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Volatility, Persistence, and Survival in Financial Markets

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  • M. Constantin
  • S. Das Sarma

Abstract

We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price fluctuations as a non-Markovian stochastic process using the first-passage statistical concepts of persistence and survival. We report the results of empirical measurements of the normalized $q$-order correlation functions $f_q(t)$, survival probability $S(t)$, and persistence probability $P(t)$ for several stock market dynamical sets. We analyze both minute-to-minute and higher frequency stock market recordings (i.e., with the sampling time $\delta t$ of the order of days). We find that the fluctuating stock price is multifractal and the choice of $\delta t$ has no effect on the qualitative multifractal behavior displayed by the $1/q$-dependence of the generalized Hurst exponent $H_q$ associated with the power-law evolution of the correlation function $f_q(t)\sim t^{H_q}$. The probability $S(t)$ of the stock price remaining above the average up to time $t$ is very sensitive to the total measurement time $t_m$ and the sampling time. The probability $P(t)$ of the stock not returning to the initial value within an interval $t$ has a universal power-law behavior, $P(t)\sim t^{-\theta}$, with a persistence exponent $\theta$ close to 0.5 that agrees with the prediction $\theta=1-H_2$. The empirical financial stocks also present an interesting feature found in turbulent fluids, the extended self-similarity.

Suggested Citation

  • M. Constantin & S. Das Sarma, 2005. "Volatility, Persistence, and Survival in Financial Markets," Papers physics/0507020, arXiv.org, revised Nov 2005.
  • Handle: RePEc:arx:papers:physics/0507020
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    Cited by:

    1. Coronado, Semei & Rojas, Omar & Venegas-Martínez, Francisco (ed.), 2018. "Recent Topics in Time Series and Finance: Theory and Applications in Emerging Markets," Sección de Estudios de Posgrado e Investigación de la Escuela Superios de Economía del Instituto Politécnico Nacional, Escuela Superior de Economía, Instituto Politécnico Nacional, edition 1, volume 1, number 022, January.
    2. Sumiyana Sumiyana & Ainun Na’im & Albertus H. L. Nugroho & Firdaus Kurniawan, 2023. "Multiple measurements of CEOs’ overconfidence and future earnings management: evidence from Asia-Pacific developing countries," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-11, December.
    3. da Cunha, C.R. & da Silva, R., 2020. "Relevant stylized facts about bitcoin: Fluctuations, first return probability, and natural phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    4. C. R. da Cunha & R. da Silva, 2019. "Relevant Stylized Facts About Bitcoin: Fluctuations, First Return Probability, and Natural Phenomena," Papers 1905.03211, arXiv.org.
    5. Fabio Vanni & David Lambert, 2024. "Aging Renewal Point Processes and Exchangeability of Event Times," Mathematics, MDPI, vol. 12(10), pages 1-26, May.
    6. Miśkiewicz, Janusz & Ausloos, Marcel, 2008. "Correlation measure to detect time series distances, whence economy globalization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6584-6594.
    7. da Silva, Roberto & Zembrzuski, Marcelo & Correa, Fabio C. & Lamb, Luis C., 2010. "Stock markets and criticality in the current economic crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(23), pages 5460-5467.

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