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Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk

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  • Bion-Nadal, Jocelyne
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    Abstract

    According to the classic no arbitrage theory of asset pricing, in a frictionless market a No Free Lunch dynamic price process associated with any essentially bounded asset is a martingale under an equivalent probability measure. However, real financial markets are not frictionless. We introduce an axiomatic approach of Time Consistent Pricing Procedure (TCPP), in a model free setting, to assign to every financial position a dynamic ask (resp. bid) price process. Taking into account both transaction costs and liquidity risk this leads to the convexity (resp. concavity) of the ask (resp. bid) price. We prove that the No Free Lunch condition for a TCPP is equivalent to the existence of an equivalent probability measure R that transforms a process between the bid price process and the ask price process of every financial instrument into a martingale. Furthermore we prove that the ask (resp. bid) price process associated with every financial instrument is then a R super-martingale (resp. R sub-martingale) which has a càdlàg version. The axiomatic of TCPP allows for the construction of pricing procedures extending the dynamics of reference assets and calibrated on option prices for a reference family of options. We characterize such TCPP in terms of their dual representation. Such TCPP provide new bounds compatible with the observed bid and ask prices for the reference options and reducing the bid ask spreads for the other financial instruments.

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    Bibliographic Info

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

    Volume (Year): 45 (2009)
    Issue (Month): 11 (December)
    Pages: 738-750

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    Handle: RePEc:eee:mateco:v:45:y:2009:i:11:p:738-750

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Dynamic price process Bid ask spreads Transaction costs Liquidity risk No-arbitrage assumption Dynamic risk measures;

    References

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    1. Föllmer Hans & Penner Irina, 2006. "Convex risk measures and the dynamics of their penalty functions," Statistics & Risk Modeling, De Gruyter, vol. 24(1/2006), pages 36, July.
    2. Jocelyne Bion-Nadal, 2008. "Time Consistent Dynamic Limit Order Books Calibrated on Options," Papers 0809.3824, arXiv.org.
    3. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Astic, Fabian & Touzi, Nizar, 2007. "No arbitrage conditions and liquidity," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 692-708, August.
    5. Jouini, Elyes, 2000. "Price functionals with bid-ask spreads: an axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 547-558, December.
    6. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
    7. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    8. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    9. Kabanov, Yu. M. & Stricker, Ch., 2001. "The Harrison-Pliska arbitrage pricing theorem under transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 185-196, April.
    10. Shige Peng, 2006. "Modelling Derivatives Pricing Mechanisms with Their Generating Functions," Papers math/0605599, arXiv.org.
    11. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    12. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, 04.
    13. Susanne Klöppel & Martin Schweizer, 2007. "Dynamic Indifference Valuation Via Convex Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 599-627.
    14. 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.
    15. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    16. Jocelyne Bion-Nadal, 2008. "Dynamic risk measures: Time consistency and risk measures from BMO martingales," Finance and Stochastics, Springer, vol. 12(2), pages 219-244, April.
    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. repec:fth:inseep:9513 is not listed on IDEAS
    19. Jeremy Staum, 2004. "Fundamental Theorems of Asset Pricing for Good Deal Bounds," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 141-161.
    20. Klöppel Susanne & Schweizer Martin, 2007. "Dynamic utility-based good deal bounds," Statistics & Risk Modeling, De Gruyter, vol. 25(4/2007), pages 25, October.
    21. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    22. 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.
    23. Bion-Nadal, Jocelyne, 2009. "Time consistent dynamic risk processes," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 633-654, February.
    24. Astic, Fabian & Touzi, Nizar, 2007. "No arbitrage conditions and liquidity," Economics Papers from University Paris Dauphine 123456789/13388, Paris Dauphine University.
    25. Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, vol. 5(2), pages 181-200.
    26. Tomas Björk & Irina Slinko, 2006. "Towards a General Theory of Good-Deal Bounds," Review of Finance, European Finance Association, vol. 10(2), pages 221-260.
    27. U. �etin & R. Jarrow & P. Protter & M. Warachka, 2006. "Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence," Review of Financial Studies, Society for Financial Studies, vol. 19(2), pages 493-529.
    28. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
    29. repec:wop:humbsf:1997-31 is not listed on IDEAS
    30. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276.
    31. Föllmer, Hans & Kramkov, D. O., 1997. "Optional decompositions under constraints," SFB 373 Discussion Papers 1997,31, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    32. 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.
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    Cited by:
    1. Ernst Eberlein & Dilip Madan & Martijn Pistorius & Wim Schoutens & Marc Yor, 2014. "Two price economies in continuous time," Annals of Finance, Springer, vol. 10(1), pages 71-100, February.
    2. Jocelyne Bion-Nadal & Giulia Nunno, 2013. "Dynamic no-good-deal pricing measures and extension theorems for linear operators on L ∞," Finance and Stochastics, Springer, vol. 17(3), pages 587-613, July.
    3. Takuji Arai & Masaaki Fukasawa, 2011. "Convex risk measures for good deal bounds," Papers 1108.1273, arXiv.org.

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