Arbitrage with Fixed Costs and Interest Rate Models

Elyès Jouini () and Clotilde Napp

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Abstract: 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.

Keywords: Arbitrage; fixed costs; contingent claims pricing; interest rate models; long zero-coupon rates; Dybvig Ingersoll and Ross; Brennan and Schwartz; barrier models (search for similar items in EconPapers)
Date: 2006-12-01
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00176496v1
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Published in Journal of Financial and Quantitative Analysis, 2006, 41 (4), pp.889-913. ⟨10.1017/S0022109000002684⟩

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Journal Article: Arbitrage with Fixed Costs and Interest Rate Models (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00176496

DOI: 10.1017/S0022109000002684

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