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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.

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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. 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.
  2. P, F, Koehl & H, Pham, 1997. "Sublinear Price Functionals under Portfolio Constraints," Working Papers 97-52, Centre de Recherche en Economie et Statistique.
  3. 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.
  4. repec:fth:inseep:9513 is not listed on IDEAS
  5. Elyès Jouini, 2003. "Market imperfections , equilibrium and arbitrage," Post-Print halshs-00167131, HAL.
  6. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short-Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232.
  7. 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.
  8. repec:fth:inseep:9514 is not listed on IDEAS
  9. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
  10. Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of security market data for models of dynamic economies," Discussion Paper / Institute for Empirical Macroeconomics 29, Federal Reserve Bank of Minneapolis.
  11. Elyès Jouini & Hédi Kallal, 1999. "Viability and Equilibrium in Securities Markets with Frictions," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 275-292.
  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. Leland, Hayne E, 1985. " Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
  14. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  15. 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.
  16. repec:fth:inseep:9647 is not listed on IDEAS
  17. 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.
  18. Koehl, Pierre-F. & Pham, Huyen, 2000. "Sublinear price functionals under portfolio constraints," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 339-351, April.
  19. Jouini, Elyès, 1997. "Market Imperfections , Equilibrium and Arbitrage," Economics Papers from University Paris Dauphine 123456789/1047, Paris Dauphine University.
  20. 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.
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Citations

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Cited by:
  1. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, HAL.
  2. 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.
  3. 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.
  4. Koehl, Pierre-F. & Pham, Huyen, 2000. "Sublinear price functionals under portfolio constraints," Journal of Mathematical Economics, Elsevier, vol. 33(3), pages 339-351, April.
  5. 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.
  6. Kaval, K. & Molchanov, I., 2006. "Link-save trading," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 710-728, September.
  7. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
  8. 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.
  9. Bosi, Gianni & Zuanon, Magali, 2001. "Existence of price functionals with bid-ask spreads on the space of all integrable contingent claims," Economics Papers from University Paris Dauphine 123456789/9322, Paris Dauphine University.
  10. 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.
  11. Katsiaryna Kaval & Ilya Molchanov, 2005. "Link-save trading and pricing of contingent claims," Finance 0511017, EconWPA.
  12. Borglin, Anders & Flåm, Sjur, 2007. "Rationalizing Constrained Contingent Claims," Working Papers 2007:12, Lund University, Department of Economics.
  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.
  14. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer, vol. 49(1), pages 1-35, January.

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