KOSPI 200을 이용한 국면전환 연속시간 확률 변동성 모형의 추정
Estimation of Regime-Switching Continuous-Time Stochastic Volatility Models Using KOSPI 200
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초록
이 논문에서는 KOSPI 200 일별 자료를 이용해 국면전환 (regime-switching) 연속시간 (continuous-time) 확률 변동성 (stochastic volatility) 모형들을 추정한다. 단일국면 Heston, GARCH, 그리고 CEV 확률 변동성 모형들과 두 가지 다른 국면 L과 H이 있는 6개의 국면전환 확률 변동성 모형들을 고려한다. 추정 방법은 해밀턴 알고리즘 (Hamilton (1989))을 이용해 우도 함수의 값을 계산하고 최우추정법을 이용한다. 우리의 확률 변동성 모형들의 전이 확률밀도 함수들을 알지 못하기에 Ait-Sahalia (2008)와 Choi (2015b)를 이용해 근사적이고 구체적인 식으로 구한다. 전이 확률이 시간에 따라 변하는 경우의 국면전환 CEV 모형이 KOSPI 200 자료를 가장 잘 설명한다는 추정 결과를 얻었다. L국면이 H국면보다 레버리지 효과가 더 컸다. 그리고 국면 L과 비교해 국면 H에서 변동성 변수가 장기적인 평균 수준으로 더 빨리 돌아오는 경향이 있었고, 변동성 변수의 변동성도 더 컸으며, 국면 H에 있을 때 다음 기에 같은 국면에 있을 확률이 더 컸고, 전이확률이 변동성 변수 보다는 주가에 의존하며 시간에 따라 변한다는 결과를 얻었다. 국면 H에 있을 확률이 높았던 시기에는 남북 관계나 대내외적으로 한국 주식 시장에 영향을 줄 수 있는 정치, 경제적인 여러 사건들이 있는 경우가 많았다.
Abstract
This article estimates regime-switching continuous-time stochastic volatility models using daily KOSPI 200. We consider single regime Heston, GARCH, and CEV stochastic volatility models and 6 regime-switching stochastic volatility models which have two different regimes L and H. We employ Hamilton algorithm (Hamilton (1989)) to compute the log-likelihood and to apply MLE. Because the true transition probability density functions (TPDFs) of our stochastic volatility models are unknown, we use Ait-Sahalia (2008) and Choi (2015b) to obtain closed-form approximate TPDF. The regime-switching CEV model where the transition probability is allowed to vary over time has been found to be the best to explain the movements of KOSPI 200. Regime L has a stronger leverage effect than regime H. Comparing to regime L, the volatility variable tends to revert to its long-run mean level more rapidly, the volatility of volatility variable is greater, the probability of staying in the same regime H in the next period is bigger in regime H. And the transition probability varies with time depending on the stock price rather than the volatility. When the probabilities of regime H are high we could identify various economic and political events between South Korea and North Korea or inside or outside South Korea that could have affected Korean stock market.
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