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Stochastic asset price dynamics and volatility using a symmetric supply and demand price equation

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  • Caginalp, Carey
  • Caginalp, Gunduz

Abstract

A symmetric supply/demand model of price dynamics is developed and used to understand the relationship between price change and volatility. This differs from the classical approach in which the expected rate of price change and variance are assumed to be independent. The microeconomic and stochastic analysis leads to the conclusion that a particular measure of the marginal volatility has a minimum shortly before the expected log-price has an extremum. The maximum of the volatility occurs when prices are likely to change most rapidly, and the supply/demand imbalance is greatest. The great bubble and collapse of Bitcoin’s price serves as a test of this analysis. The volatility reached a minimum shortly prior to the peak of Bitcoin’s price in December 2018. The model is further developed under the assumption that supply and demand depend on the fundamental value of the asset. Thus the paper is a key step in understanding the issue of whether volatility highs and lows can forecast trading price tops and bottoms. The methodology can be extended beyond log-normal returns and is further compared with an empirical study of 40 sharp market boom/bust events studied by Sornette et. al. (2017).

Suggested Citation

  • Caginalp, Carey & Caginalp, Gunduz, 2019. "Stochastic asset price dynamics and volatility using a symmetric supply and demand price equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 807-824.
    • Handle: RePEc:eee:phsmap:v:523:y:2019:i:c:p:807-824
    DOI: 10.1016/j.physa.2019.02.049
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    References listed on IDEAS

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    1. Davis, Douglas D. & Holt, Charles a., 1993. "Experimental economics: Methods, problems and promise," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 8(2), pages 179-212.
    2. Shefrin, Hersh, 2008. "A Behavioral Approach to Asset Pricing," Elsevier Monographs, Elsevier, edition 2, number 9780123743565.
    3. Carey Caginalp & Gunduz Caginalp, 2018. "Asset Price Volatility and Price Extrema," Papers 1802.04774, arXiv.org, revised Jul 2018.
    4. Caginalp, Carey & Caginalp, Gunduz, 2018. "The quotient of normal random variables and application to asset price fat tails," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 457-471.
    5. Eloísa Díaz-Francés & Francisco Rubio, 2013. "On the existence of a normal approximation to the distribution of the ratio of two independent normal random variables," Statistical Papers, Springer, vol. 54(2), pages 309-323, May.
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    7. Smith, Vernon L & Suchanek, Gerry L & Williams, Arlington W, 1988. "Bubbles, Crashes, and Endogenous Expectations in Experimental Spot Asset Markets," Econometrica, Econometric Society, vol. 56(5), pages 1119-1151, September.
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    Cited by:

    1. Lu, Jin-Ray & Yang, Ya-Huei, 2021. "Option valuations and asset demands and supplies," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 49-64.
    2. Caginalp, Carey & Caginalp, Gunduz & Swigon, David, 2021. "Stochastic asset flow equations: Interdependence of trend and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    3. Caginalp, Carey & Caginalp, Gunduz, 2020. "Derivation of non-classical stochastic price dynamics equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    4. Carey Caginalp & Gunduz Caginalp, 2019. "Derivation of non-classical stochastic price dynamics equations," Papers 1908.01103, arXiv.org, revised Aug 2020.

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