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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 [Jouini, E., Kallal, H., 1995. Martinagles and arbitrage in securities markets with transaction costs. Journal of Economic Theory 66 (1) 178-197], 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 amore general definition of the contingent claims but assuming some specific price processes and transaction costs rather than bid–ask spreadsin general (see for instance, Cvitanic and Karatzas [Cvitanic, J., Karatzas, I., 1996. Hedging andportfolio optimization under transaction costs: a martinangle approach. Mathematical Finance 6,133-166]). The main difference consists of the fact that the bid–ask ratio is constant in this lastreference. This assumption does not permit to encompass situations where the prices are determinedby the buying and selling limit orders or by a (resp. competitive) specialist (resp. market-makers).Wederive in this paper some implications from the no-arbitrage assumption on the price functionalsthat generalizes all the previous results in a very general setting. Indeed, under some minimalassumptions on the price functional, we prove that the prices of the contingent claims are necessarilyin some minimal interval. This result opens the way to many empirical analyses
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  • 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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    1. 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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    Cited by:

    1. Araujo, Aloisio & Chateauneuf, Alain & Faro, José Heleno, 2018. "Financial market structures revealed by pricing rules: Efficient complete markets are prevalent," Journal of Economic Theory, Elsevier, vol. 173(C), pages 257-288.
    2. repec:dau:papers:123456789/9322 is not listed on IDEAS
    3. Katsiaryna Kaval & Ilya Molchanov, 2005. "Link-save trading and pricing of contingent claims," Finance 0511017, University Library of Munich, Germany.
    4. Alet Roux & Tomasz Zastawniak, 2016. "Game options with gradual exercise and cancellation under proportional transaction costs," Papers 1612.02312, arXiv.org.
    5. 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.
    6. Bellini, Fabio & Koch-Medina, Pablo & Munari, Cosimo & Svindland, Gregor, 2021. "Law-invariant functionals that collapse to the mean," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 83-91.
    7. Kaval, K. & Molchanov, I., 2006. "Link-save trading," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 710-728, September.
    8. Salvatore Federico & Paul Gassiat, 2014. "Viscosity Characterization of the Value Function of an Investment-Consumption Problem in Presence of an Illiquid Asset," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 966-991, March.
    9. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.
    10. Aloisio Araujo & Alain Chateauneuf & José Heleno Faro & Bruno Holanda, 2019. "Updating pricing rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 335-361, September.
    11. Fabio Bellini & Pablo Koch-Medina & Cosimo Munari & Gregor Svindland, 2020. "Law-invariant functionals that collapse to the mean," Papers 2009.04144, arXiv.org, revised Jan 2021.
    12. Bruno Bouchard & Elyès Jouini, 2010. "Transaction Costs in Financial Models," Post-Print halshs-00703138, HAL.
    13. Marcello Basili & Alain Chateauneuf & Giuliano Antonio & Giuseppe Scianna, 2023. "A representation of Keynes's long-term expectation in financial markets," Working Papers hal-03999320, HAL.
    14. Alain Chateauneuf & Bernard Cornet, 2022. "Submodular financial markets with frictions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 721-744, April.
    15. Marcello Basili & Alain Chateauneuf & Giuseppe Scianna, 2019. "A consistent representation of Keynes’s long-term expectation in ?nancial market," Department of Economics University of Siena 808, Department of Economics, University of Siena.
    16. 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.
    17. 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.
    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. Fabio Bellini & Pablo Koch-Medina & Cosimo Munari & Gregor Svindland, 2018. "Law-invariant functionals on general spaces of random variables," Papers 1808.00821, arXiv.org, revised Jan 2021.
    20. Borglin, Anders & Flåm, Sjur, 2007. "Rationalizing Constrained Contingent Claims," Working Papers 2007:12, Lund University, Department of Economics.
    21. 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.
    22. Esmaeil Babaei, 2024. "Asset pricing and hedging in financial markets with fixed and proportional transaction costs," Annals of Finance, Springer, vol. 20(2), pages 259-275, June.
    23. 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.
    24. 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.
    25. 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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    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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