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Optimal Trading Strategies as Measures of Market Disequilibrium

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  • Valerii Salov

Abstract

For classification of the high frequency trading quantities, waiting times, price increments within and between sessions are referred to as the a-, b-, and c-increments. Statistics of the a-b-c-increments are computed for the Time & Sales records posted by the Chicago Mercantile Exchange Group for the futures traded on Globex. The Weibull, Kumaraswamy, Riemann and Hurwitz Zeta, parabolic, Zipf-Mandelbrot distributions are tested for the a- and b-increments. A discrete version of the Fisher-Tippett distribution is suggested for approximating the extreme b-increments. Kolmogorov and Uspenskii classification of stochastic, typical, and chaotic random sequences is reviewed with regard to the futures price limits. Non-parametric L1 and log-likelihood tests are applied to check dependencies between the a- and b-increments. The maximum profit strategies and optimal trading elements are suggested as measures of frequency and magnitude of the market offers and disequilibrium. Empirical cumulative distribution functions of optimal profits are reported. A few classical papers are reviewed with more details in order to trace the origin and foundation of modern finance.

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  • Valerii Salov, 2013. "Optimal Trading Strategies as Measures of Market Disequilibrium," Papers 1312.2004, arXiv.org.
    • Handle: RePEc:arx:papers:1312.2004
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    References listed on IDEAS

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    1. Alfonso Dufour & Robert F. Engle, 2000. "Time and the Price Impact of a Trade," Journal of Finance, American Finance Association, vol. 55(6), pages 2467-2498, December.
    2. Goodhart, Charles A. E. & O'Hara, Maureen, 1997. "High frequency data in financial markets: Issues and applications," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 73-114, June.
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    6. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Valerii Salov, 2015. "The Role of Time in Making Risky Decisions and the Function of Choice," Papers 1512.08792, arXiv.org.
    2. Valerii Salov, 2017. "The Wandering of Corn," Papers 1704.01179, arXiv.org.
    3. Valerii Salov, 2017. "Trading Strategies with Position Limits," Papers 1712.07649, arXiv.org.

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