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Viability and Equilibrium in Securities Markets with Frictions

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  • Elyès Jouini
  • Hédi Kallal

Abstract

In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium if there exist price-taking maximizing agents who are happy with their initial endowment, given the opportunity set, and hence for whom supply equals demand. This is equivalent to the existence of a positive lineaar pricing rule on the entirespace of contingent claims-an underlying frictionless linear pricing rule-that lies below the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free lunches-a generalization of opportunities of arbitrage. When a market for a nonmarketed contingent claim opens, a bid-ask price pair for this claim is said to be consistent if it is a bid-ask price pair in at least a viable economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also show that there exists a unique extended consistent sublinear pricing rule-the supremum of the underlying frictionless linear pricing rules-for which the original equilibrium does not collapse when a new market opens, regardless of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model, we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing rules. Copyright Blackwell Publishers Inc 1999.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Mathematical Finance.

Volume (Year): 9 (1999)
Issue (Month): 3 ()
Pages: 275-292

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Handle: RePEc:bla:mathfi:v:9:y:1999:i:3:p:275-292

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References

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  1. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
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  13. 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.
  14. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  15. 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.
  16. Freddy Delbaen & Walter Schachermayer, 1994. "Arbitrage And Free Lunch With Bounded Risk For Unbounded Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 343-348.
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  18. 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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Citations

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Cited by:
  1. 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.
  2. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, HAL.
  3. Elyès Jouini & Hédi Kallal & Clotilde Napp, 1999. "Arbitrage and Viability in Securities Markets with Fixed Trading Costs," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-033, New York University, Leonard N. Stern School of Business-.
  4. Elyès Jouini, 1997. "Price Functionals with Bid-Ask Spreads : An Axiomatic Approach," Working Papers 97-05, Centre de Recherche en Economie et Statistique.
  5. Elyès Jouini & Clotilde Napp, 2002. "Arbitrage pricing and equilibrium pricing : compatibility conditions," Post-Print halshs-00176423, HAL.
  6. Jouini, Elyès & Napp, Clotilde & Kallal, Hedi, 2001. "Arbitrage and viability in securities markets with fixed trading costs," Economics Papers from University Paris Dauphine 123456789/5593, Paris Dauphine University.
  7. Jouini, Elyès, 2001. "Arbitrage and control problems in finance: A presentation," Economics Papers from University Paris Dauphine 123456789/5590, Paris Dauphine University.
  8. M. Dempster & I. Evstigneev & M. Taksar, 2006. "Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model," Annals of Finance, Springer, vol. 2(4), pages 327-355, October.
  9. Elyès Jouini & Hédi Kallal, 1998. "Efficient Trading Strategies in the Presence of Market Frictions," Working Papers 98-31, Centre de Recherche en Economie et Statistique.
  10. Elyès Jouini, 2001. "Arbitrage and Control Problems in Finance. Presentation," Post-Print halshs-00167152, HAL.
  11. Cass, David & Siconolfi, Paolo & Villanacci, Antonio, 2001. "Generic regularity of competitive equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 61-76, September.
  12. Baccara, Mariagiovanna & Battauz, Anna & Ortu, Fulvio, 2006. "Effective securities in arbitrage-free markets with bid-ask spreads at liquidation: a linear programming characterization," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 55-79, January.

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