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

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  • Bion-Nadal, Jocelyne

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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  • 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.
    • Handle: RePEc:eee:mateco:v:45:y:2009:i:11:p:738-750
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    Cited by:

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    2. Dilip B. Madan & Yazid M. Sharaiha, 2015. "Option overlay strategies," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1175-1190, July.
    3. Dilip B. Madan & Wim Schoutens, 2019. "Conic asset pricing and the costs of price fluctuations," Annals of Finance, Springer, vol. 15(1), pages 29-58, March.
    4. Dilip B. Madan, 2016. "Benchmarking in two price financial markets," Annals of Finance, Springer, vol. 12(2), pages 201-219, May.
    5. Takuji Arai, 2015. "Good deal bounds with convex constraints," Papers 1506.00396, arXiv.org.
    6. Tomasz R. Bielecki & Igor Cialenco & Tao Chen, 2014. "Dynamic Conic Finance via Backward Stochastic Difference Equations," Papers 1412.6459, arXiv.org, revised Dec 2014.
    7. Mehdi Vazifedan & Qiji Jim Zhu, 2020. "No-Arbitrage Principle in Conic Finance," Risks, MDPI, vol. 8(2), pages 1-34, June.
    8. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2016. "A survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective," Papers 1603.09030, arXiv.org, revised Jan 2017.
    9. Dilip B. Madan, 2016. "Conic Portfolio Theory," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-42, May.
    10. Takuji Arai, 2016. "Good deal bounds with convex constraints: --- examples and proofs ---," Keio-IES Discussion Paper Series 2016-017, Institute for Economics Studies, Keio University.
    11. 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.
    12. Madan, Dilip B., 2014. "Modeling and monitoring risk acceptability in markets: The case of the credit default swap market," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 63-73.
    13. Grigorova Miryana, 2014. "Stochastic orderings with respect to a capacity and an application to a financial optimization problem," Statistics & Risk Modeling, De Gruyter, vol. 31(2), pages 1-31, June.
    14. Takuji Arai & Masaaki Fukasawa, 2011. "Convex risk measures for good deal bounds," Papers 1108.1273, arXiv.org.
    15. Dilip B Madan, 2016. "Marking to two-price markets," Journal of Asset Management, Palgrave Macmillan, vol. 17(2), pages 100-118, March.
    16. 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.
    17. Dilip B. Madan & Wim Schoutens & King Wang, 2020. "Bilateral multiple gamma returns: Their risks and rewards," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-27, March.
    18. Jocelyne Bion-Nadal & Giulia Di Nunno, 2011. "Extension theorems for linear operators on $L_\infty$ and application to price systems," Papers 1102.5501, arXiv.org.
    19. Karl F. Bann�r & Matthias Scherer, 2014. "On the calibration of distortion risk measures to bid-ask prices," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1217-1228, July.
    20. Takuji Arai, 2017. "Good Deal Bounds With Convex Constraints," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-15, March.

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