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Arbitrage with Fixed Costs and Interest Rate Models

Jouini, Elyès; Napp, Clotilde (2006), Arbitrage with Fixed Costs and Interest Rate Models, Journal of Financial and Quantitative Analysis, 41, 4, p. 889-913. http://www.dx.doi.org/10.1017/S0022109000002684

Type
Article accepté pour publication ou publié
External document link
http://halshs.archives-ouvertes.fr/halshs-00176496/en/
Date
2006
Journal name
Journal of Financial and Quantitative Analysis
Volume
41
Number
4
Publisher
Cambridge University Press
Pages
889-913
Publication identifier
http://www.dx.doi.org/10.1017/S0022109000002684
Metadata
Show full item record
Author(s)
Jouini, Elyès
Napp, Clotilde cc
Abstract (EN)
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.
Subjects / Keywords
Arbitrage; fixed costs; contingent claims pricing; interest rate models; long zero-coupon rates; Dybvig Ingersoll and Ross; Brennan and Schwartz; barrier models
JEL
E43 - Interest Rates: Determination, Term Structure, and Effects

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