Interdependence Modeling for the Major Stock Markets and the Stock Portfolio Risk Management

We employ a variety of dependence measures to test interdependence structure of the Korean and the US stock markets. We use daily returns on the KOSPI 200 and S&P 500. We measure a variety of dependence measures other than the linear correlation coefficient to characterize the copula function. The scale invariant dependence measure whose attribute can determine the form of the copula is a function of the ranks and is solely dependent upon the copula and not the marginal distributions of the data. Firstly, we calculate the quantile dependence which provides with the degree of asymmetric dependence in the extreme quantile by weighing the left tail to the right. Quantile dependence between the two variables is different from linear correlation or rank correlation whose values are scalars in the sense that it provides with varying degrees of asymmetric dependence from the center of the distribution to each extreme. Secondly, we compute the tail dependence which measures the synchronicity between extreme events and can be calculated as the population quantile dependence at the limit. Thirdly, we test for the existence of asymmetric and time-varying dependence. The time-varying conditional volatility of each series may induce time-varying conditional dependence. The test for time-varying dependence between the KOSPI 200 and S&P 500 standardized residuals is implemented. We then use the stationary bootstrap to construct the confidence intervals for the dependence measures. Lastly, we use the multi-stage GMM to estimate the constant parametric copula function and the time-varying copula function.