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Bid-Ask Dynamic Pricing in Financial Markets with Transaction Costs and Liquidity Risk

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  • Jocelyne Bion-Nadal

Abstract

We introduce, in continuous time, an axiomatic approach to assign to any 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. Time consistency is a crucial property for dynamic pricing. Generalizing the result of Jouini and Kallal, we prove that the No Free Lunch condition for a time consistent dynamic pricing procedure (TCPP) is equivalent to the existence of an equivalent probability measure $R$ that transforms a process between the bid process and the ask process of any financial instrument into a martingale. Furthermore we prove that the ask price process associated with any financial instrument is then a $R$-supermartingale process which has a cadlag modification. Finally we show that time consistent dynamic pricing allows both to extend the dynamics of some reference assets and to be consistent with any observed bid ask spreads that one wants to take into account. It then provides new bounds reducing the bid ask spreads for the other financial instruments.

Suggested Citation

  • Jocelyne Bion-Nadal, 2007. "Bid-Ask Dynamic Pricing in Financial Markets with Transaction Costs and Liquidity Risk," Papers math/0703074, arXiv.org.
    • Handle: RePEc:arx:papers:math/0703074
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    References listed on IDEAS

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    Cited by:

    1. Jocelyne Bion-Nadal, 2008. "Time Consistent Dynamic Limit Order Books Calibrated on Options," Papers 0809.3824, arXiv.org.
    2. Marie-Amelie Morlais, 2008. "Reflected backward stochastic differential equations and a class of non linear dynamic pricing rule," Papers 0802.2172, arXiv.org, revised May 2008.

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