On return-volatility correlation in financial dynamics

We investigate the return-volatility correlation both local and nonlocal in time with daily and minutely data of the German DAX and Chinese indices, and observe a leverage effect for the German DAX, while an antileverage effect for the Chinese indices. In the negative time direction, i.e., for the volatility-return correlation, an antileverage effect nonlocal in time is detected for both the German DAX and Chinese indices, although the duplicate local in time does not exist. A retarded volatility model may describe the asymmetric properties of the financial indices in the positive time direction.

[1]  V. Plerou,et al.  A theory of power-law distributions in financial market fluctuations , 2003, Nature.

[2]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[3]  J. Bouchaud,et al.  Leverage Effect in Financial Markets , 2001 .

[4]  Ingve Simonsen,et al.  Optimal investment horizons , 2002 .

[5]  Generalized persistence probability in a dynamic economic index , 2003 .

[6]  Bo Zheng,et al.  Monte Carlo simulations of short-time critical dynamics , 1999 .

[7]  Yi-Cheng Zhang,et al.  Emergence of cooperation and organization in an evolutionary game , 1997 .

[8]  P. Cizeau,et al.  Statistical properties of the volatility of price fluctuations. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Cornell,et al.  Nontrivial Exponent for Simple Diffusion. , 1996, Physical review letters.

[10]  Multiscaling and Structure Functions in Turbulence: An Alternative Approach , 1999, chao-dyn/9901021.

[11]  Dietrich Stauffer,et al.  MONTE CARLO SIMULATION OF VOLATILITY CLUSTERING IN MARKET MODEL WITH HERDING , 1999 .

[12]  D. Helbing,et al.  Volatility clustering and scaling for financial time series due to attractor bubbling. , 2002, Physical review letters.

[13]  E. Bacry,et al.  Modelling fluctuations of financial time series: from cascade process to stochastic volatility model , 2000, cond-mat/0005400.

[14]  Guojun Wu,et al.  Asymmetric Volatility and Risk in Equity Markets , 1997 .

[15]  Bo Zheng,et al.  A generalized dynamic herding model with feed-back interactions , 2004 .

[16]  Ingve Simonsen,et al.  Inverse statistics in economics: the gain–loss asymmetry , 2002 .

[17]  John Y. Campbell,et al.  No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns , 1991 .

[18]  J. Masoliver,et al.  Random diffusion and leverage effect in financial markets. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  M. Marchesi,et al.  Scaling and criticality in a stochastic multi-agent model of a financial market , 1999, Nature.

[20]  J. Bouchaud,et al.  Herd Behavior and Aggregate Fluctuations in Financial Markets , 1997 .

[21]  J. Bouchaud,et al.  Leverage effect in financial markets: the retarded volatility model. , 2001, Physical review letters.

[22]  T. Andersen.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1998, Econometric Theory.

[23]  Matteo Marsili,et al.  Stylized Facts of Financial Markets and Market Crashes in Minority Games , 2001, cond-mat/0101326.

[24]  A. Christie,et al.  The stochastic behavior of common stock variances: value , 1982 .

[25]  Persistence probabilities of the German DAX and Shanghai Index , 2005, nlin/0511048.

[26]  Yoram Louzoun,et al.  Volatility driven market in a generalized Lotka–Voltera formalism , 2001 .

[27]  V. Eguíluz,et al.  Transmission of information and herd Behavior: an application to financial markets. , 1999, Physical review letters.

[28]  R. Mantegna,et al.  Scaling behaviour in the dynamics of an economic index , 1995, Nature.

[29]  M. Mézard,et al.  Microscopic models for long ranged volatility correlations , 2001, cond-mat/0105076.

[30]  B. Zheng,et al.  Two-phase phenomena, minority games, and herding models. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  V. Plerou,et al.  Scaling of the distribution of fluctuations of financial market indices. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.