Arbitrage and Viability in Securities Markets with Fixed Trading Costs

Posted: 15 Jul 2006

See all articles by Elyes Jouini

Elyes Jouini

Univ. Paris Dauphine - CEREMADE

Hedi Kallal

Salomon Smith Barney, Inc.

Clotilde Napp

CNRS and Université Paris-Dauphine ; IZA

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Abstract

This paper studies foundational issues in securities markets models with fixed costs of trading, i.e. transactions costs that are bounded regardless of the transaction size, such as fixed brokerage fees, investment taxes, operational, and processing costs or opportunity costs. We show that the absence of free lunches in such models is equivalent to the existence of a family of absolutely continuous probability measures for which the normalized securities price processes are martingales. This is a weaker condition than the absence of free lunch in frictionless models, which is equivalent to the existence of an equivalent martingale measure. We also show that the only arbitrage-free pricing rules on the set of attainable contingent claims are those that are equal to the sum of an expected value with respect to any absolutely continuous martingale measure and of a bounded fixed cost functional. Moreover, these pricing rules are the only ones to be viable as models of economic equilibrium.

Keywords: Arbitrage, Fixed costs, Absolutely continuous Martingale measure, Contingent claims pricing

Suggested Citation

Jouini, Elyes and Kallal, Hedi and Napp, Clotilde, Arbitrage and Viability in Securities Markets with Fixed Trading Costs. Journal of Mathematical Economics, Vol. 35, pp. 197-221, 2001, Available at SSRN: https://ssrn.com/abstract=915376

Elyes Jouini (Contact Author)

Univ. Paris Dauphine - CEREMADE ( email )

Place du Marechal de Lattre de Tassigny
Paris Cedex 16, 75775
France
+ 33 1 44 05 46 75 (Phone)
+ 33 1 44 05 45 99 (Fax)

Hedi Kallal

Salomon Smith Barney, Inc.

New York, NY 10013
United States

Clotilde Napp

CNRS and Université Paris-Dauphine ( email )

Place de Lattre de Tassigny
Paris, 75775
France

IZA ( email )

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