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Price Functionals with Bid-Ask Spreads : An Axiomatic Approach

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  • Elyès Jouini

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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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Suggested Citation

  • Elyès Jouini, 1997. "Price Functionals with Bid-Ask Spreads : An Axiomatic Approach," Working Papers 97-05, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:97-05
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    References listed on IDEAS

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    2. Elyès Jouini, 2003. "Market imperfections , equilibrium and arbitrage," Post-Print halshs-00167131, HAL.
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    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.
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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. Elyégs Jouini & Hédi Kallal, 1995. "Arbitrage In Securities Markets With Short-Sales Constraints," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 197-232.
    12. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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    15. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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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. 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.
    3. repec:dau:papers:123456789/9322 is not listed on IDEAS
    4. Katsiaryna Kaval & Ilya Molchanov, 2005. "Link-save trading and pricing of contingent claims," Finance 0511017, EconWPA.
    5. Alet Roux & Tomasz Zastawniak, 2016. "Game options with gradual exercise and cancellation under proportional transaction costs," Papers 1612.02312, arXiv.org.
    6. Borglin, Anders & Flåm, Sjur, 2007. "Rationalizing Constrained Contingent Claims," Working Papers 2007:12, Lund University, Department of Economics.
    7. 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.
    8. Kaval, K. & Molchanov, I., 2006. "Link-save trading," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 710-728, September.
    9. Salvatore Federico & Paul Gassiat, 2012. "Viscosity characterization of the value function of an investment-consumption problem in presence of illiquid assets," Papers 1211.1286, arXiv.org.
    10. repec:spr:joptap:v:160:y:2014:i:3:d:10.1007_s10957-013-0372-y is not listed on IDEAS
    11. 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.
    12. Baojun Bian & 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, revised Oct 2014.
    13. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    14. 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.
    15. Aloisio Araujo & Alain Chateauneuf & José Faro, 2012. "Pricing rules and Arrow–Debreu ambiguous valuation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 1-35, January.
    16. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, HAL.
    17. repec:eee:jetheo:v:173:y:2018:i:c:p:257-288 is not listed on IDEAS

    More about this item

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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