Fengzhong Wang

Gravity model in the Korean highway

We investigate the traffic flows of the Korean highway system, which contains both public and private transportation information. We find that the traffic flow Tij between city i and j forms a gravity model, the metaphor of physical gravity as described in Newtons law of gravity, PiPj/rij2, where Pi represents the population of city i and rij the distance between cities i and j. It is also shown that the highway network has a heavy tail even though the road network is a rather uniform and homogeneous one. Compared to the highway network, air and public ground transportation establish inhomogeneous systems and have power law behaviors.

Scaling and memory of intraday volatility return intervals in stock markets.

We study the return interval tau between price volatilities that are above a certain threshold q for 31 intraday data sets, including the Standard and Poors 500 index and the 30 stocks that form the Dow Jones Industrial index. For different threshold q, the probability density function Pq(tau)scales with the mean interval tau as [Formula: see text], similar to that found in daily volatilities. Since the intraday records have significantly more data points compared to the daily records, we could probe for much higher thresholds and still obtain good statistics. We find that the scaling function f(x)is consistent for all 31 intraday data sets in various time resolutions, and the function is well-approximated by the stretched exponential, f(x) similar to e(-ax)(gamma), with gamma=0.38+/-0.05 and a=3.9+/-0.5, which indicates the existence of correlations. We analyze the conditional probability distribution Pq(tau/tau0) for tau following a certain interval tau0, and find Pq(tau/tau0) depends on tau0, which demonstrates memory in intraday return intervals. Also, we find that the mean conditional interval (tau/tau0) increases with tau0, consistent with the memory found for Pq(tau/tau0). Moreover, we find that return interval records, in addition to having short-term correlations as demonstrated by Pq(tau/tau0), have long-term correlations with correlation exponents similar to that of volatility records.

Indication of multiscaling in the volatility return intervals of stock markets

The distribution of the return intervals tau between price volatilities above a threshold height q for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined nonlinear mechanism, we investigate intraday data sets of 500 stocks which consist of Standard & Poors 500 index. We show that the cumulative distribution of return intervals has systematic deviations from scaling. We support this finding by studying the m -th moment micro_{m} identical with(tau/tau);{m};{1/m} , which show a certain trend with the mean interval tau . We generate surrogate records using the Schreiber method, and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most ranges of tau . Those substantial differences suggest that nonlinear correlations in the original volatility sequence account for the deviations from a single scaling law. We also find that the original and surrogate records exhibit slight tendencies for short and long tau , due to the discreteness and finite size effects of the records, respectively. To avoid as possible those effects for testing the multiscaling behavior, we investigate the moments in the range 10<tau< or =100 , and find that the exponent alpha from the power law fitting micro_{m} approximately tau;{alpha} has a narrow distribution around alpha not equal0 which depends on m for the 500 stocks. The distribution of alpha for the surrogate records are very narrow and centered around alpha=0 . This suggests that the return interval distribution exhibits multiscaling behavior due to the nonlinear correlations in the original volatility.

Group dynamics of the Japanese market

We investigated the network structures of the Japanese stock market using the minimum spanning tree. We defined a grouping coefficient to test the validity of the conventional grouping by industrial categories, and found a decreasing in trend for the coefficient. This phenomenon supports the increasing external influences on the market due to globalization. To reduce this influence, we used S&P500 index as the international market and removed its correlation with every stock. We found stronger a grouping in this measurement when compared to the original analysis, which agrees with our assumption that the international market influences to the Japanese market.

Multifactor analysis of multiscaling in volatility return intervals

We study the volatility time series of 1137 most traded stocks in the U.S. stock markets for the two-year period 2001-2002 and analyze their return intervals tau , which are time intervals between volatilities above a given threshold q . We explore the probability density function of tau , P_(q)(tau) , assuming a stretched exponential function, P_(q)(tau) approximately e;(-tau;(gamma)) . We find that the exponent gamma depends on the threshold in the range between q=1 and 6 standard deviations of the volatility. This finding supports the multiscaling nature of the return interval distribution. To better understand the multiscaling origin, we study how gamma depends on four essential factors, capitalization, risk, number of trades, and return. We show that gamma depends on the capitalization, risk, and return but almost does not depend on the number of trades. This suggests that gamma relates to the portfolio selection but not on the market activity. To further characterize the multiscaling of individual stocks, we fit the moments of tau , mu_(m) identical with(tautau);(m);(1m) , in the range of 10<tau< or =100 by a power law, micro_(m) approximately tau;(delta). The exponent delta is found also to depend on the capitalization, risk, and return but not on the number of trades, and its tendency is opposite to that of gamma . Moreover, we show that delta decreases with increasing gamma approximately by a linear relation. The return intervals demonstrate the temporal structure of volatilities and our findings suggest that their multiscaling features may be helpful for portfolio optimization.

Financial factor influence on scaling and memory of trading volume in stock market

We study the daily trading volume volatility of 17,197 stocks in the US stock markets during the period 1989-2008 and analyze the time return intervals τ between volume volatilities above a given threshold q. For different thresholds q, the probability density function P(q)(τ) scales with mean interval 〈τ〉 as P(q)(τ)=〈τ〉(-1)f(τ/〈τ〉), and the tails of the scaling function can be well approximated by a power law f(x)∼x(-γ). We also study the relation between the form of the distribution function P(q)(τ) and several financial factors: stock lifetime, market capitalization, volume, and trading value. We find a systematic tendency of P(q)(τ) associated with these factors, suggesting a multiscaling feature in the volume return intervals. We analyze the conditional probability P(q)(τ|τ(0)) for τ following a certain interval τ(0), and find that P(q)(τ|τ(0)) depends on τ(0) such that immediately following a short (long) return interval a second short (long) return interval tends to occur. We also find indications that there is a long-term correlation in the daily volume volatility. We compare our results to those found earlier for price volatility.

Statistical analysis of the overnight and daytime return

We investigate the two components of the total daily return (close-to-close), the overnight return (close-to-open), and the daytime return (open-to-close), as well as the corresponding volatilities of the 2215 New York Stock Exchange stocks for the 20 year period from 1988 to 2007. The tail distribution of the volatility, the long-term memory in the sequence, and the cross correlation between different returns are analyzed. Our results suggest that (i) the two component returns and volatilities have features similar to that of the total return and volatility. The tail distribution follows a power law for all volatilities, and long-term correlations exist in the volatility sequences but not in the return sequences. (ii) The daytime return contributes more to the total return. Both the tail distribution and the long-term memory of the daytime volatility are more similar to that of the total volatility, compared to the overnight records. In addition, the cross correlation between the daytime return and the total return is also stronger. (iii) The two component returns tend to be anticorrelated. Moreover, we find that the cross correlations between the three different returns (total, overnight, and daytime) are quite stable over the entire 20 year period.

Volatility return intervals analysis of the Japanese market

Abstract.We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold q for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the return interval τ and its mean 〈τ〉. We also find memory effects such that a large (or small) return interval follows a large (or small) interval by investigating the conditional distribution and mean return interval. The results are similar to previous studies of other markets and indicate that similar statistical features appear in different financial markets. We also compare our results between the period before and after the big crash at the end of 1989. We find that scaling and memory effects of the return intervals show similar features although the statistical properties of the returns are different.

Statistical analysis of bankrupting and non-bankrupting stocks

The recent financial crisis has caused extensive world-wide economic damage, affecting in particular those who invested in companies that eventually filed for bankruptcy. A better understanding of stocks that become bankrupt would be helpful in reducing risk in future investments. Economists have conducted extensive research on this topic, and here we ask whether statistical physics concepts and approaches may offer insights into pre-bankruptcy stock behavior. To this end, we study all 20092 stocks listed in US stock markets for the 20-year period 1989–2008, including 4223 (21 percent) that became bankrupt during that period. We find that, surprisingly, the distributions of the daily returns of those stocks that become bankrupt differ significantly from those that do not. Moreover, these differences are consistent for the entire period studied. We further study the relation between the distribution of returns and the length of time until bankruptcy, and observe that larger differences of the distribution of returns correlate with shorter time periods preceding bankruptcy. This behavior suggests that sharper fluctuations in the stock price occur when the stock is closer to bankruptcy. We also analyze the cross-correlations between the return and the trading volume, and find that stocks approaching bankruptcy tend to have larger return-volume cross-correlations than stocks that are not. Furthermore, the difference increases as bankruptcy approaches. We conclude that before a firm becomes bankrupt its stock exhibits unusual behavior that is statistically quantifiable.

Temporal Structure of Volatility Fluctuations

Volatility fluctuations are of great importance for the study of financial markets, and the temporal structure is an essential feature of fluctuations. To explore the temporal structure, we employ a new approach based on the return interval, which is defined as the time interval between two successive volatility values that are above a given threshold. We find that the distribution of the return intervals follows a scaling law over a wide range of thresholds, and over a broad range of sampling intervals. Moreover, this scaling law is universal for stocks of different countries, for commodities, for interest rates, and for currencies. However, further and more detailed analysis of the return intervals shows some systematic deviations from the scaling law. We also demonstrate a significant memory effect in the return intervals time organization. We find that the distribution of return intervals is strongly related to the correlations in the volatility.