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Price Functionals with Bid-Ask Spreads : An Axiomatic Approach

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  • Elyès Jouini

    (Crest)

Abstract

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.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 97-05.

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Date of creation: 1997
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Handle: RePEc:crs:wpaper:97-05

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References

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  1. 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.
  2. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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  4. Elyès Jouini, 2003. "Market imperfections, equilibrium and arbitrage," Finance 0312005, EconWPA.
  5. Koehl, Pierre-F. & Pham, Huyen, 2000. "Sublinear price functionals under portfolio constraints," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 339-351, April.
  6. Jouini, Elyès & Kallal, Hedi, 1999. "Viability and equilibrium in securities markets with frictions," Open Access publications from Université Paris-Dauphine urn:hdl:123456789/5603, Université Paris-Dauphine.
  7. 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.
  8. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  9. P, F, Koehl & H, Pham, 1997. "Sublinear Price Functionals under Portfolio Constraints," Working Papers 97-52, Centre de Recherche en Economie et Statistique.
  10. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
  11. 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.
  12. 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.
  13. repec:fth:inseep:9514 is not listed on IDEAS
  14. repec:fth:inseep:9647 is not listed on IDEAS
  15. 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.
  16. 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.
  17. 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.
  18. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short-Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232.
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Citations

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Cited by:
  1. Kaval, K. & Molchanov, I., 2006. "Link-save trading," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 710-728, September.
  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. Koehl, Pierre-F. & Pham, Huyen, 2000. "Sublinear price functionals under portfolio constraints," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 339-351, April.
  4. Tokarz, Krzysztof & Zastawniak, Tomasz, 2006. "American contingent claims under small proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 65-85, December.
  5. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer, vol. 49(1), pages 1-35, January.
  6. M A H Dempster & I V Evstigneev & M I Taksar, 2005. "Asset pricing and hedging in financial markets with transaction costs: an approach based on the von Neumann-Gale model," Working Papers 062005, University of Cambridge, Judge Business School, Centre for Financial Research.
  7. Katsiaryna Kaval & Ilya Molchanov, 2005. "Link-save trading and pricing of contingent claims," Finance 0511017, EconWPA.
  8. Deelstra, Griselda & Grasselli, Martino & Koehl, Pierre-Francois, 1999. "Conditional dominance criteria: definition and application to risk-management," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 295-306, December.
  9. Nan Wu & Harry Zheng, 2012. "Optimal Liquidation in a Finite Time Regime Switching Model with Permanent and Temporary Pricing Impact," Papers 1212.3145, arXiv.org.
  10. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
  11. Borglin, Anders & Flåm, Sjur, 2007. "Rationalizing Constrained Contingent Claims," Working Papers 2007:12, Lund University, Department of Economics.
  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.
  13. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.

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