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Arbitrage with Fixed Costs and Interest Rate Models

  • Elyès Jouini

    ()

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX)

  • Clotilde Napp

    (DRM - Dauphine Recherches en Management - CNRS : UMR7088 - Université Paris Dauphine - Paris IX)

In this paper, we study securities market models with fixed costs. We characterize the absence of arbitrage opportunities and we provide fair pricing rules. We then apply these results to extend some popular interest rate and option pricing models, which 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 ones. For instance, models where the long-term rate follows a diffusion process are arbitrage-free in the presence of fixed costs (including arbitrarily small ones). We also rationalize models with partially absorbing or reflecting barriers on the price processes. In particular, we propose a version of the Cox, Ingersoll, and Ross (1985) model which, as in 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-00176496.

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Date of creation: 01 Dec 2006
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Publication status: Published, Journal of Financial and Quantitative Analysis, 2006, 889-913
Handle: RePEc:hal:journl:halshs-00176496
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00176496/en/
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