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Stochastic asset flow equations: Interdependence of trend and volatility

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  • Caginalp, Carey
  • Caginalp, Gunduz
  • Swigon, David

Abstract

The complex interaction between the volatility and the price trend is examined. We model stochastic asset prices using the asset flow model with randomness arising directly from supply and demand. We show that the volatility is smallest at the extrema of the expected logarithm of the price. Linearizing the stochastic differential equation (SDE) about equilibrium, we obtain an exact relation for the autocovariance function, and relate it to the (3 by 3) Jacobian of the linearized SDE. In particular, we find the conditions under which one has a pair of complex conjugate eigenvalues of the Jacobian resulting in oscillations. The frequency of the oscillations depends only on the imaginary part of the complex pair, while the decay rate depends only on the real eigenvalue and the real parts of the complex pair. For the deterministic system, oscillations typically decay rapidly. However, randomness induces oscillations to continue indefinitely with a frequency that depends on the parameters of the deterministic system. The computations and analytical results presented here demonstrate that volatility increases when traders place greater emphasis on trend, confirming a generally held belief among practitioners.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:574:y:2021:i:c:s0378437121002570
    DOI: 10.1016/j.physa.2021.125985
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    References listed on IDEAS

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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
    2. Erik Kropat & Ruben A. Tikidji-Hamburyan & Gerhard-Wilhelm Weber, 2017. "Operations research in neuroscience," Annals of Operations Research, Springer, vol. 258(1), pages 1-4, November.
    3. 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.
    4. Caginalp, Carey & Caginalp, Gunduz, 2019. "Price equations with symmetric supply/demand; implications for fat tails," Economics Letters, Elsevier, vol. 176(C), pages 79-82.
    5. David Porter & Vernon Smith, 1994. "Stock market bubbles in the laboratory," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(2), pages 111-128.
    6. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
    7. Betül Kalaycı & Ayşe Özmen & Gerhard-Wilhelm Weber, 2020. "Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS," Annals of Operations Research, Springer, vol. 295(1), pages 183-206, December.
    8. Philip Hans Franses & Michael McAleer, 2002. "Financial volatility: an introduction," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 419-424.
    9. Mark DeSantis & David Swigon, 2018. "Slow-fast analysis of a multi-group asset flow model with implications for the dynamics of wealth," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-25, November.
    10. Caginalp, Gunduz & DeSantis, Mark & Sayrak, Akin, 2014. "The nonlinear price dynamics of U.S. equity ETFs," Journal of Econometrics, Elsevier, vol. 183(2), pages 193-201.
    11. 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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