1985) model which, consistent with Longstaff (1992), produces yield curves with realistic humps, but does not assume an absorbing barrier for the short-term rate. This is made possible by the presence of (even arbitrarily small) fixed costs.

Mots clés: interest rates; pricing; fixed costs; arbitrage

Domaines: Economies et finances; Gestion et management; Méthodes et statistiques

Clotilde Napp, Elyès Jouini. Arbitrage with fixed costs and interest rate models. Journal of Financial and Quantitative Analysis, 2006, 41 (4), pp.889-913. ⟨halshs-00151556⟩