Clotilde Napp () (DRM - Dauphine Recherches en Management - CNRS : UMR7088 - Université Paris Dauphine - Paris IX, CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique) Elyès Jouini () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX)
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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.
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Paper provided by HAL in its series Post-Print with number
halshs-00151556_v1.
Length: Date of creation: 2006 Date of revision: Publication status: Published, Journal of Financial and Quantitative Analysis, 2006, 41, 4, 889-913 Handle: RePEc:hal:journl:halshs-00151556_v1
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