dorsal/arxiv
View SchemaVolatility, Persistence, and Survival in Financial Markets
| Authors | M. Constantin, S. Das Sarma |
|---|---|
| Categories | |
| ArXiv ID | physics/0507020 |
| URL | https://arxiv.org/abs/physics/0507020 |
| DOI | 10.1103/PhysRevE.72.051106 |
| Journal | Phys. Rev. E 72, 051106 (2005) |
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.
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"abstract": "We study the temporal fluctuations in time-dependent stock prices (both\nindividual and composite) as a stochastic phenomenon using general techniques\nand methods of nonequilibrium statistical mechanics. In particular, we analyze\nstock price fluctuations as a non-Markovian stochastic process using the\nfirst-passage statistical concepts of persistence and survival. We report the\nresults of empirical measurements of the normalized $q$-order correlation\nfunctions $f_q(t)$, survival probability $S(t)$, and persistence probability\n$P(t)$ for several stock market dynamical sets. We analyze both\nminute-to-minute and higher frequency stock market recordings (i.e., with the\nsampling time $\\delta t$ of the order of days). We find that the fluctuating\nstock price is multifractal and the choice of $\\delta t$ has no effect on the\nqualitative multifractal behavior displayed by the $1/q$-dependence of the\ngeneralized Hurst exponent $H_q$ associated with the power-law evolution of the\ncorrelation function $f_q(t)\\sim t^{H_q}$. The probability $S(t)$ of the stock\nprice remaining above the average up to time $t$ is very sensitive to the total\nmeasurement time $t_m$ and the sampling time. The probability $P(t)$ of the\nstock not returning to the initial value within an interval $t$ has a universal\npower-law behavior, $P(t)\\sim t^{-\\theta}$, with a persistence exponent\n$\\theta$ close to 0.5 that agrees with the prediction $\\theta=1-H_2$. The\nempirical financial stocks also present an interesting feature found in\nturbulent fluids, the extended self-similarity.",
"arxiv_id": "physics/0507020",
"authors": [
"M. Constantin",
"S. Das Sarma"
],
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"physics.soc-ph",
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"q-fin.ST"
],
"doi": "10.1103/PhysRevE.72.051106",
"journal_ref": "Phys. Rev. E 72, 051106 (2005)",
"title": "Volatility, Persistence, and Survival in Financial Markets",
"url": "https://arxiv.org/abs/physics/0507020"
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