Extracting Stochastic Volatilities and Jumps for the Korean Stock Index Using Optimal Filter (in Korean)

In this paper, by using the optimal filtering method proposed by Johannes et al. (2009), we extract stochastic volatilities and jumps for the KOSPI (Korea Composite Stock Price Index), and assess whether this extraction can give information to forecast future stock index volatility. First, we evaluate density forecast performances for a variety of stock return models, such as various GARCH and square-root stochastic volatility models, via the non-parametric specification testing method developed by Hong and Li (2005) and Yun and Hong (2009). Our results show that the stochastic volatility model with a jump-in-return (SVJ model) exhibits better performance than popularly used GARCH models. Second, we extract stochastic volatilities and jumps from our SVJ model, which showed the best density forecasting performance by using optimal filter. By observing the extracted stochastic volatilities and jumps, we find that the stock index collapse following the 9/11 attacks was due to a downward jump of the stock index, whereas the stock market turbulence right after the Lehman Brothers failure was due mainly to high and persistent stochastic volatility. This implies a longer persistence of stock market uncertainty following the global financial crisis than the 9/11 attacks. Our empirical study shows that the optimal filtering method can be a useful method, by which we can extract stochastic volatilities and jumps and forecast future stock volatilities in a timely manner.