Volatility, Persistence, and Survival in Financial Markets

M. Constantin and S. Das Sarma

Papers from arXiv.org

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.

Date: 2005-07, Revised 2005-11
References: Add references at CitEc
Citations: View citations in EconPapers (8)

Published in Phys. Rev. E 72, 051106 (2005)

Downloads: (external link)
http://arxiv.org/pdf/physics/0507020 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:physics/0507020

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().