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Arbitrage and Viability in Securities Markets with Fixed Trading Costs

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  • Elyès Jouini
  • Hédi Kallal
  • Clotilde Napp

Abstract

This paper studies foundational issues in securities markets models with fixed costs of trading, i.e. transaction 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 price processes are martingales, conditional to any possible future event. This is a weaker condition than the absence of free lunches 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.

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Bibliographic Info

Paper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 99-033.

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Date of creation: Jul 1999
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Handle: RePEc:fth:nystfi:99-033

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Postal: U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126
Phone: (212) 998-0100
Web page: http://w4.stern.nyu.edu/finance/
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References

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  1. Andrew J. Morton & Stanley R. Pliska, 1995. "Optimal Portfolio Management With Fixed Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 5(4), pages 337-356.
  2. Dybvig, Philip H & Ross, Stephen A, 1986. " Tax Clienteles and Asset Pricing," Journal of Finance, American Finance Association, vol. 41(3), pages 751-62, July.
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  4. Jaksa Cvitanić & Ioannis Karatzas, 1996. "HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH-super-2," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 133-165.
  5. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short-Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232.
  6. Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Infinite Dimensional Case," Research Program in Finance Working Papers RPF-191, University of California at Berkeley.
  7. Sanford J Grossman & Guy Laroque, 2003. "Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods," Levine's Working Paper Archive 618897000000000803, David K. Levine.
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  10. Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86.
  11. Ross, Stephen A, 1987. "Arbitrage and Martingales with Taxation," Journal of Political Economy, University of Chicago Press, vol. 95(2), pages 371-93, April.
  12. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
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  14. Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478.
  15. Duffie, Darrell & Sun, Tong-sheng, 1990. "Transactions costs and portfolio choice in a discrete-continuous-time setting," Journal of Economic Dynamics and Control, Elsevier, vol. 14(1), pages 35-51, February.
  16. Prisman, Eliezer Z, 1986. " Valuation of Risky Assets in Arbitrage Free Economies with Frictions," Journal of Finance, American Finance Association, vol. 41(3), pages 545-57, July.
  17. Elyès Jouini & Hédi Kallal, 1999. "Viability and Equilibrium in Securities Markets with Frictions," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-036, New York University, Leonard N. Stern School of Business-.
  18. Jouini Elyes & Kallal Hedi, 1995. "Martingales and Arbitrage in Securities Markets with Transaction Costs," Journal of Economic Theory, Elsevier, vol. 66(1), pages 178-197, June.
  19. Kallal, Hedi & Jouini, Elyès, 1995. "Martingales and arbitrage in securities markets with transaction costs," Economics Papers from University Paris Dauphine 123456789/5630, Paris Dauphine University.
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  22. Magill, Michael J. P. & Constantinides, George M., 1976. "Portfolio selection with transactions costs," Journal of Economic Theory, Elsevier, vol. 13(2), pages 245-263, October.
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  24. Constantinides, George M, 1986. "Capital Market Equilibrium with Transaction Costs," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 842-62, August.
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  26. Duffie, Darrell & Huang, Chi-fu, 1986. "Multiperiod security markets with differential information : Martingales and resolution times," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 283-303, June.
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Cited by:
  1. Chambers, Robert G. & Quiggin, John C., 2002. "Resource Allocation And Asset Pricing," Working Papers 28571, University of Maryland, Department of Agricultural and Resource Economics.
  2. Napp, Clotilde, 2001. "Pricing issues with investment flows Applications to market models with frictions," Journal of Mathematical Economics, Elsevier, vol. 35(3), pages 383-408, June.
  3. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, HAL.

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