English

Volatility, Persistence, and Survival in Financial Markets

Physics and Society 2008-12-02 v2 Statistical Mechanics Data Analysis, Statistics and Probability Statistical Finance

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 qq-order correlation functions fq(t)f_q(t), survival probability S(t)S(t), and persistence probability P(t)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 δt\delta t of the order of days). We find that the fluctuating stock price is multifractal and the choice of δt\delta t has no effect on the qualitative multifractal behavior displayed by the 1/q1/q-dependence of the generalized Hurst exponent HqH_q associated with the power-law evolution of the correlation function fq(t)tHqf_q(t)\sim t^{H_q}. The probability S(t)S(t) of the stock price remaining above the average up to time tt is very sensitive to the total measurement time tmt_m and the sampling time. The probability P(t)P(t) of the stock not returning to the initial value within an interval tt has a universal power-law behavior, P(t)tθP(t)\sim t^{-\theta}, with a persistence exponent θ\theta close to 0.5 that agrees with the prediction θ=1H2\theta=1-H_2. The empirical financial stocks also present an interesting feature found in turbulent fluids, the extended self-similarity.

Keywords

Cite

@article{arxiv.physics/0507020,
  title  = {Volatility, Persistence, and Survival in Financial Markets},
  author = {M. Constantin and S. Das Sarma},
  journal= {arXiv preprint arXiv:physics/0507020},
  year   = {2008}
}

Comments

11 pages, 14 figures