Methods Of Measuring Cross-correlations In Financial Markets And The Empirical Study

Actually understanding and describing cross-correlations in financial markets, onthe one hand, it can help market participants and regulators capture market informationand make economic policy; on the other hand, it can help us understand the formationmechanism of financial asset prices, and it has an important practical guidingsignificance on the optimization allocation and risk management of financial assets.Because interactions among financial agents are complex and dynamic, we cannotactually describe the internal and external operating mechanisms and trends in financialmarkets. Therefore, considering that financial markets are complex dynamical systems,based on the complex system theory, we study cross-correlations in financial marketsfrom the perspective of fractal analysis theory, complex network theory, and randommatrix theory (RMT).In the part of mechanism study of measuring cross-correlations in financialmarkets, we first clarify the definitions of financial markets and cross-correlations, andpresent the disadvantages of the traditional measures of cross-correlations. Then, weanalyze the stylized facts of financial markets including nonlinear, self-similarity,complexity, and dynamics, which can help us find the clues and ideas of the theory andmethod for measuring cross-correlations in financial markets. Finally, we introducesome methods for measuring cross-correlations in financial markets based on thecomplex system theory.As for the methods of measuring cross-correlations in financial markets and theempirical study, we use the fractal analysis theory, complex network theory, and RMTto investigate the cross-correlations between two financial markets, cross-correlationsamong multiple financial markets, and cross-correlations in financial markets,respectively. Firstly, based on the fractal analysis theory, we carry out three studies asfollows.(i) We employ the detrended cross-correlation analysis (DCCA) method andthe DCCA coefficient approach to study cross-correlations between RMB and fourmajor currencies (i.e., USD, EUR, JPY, and KRW) in the RMB currency basket. Theempirical results show that the four pairs of cross-correlations are weakly persistent, andthat the currency weight in the RMB currency basket is arranged in the order ofUSD EUR JPY KRW.(ii) We adopt the method of multifractal detrendingmoving-average cross-correlation analysis to examine cross-correlations between the CSI300spot and futures markets, and find that cross-correlations between the twomarkets are multifractal and nonlinear. Using the method of rolling windows, which cancapture the time-varying cross-correlation scaling exponents, we find that thecross-correlations are positive over time.(iii) We propose a new method for hedge ratio,i.e., the detrended minimum-variance (D-MV) hedge ratio, which can measure thehedge ratio at different time scales. We define the D-MV hedge ratio as the detrendedcovariance function between spot and futures returns divided by the detrended variancefunction of futures returns. Through the simulated and empirical analysis, we find thatthe proposed D-MV hedge ratio has a better hedging performance and a greaterpotential to determine the hedge ratio because its results of hedging effectiveness atmost of time scales are better than those of the traditional MV hedge ratio. Secondly,based on the complex network theory, we also perform three studies as follows.(i)Based on the dynamic time wrapping method and the minimum spanning tree (MST)approach, we propose a new correlation network-based method to investigatecross-correlations in the international foreign exchange (FX) market and its networks’topological features under the US sub-prime crisis. The empirical results show that thetopological structure of the FX network after the US sub-prime crisis is more robustthan that of before the crisis and that SGD becomes a new center currency for thenetwork after the crisis.(ii) On the basis of methods of the DCCA coefficient and theMST, we propose a multi-scale correlation network-based approach to analyzecross-correlation in the international FX market and its networks’ topological andstatistical properties at different time scales. We find that the MSTs of the internationalFX market present diverse topological and statistical properties at different time scalesand have the scale-free behavior at most of time scales.(iii) Based on a time-varyingcopula approach and the MST method, we propose a time-varying correlationnetwork-based approach to study cross-correlation in the international FX market andits networks’ dynamic topological and statistical properties. The empirical findingsreveal that the FX network has a long-term memory effect and presents a scale-freebehavior in the most of time. The tight relationships among the international FX rateson the short-term are hardly broken and have a strong robustness, while their long-termstability decreases sharply as the time increases. Finally, we combine the DCCAcoefficient approach and RMT to research cross-correlations in the US stock market atdifferent time scales. We find that empirical cross-correlation matrices show diverseproperties at different time scales, which are useful to the risk management and optimalportfolio selection, especially to the diversity of the asset portfolio.