최적필터(optimal filter)를 이용한 우리나라 주가지수의 확률변동성 및 점프 추출 = Extracting Stochastic Volatilities and Jumps for the Korean Stock Index Using Optimal Filter

다국어 초록 (Multilingual Abstract)

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.

국문 초록 (Abstract)

본 연구는 Johannes et al.(2009)이 제안한 최적필터(optimal filter) 방법을 이용하여 우리나라 주가지수의 확률변동성 및 점프를 추출하고 이러한 구분이 주가의 향후 불확실성을 예측할 수 있는 정보로 활용될 수 있는지 검토하였다.
먼저 다양한 주가 시계열 모형을 대상으로 Hong and Li(2005), Yun and Hong(2009) 등이 개발한 비모수 적합성 검정방법을 통해 모형의 현실적합성을 살펴본 결과, 종래 많이 이용되어온 GARCH 모형에 비해 제곱근 확률변동성 모형(square-root stochastic volatility models)이 우수했으며 그중에서도 특히 주가 점프를 고려한 제곱근 확률변동성 모형(SVJ 모형)이 가장 우수한 것으로 나타났다. 다음으로 SVJ 모형을 대상으로 최적필터를 이용하여 확률변동성 및 점프를 추출한 결과, 9.11 테러사태시의 주가급락은 주가의 하방점프에 기인한 반면, 2008년 금융위기시의 주가급변은 확률변동성이 높게 지속된 데 기인한 것으로 분석되었다. 이는 9.11 테러시에 비해 2008년 금융위기시 주가 불확실성의 지속성이 더 컸음을 의미한다. 이와 같이 최적필터는 주가의 확률변동성과 점프를 신속하게 추출함으로써 주가 변동의 원인 분석은 물론 향후 주가변동성을 예측하는 데 있어서도 유용한 수단이 될 것으로 보인다.

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