Direct Evidence for Inversion Formula in Multifractal Financial Volatility Measure

The inversion formula for conservative multifractal measures was unveiled mathematically a decade ago, which is however not well tested in real complex systems. We propose to verify the inversion formula using high-frequency turbulent financial data. We construct conservative volatility measure based on minutely S＆P 500 index from 1982 to 1999 and its inverse measure of exit time. Both the direct and inverse measures exhibit nice multifractal nature, whose sealing ranges are not irrelevant. Empirical investigation shows that the inversion formula holds in financial markets.

An empirical behavioral order‑driven model with price limit rules

We propose an empirical behavioral order-driven(EBOD)model with price limit rules,which consists of an order placement process and an order cancellation process.All the ingredients of the model are determined based on the empirical microscopic regularities in the order flows of stocks traded on the Shenzhen Stock Exchange.The model can reproduce the main stylized facts in real markets.Computational experiments unveil that asymmetric setting of price limits will cause the stock price to diverge exponentially when the up price limit is higher than the down price limit and to vanish vice versa.We also find that asymmetric price limits have little influence on the correlation structure of the return series and the volatility series,but cause remarkable changes in the average returns and the tail exponents of returns.Our EBOD model provides a suitable computational experiment platform for academics,market participants,and policy makers.

Economic importance and structural robustness of the international pesticide trade networks

Pesticides are agricultural inputs that can significantly reduce yield losses,regulate plant growth,effectively liberate agricultural productivity,and improve food security.The availability of pesticides in economies worldwide is ensured by redistribution through international trade,with different economies playing different roles in this process.In this study,we measured and ranked the importance of economies using nine node metrics.We found that the clustering coefficient was negatively correlated with the other eight node metrics,whereas the other eight node metrics were positively correlated with each other and could be grouped into three communities(betweenness;in-degree,PageRank,authority,and in-closeness;out-degree,hub,and out-closeness).We further investigated the structural robustness of international pesticide trade networks proxied by large component size under three types of shocks to economies(node removal in descending,random,and ascending orders).The results showed that,except for the clustering coefficient,international pesticide trade networks are relatively robust under shocks to economies in ascending order but fragile under shocks to economies in descending order.By contrast,removing nodes with a clustering coefficient in ascending and descending order yielded similar robustness curves.Moreover,the structural robustness related to large component size evolved over time and exhibited an inverse U-shaped pattern.

Joint multifractal analysis based on wavelet leaders

Mutually interacting components form complex systems and these components usually have long- range cross-correlated outputs. Using wavelet leaders, we propose a method for characterizing the joint multifractal nature of these long-range cross correlations; we call this method joint multifractal analysis based on wavelet leaders （MF-X-WL）. We test the validity of tile MF-X-WL method by performing extensive numerical experiments on dual binomial measures with multifractal cross correlations and bivariate fractional Brownian motions （bFBMs） with monofractal cross correlations. Both experiments indicate that MF-X-WL is capable of detecting cross correlations in synthetic data with acceptable estimating errors. We also apply the MF-X-WL method to pairs of series from financial markets （returns and volatilities） and online worlds （online numbers of different genders and different societies） and determine intriguing joint multifractal behavior.

Intraday Volatility Spillover between the Shanghai and Hong Kong Stock Markets—Evidence from A+H Shares after the Launch of the Shanghai-Hong Kong Stock Connect

Using minute data of eligible A+H stocks under the Shanghai-Hong Kong Stock Connect(SHHKSC),we investigate the volatility spillover between the Shanghai and Hong Kong stock markets based on a generalized autoregressive conditional heteroskedasticity-X(GARCH-X)model with four exogenous variables,namely,volatilities of the corresponding stocks on the other market,volatilities of the indexes of both stock markets,and volatilities of the correlated stocks,which are selected using the dynamic conditional correlation model and bootstrap approach.Results show that after the launch of the SHHKSC,volatility spillovers are significant in both directions almost all the time,and the volatility spillover between the two stock markets tends to be larger when bidirectional capital flows under the SHHKSC increase or when important financial events occur.We also analyze the influences of the volatilities of correlated stocks and industries on the volatility spillover and volatilities of A+H stocks.The bidirectional volatility spillovers between Shanghai and Hong Kong stock markets do not change qualitatively after incorporating the volatilities of correlated stocks and industries in the GARCH-X model.Moreover,the average volatilities of the correlated stocks are shown to have significant influences on the volatilities of individual A+H stocks,and the influences increase when the local stock market shows a sharp rise or fall.Compared with the market indexes,the correlated stocks could be regarded as a more important and indispensable factor for individual A+H stocks’volatilities modeling,which may carry more information than the industry.