Modeling The Dependence Of Financial Assets Based On Dynamic Copulas And Its Applications

This paper is an empirical study based on Copula models. Along with the process of international financial integration, modeling the dependence of different financial markets or assets has become increasingly important in modern financial analysis. It is widely used in asset allocation, risk management and derivatives pricing. The dependence of financial assets generally has two features. One is that these assets display asymmetric dependence patterns, which means they are more correlated in market downturns(upturns) than upturns(downturns). The other feature is that the dependence is dynamic rather than constant in the sample interval. In order to simultaneously capture these two features, we improve static Copula models in existing literatures and develop four types of dynamic Copula models to empirically analyze the problems in financial markets. The conclusions from these models will provide suggestions for investors in assets allocation and portfolio risk management.Specially, this paper consists of four sections as follows.First, we use stochastic Copula with explanatory variables to study the stochastic dependence pattern of stock style indices. The dependence of stock style indices have been shown to be related with liquidity and other market variables. As these market variables are stochastic per se, it seems more reasonable to assume the dependence is also stochastic. Therefore, we improve Hafner and Manner(2012)’s stochastic autoregressive copula models by introducing stock turnover as an explanatory variable. The improved model is then used to analyze the dependence of stock style indices, and the economic significance of characterizing this stochastic feature is discussed from the perspective of risk management. Our results show that the tail dependence between small and large cap indices(growth and value indices) are stochastic dynamic processes, and their dependence is affected by market liquidity shocks measured by stock turnover. The short-term investors, who adjust their portfolios each day, each week or each month, are suggested to account for the stochastic feature in dependence as it can efficiently reduce their portfolio risk.Second, we use Copula models with contemporaneous long memory dependence to investigate the long memory effects lying in the tail dependence of London Metal Exchange(LME) and Shanghai Futures Exchanges(SHFE) aluminum futures. Existing literatures only focus on the long memory property in the correlations of different assets; however, few of them study long memory in their non-linear dependence, such as tail dependence. We then incorporate long memory feature into the short memory dynamic Copula and apply the new model to analyze the dependence of LME and SHFE aluminum futures markets. Empirical results show that the two markets exhibit asymmetric dependence: they are more correlated during market recessions than market booms. Furthermore, long memory is present in the dynamics of both upper and lower-tail dependence. The length of non-cycling period is about 100 trading days, indicating that the shocks to cross-market dependence will last about 5 months before decaying to zero. The presence of long memory in dependence indicates that investors can use current information to modify their forecast of cross-market dependence in the next 5 months, thus improving their portfolio’s performance.Third, we use the Copula model with mixed-data-sampling(MIDAS) scheme to study the economic factors of stock and T-bond co-movement in China. The dependence of stock and bond markets can be affected by many factors. Among the potential factors, macroeconomic variables are monthly, while market liquidity can be observed daily. The traditional approach is to aggregate daily variables into monthly, however, it losses intra-month information and is inapplicable to Chinese markets with a small number of observations. To solve the problem of different data frequencies, we introduce mixed data sampling approach into Copula models, and propose Copula-MIDAS model to simultaneously analyze the impacts of monthly macroeconomic and daily liquidity factors on stock and bond co-movements. It is found that, in China macroeconomic fundamentals and market uncertainty are the true economic sources of stock and bond co-movements, while market liquidity factors play a less important role.Fourth, we use multivariate dynamic skewed t Copula to study the dependence structure of high-dimensional variables. Existing skewed t Copula only has one scalar skewness parameter and such specification on dependence is too strict to capture the time-varying dependence of multivariate variables. To make the model more flexible, we not only allow each variable to have its individual skewness parameter, but also introduce autoregressive dynamic mechanism into the evolution of these skewness parameters. Our empirical analysis is based on 50 Exchange Trade Fund(ETF) indices including stock, bond, foreign exchange, gold, oil and real estate. Results show that the dynamic specification on skewness vector enables us to well describe the dynamic dependence of high-dimensional variables, in particular, the different dependence patterns in extreme conditions. In comparison with existing skewed t Copula, our dynamic skewed t Copula has higher in-sample goodness-of-fit and out-of-sample predictive ability. Investors can benefit from using this model when constructing their optimal portfolios.