The Wandering of Corn

Preprint English OPEN
Salov, Valerii (2017)
  • Subject: Quantitative Finance - General Finance

Time and Sales of corn futures traded electronically on the CME Group Globex are studied. Theories of continuous prices turn upside down reality of intra-day trading. Prices and their increments are discrete and obey lattice probability distributions. A function for systematic evolution of futures trading volume is proposed. Dependence between sample skewness and kurtosis of waiting times does not support hypothesis of Weibull distribution. Kumaraswamy distribution is more suitable for waiting times. Relationships between trading volume and maximum profit strategies are presented. Frequencies of absolute b-increments are approximated by a Hurwitz Zeta distribution. Relative b-increments are non-Gaussian too. Dependence between b- and a-increments allows to interpret the sample variances of b-increments as a stochastic process. Mean sample variance of b-increments vs. a-increments is presented. The L1 distance and Log-likelihood statistics for independence between a- and b-increments are controversial. Corn price jumps remind of chain branching reactions. Bi-logarithmic plots of the empirical frequencies of extreme b-increments vs. ranks are presented. Corresponding distributions resemble snakes forked tongues. The maximum profit strategy is discussed as a measure of non-equilibrium.
  • References (54)
    54 references, page 1 of 6

    [1] Andreev, V., L., Nagorsky, A., A., Shapiro, Alexander, P. Modeling population of fish with two year life cycle and one time spawning. Problemy Kibernetiki, Edited by Lyapunov Alexei A., Issue 25, Moscow: Nauka, 1972, pp. 167 - 175 (in Russian).

    [2] Aoyama, Takashiro, Nakamura, Takashi. Multidimensional Polynomial Euler Products and Infinitely Divisible Distributions on Rd. Arxiv, Mathematics, Probability, Number Theory, June 20, 2013, pp. 1 - 21, abs/1204.4041.

    [4] Arnold, Vladimir, I. A.N. Kolmogorov and Natural Science. Uspehi Matematicheskih Nauk, Volume 59, No. 1, January - February 2004, pp. 25 - 44 (in Russian); and Russ. Math. Surv., 2004, Volume 59, pp. 27 - 46.

    [6] von Bertalanffy, Ludwig. Quantitative Laws in Metabolism and Growth, The Quarterly Review of Biology, Volume 32. No. 3, September 1957, pp. 217 - 231.

    [7] Black, Fischer, Scholes, Myron. The Pricing of Options and Corporate Liabilities. The Journal of Political Economy, Volume 81, May - June 1973, pp. 637 - 659.

    [8] Bochner, Salomon. Harmonic Analysis and the Theory of Probability. Mineola, New York: Dover Publications, Inc., 2005, an unbridged republication of the work originally published by the University of California Press, Berkeley and Los Angeles in 1955.

    [9] Bohr, Niels. On the Constitution of Atoms and Molecules, Part I, Philosophical Magazine, Series 6, Volume 26, No. 151, July 1913, pp. 1 - 24.

    [10] Bohr, Niels. The Structure of the Atom, Nobel Lecture, December 11, 1922, 1922/bohr-lecture.html.

    [11] de Broglie, Prince Louis-Victor Pierre Raymond. The Wave Nature of the Electron, Nobel Lecture, December 12, 1929, nobel_prizes/physics/laureates/1929/broglie-lecture.html.

    [12] Carr, Peter, Maden, Dilip, B. Option valuation using the fast Fourier transform, Journal of Computational Finance, Volume 2, No. 4, Summer 1999, pp. 61 - 73.

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