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Patience vs. impatience of traders: Formation of the value-at-price distribution through competition for liquidity

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  • Peter Lerner

    (SciTech Analytical Services, LLC Woodland Drive, State College, PA 16803, United States)

Abstract

The ability to postpone one's execution in the market without penalty in search of a better price is an important strategic advantage in high-frequency trading. To elucidate competition between traders one has to formulate to a quantitative theory of formation of the execution price from market expectations and quotes. Equilibrium theory was provided in 2005 by Foucault, Kadan and Kandel. I derive an asymptotic distribution of the bids/offers as a function of the ratio of patient and impatient traders using the dynamic version of the Foucault, Kadan and Kandel limit order book (LOB) model. Our version of the LOB model allows stylized, but sufficiently realistic representation of the trading markets. In particular, dynamic LOB allows simulation of the distribution of execution times and spreads from high-frequency quotes. Significant analytic progress is made toward framing of short-term trading as competition for immediacy of execution between traders under imperfect information. The results are qualitatively compared with empirical volume-at-price distribution of highly liquid stocks.

Suggested Citation

  • Peter Lerner, 2015. "Patience vs. impatience of traders: Formation of the value-at-price distribution through competition for liquidity," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(03), pages 1-30.
    • Handle: RePEc:wsi:ijfexx:v:02:y:2015:i:03:n:s2424786315500292
    DOI: 10.1142/S2424786315500292
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    References listed on IDEAS

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    1. Didier SORNETTE & Susanne VON DER BECKE, 2011. "Crashes and High Frequency Trading," Swiss Finance Institute Research Paper Series 11-64, Swiss Finance Institute.
    2. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    3. Didier SORNETTE & Susanne VON DER BECKE, 2011. "Crashes and High Frequency Trading," Swiss Finance Institute Research Paper Series 11-63, Swiss Finance Institute.
    4. Johannes A. Skjeltorp & Elvira Sojli & Wing Wah Tham, 2012. "Identifying cross-sided liquidity externalities," Working Paper 2012/20, Norges Bank.
    5. de Jong,Frank & Rindi,Barbara, 2009. "The Microstructure of Financial Markets," Cambridge Books, Cambridge University Press, number 9780521867849, September.
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    Cited by:

    1. Peter B. Lerner, 2022. "Fourier Integral Operator Model of Market Liquidity: The Chinese Experience 2009–2010," Mathematics, MDPI, vol. 10(14), pages 1-25, July.
    2. P. B. Lerner, 2020. "Dual State-Space Model of Market Liquidity: The Chinese Experience 2009-2010," Papers 2004.06200, arXiv.org, revised May 2020.

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    More about this item

    Keywords

    Limit order book; Foucault; Kadan and Kandel model; bid-ask spread; market microstructure; G14; G12; C63;
    All these keywords.

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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