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Price functionals with bid-ask spreads: an axiomatic approach

  • Jouini, Elyes

In Jouini and Kallal (1995a), the authors characterized the absence of arbitrage opportunities for contingent claims with cash delivery in the presence of bid-ask spreads. Other authors obtained similar results for a more general definition of the contingent claims but assuming some specific price processes and transaction costs rather than bid-ask spreads in general see for instance, Cvitanic and Karatzas, 1996). The main difference consists in the fact that the bid-ask ratio is constant in this last reference. This assumption does not permit to encompass situations where the prices are determined by the buying and selling limit orders or by a (resp. competitive) specialist (resp. market-makers). We derive in this paper some implications from the no-arbitrage assumption on the price functionals that generalizes all the previous results in a very general setting. Indeed, under some minimal assumptions on the price functional, we prove that the prices of the contingent claims are necessarily in some minimal interval. This result opens the way to many empirical analyses.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 34 (2000)
Issue (Month): 4 (December)
Pages: 547-558

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Handle: RePEc:eee:mateco:v:34:y:2000:i:4:p:547-558
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. 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.
  2. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
  3. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  4. 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-.
  5. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-62, April.
  6. 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.
  7. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
  8. Elyès Jouini, 2003. "Market imperfections, equilibrium and arbitrage," Finance 0312005, EconWPA.
  9. Koehl, Pierre-F. & Pham, Huyen, 2000. "Sublinear price functionals under portfolio constraints," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 339-351, April.
  10. Jouini, Elyès, 1997. "Market Imperfections , Equilibrium and Arbitrage," Economics Papers from University Paris Dauphine 123456789/1047, Paris Dauphine University.
  11. repec:fth:inseep:9647 is not listed on IDEAS
  12. 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.
  13. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  14. 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.
  15. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short-Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232.
  16. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  17. repec:fth:inseep:9513 is not listed on IDEAS
  18. Boyle, Phelim P & Vorst, Ton, 1992. " Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, vol. 47(1), pages 271-93, March.
  19. P, F, Koehl & H, Pham, 1997. "Sublinear Price Functionals under Portfolio Constraints," Working Papers 97-52, Centre de Recherche en Economie et Statistique.
  20. repec:fth:inseep:9514 is not listed on IDEAS
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