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
TypeArticle accepté pour publication ou publié
External document linkhttp://halshs.archives-ouvertes.fr/halshs-00176496/en/
Journal nameJournal of Financial and Quantitative Analysis
Cambridge University Press
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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 / KeywordsArbitrage; fixed costs; contingent claims pricing; interest rate models; long zero-coupon rates; Dybvig Ingersoll and Ross; Brennan and Schwartz; barrier models
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