The Relationship between the U. S. Stock Market Volatility and Korean Stock Market Volatility
Authors:   Asia-Europe Perspective Association, Yoo Han-Soo 
Published: June 2018

In this paper, I investigate whether Korean stock market volatility is influenced by the U. S. stock market volatility. The liberalization of stock markets and the development of IT made stock market interdependence stronger. And the U. S. stock market leadership was documented in many papers. Analyzing the relationship and behavior of stock price volatility is important for portfolio formation and investment strategy. Prior studies have been concentrated only on observed volatility. But this study is distinguished from previous studies in the respect that observed volatility is decomposed into permanent volatility and temporary volatility.
The descriptive statistics show the mean of Korean stock market return is higher than that of the U. S. stock market return. And the standard deviation of Korean market is higher than that of the U.S. market. The negative skewness and excess kurtosis are observed in two markets, and the Jarque-Bera normality test reveal non-normalities of two series.
Therefore, GARCH type model is appropriate for anlayzing these data. As autocorrelation coefficient of time series data is not significantly different from zero, the mean equation in GJR GARCH model do not contain AR(1) term or MA(1) term.
The procedure used in this paper involved the following steps. First, in order to estimate KOSPI observed volatility and S&P500 volatility, GJR GARCH model is employed. In estimated GJR GARCH model, it turns out that the coefficient of asymmetric volatility term is statistically significant. Because the LB Q-statistic applied on residuals and squared residuals is insignificant, and persistence parameter is smaller than one, therefore the GJR GARCH model is well estimated.
Second, to decompose observed volatility, this study employs state space model and Kalman filtering method. State space model is useful in analyzing time series model that involve unobservable variables. And Kalman filter is the basic tool to deal with state space model. In this paper, permanent volatility and temporary volatility are unobservable variables. Permanent volatility is trend component and is modelled as a random walk with drift. And temporary volatility is assumed as AR(1) process because it passes away with time.
Third, to test for unit root behavior of volatility series data, ADF test is used. If the process of series is unit root process, it is to be transformed to stationary process by differencing the series. ADF test results show that all variables are I(0), that is, all series do not contain trends. In other words, each volatility series is stationary time series. As there is not unit root, raw data is used in this study. The effects of shocks to stationary time series will dissipate over time and this process reverts to mean. Fourth, to analyze the relationship between KOSPI volatility and S&P500 volatility, this study employs regression analysis.
This paper uses daily data from January 2001 to April 2008. Because Korean stock market holidays differ from the U. S. stock market holidays, the corresponding date which is holiday in another country is deleted in the data set. The Second difference is time difference. Because Korean stock market of day t opens 4 hours after the U. S. market of day t-1 closes, the information occurred in the U. S. market of day t-1 influences Korean market of day t. Therefore, I examine the relationship between the U. S. data of day t-1 and Korean data of day t.
The findings in this paper are as follows. First, KOSPI observed volatility is significantly related to S&P500 observed volatility. This means that there exists significant linkage in volatility between two markets. This finding is in line with most existing studies.