실현변동성의 분수적 공적분과 예측력에 관한 연구
The Fractional Cointegration of the Implied Volatility and the Realized Volatility
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초록
이 논문은 KOSPI200지수옵션 내재변동성의 예측력에 대해 살펴보고 있다. 이론적으로는 내재변동성이 사후적인 실현변동성의 불편추정량인 것으로 받아들여지지만 이것을 실증적으로 규명하기 위한 내재변동성 예측회귀모형은 관찰 불가능한 변동성 위험프리미엄으로 인한 누락변수문제와 비동시적 마감거래로 인한 측정오차문제를 내포하고 있기 때문에 OLS추정상에 문제를 야기한다. 이 문제를 해결하기 위해 우리는 시간영역(time domain) 대신 주파수영역(frequency domain)에 기반한 예측회귀모형을 사용하였다. 실증분석결과를 요약하면 다음과 같다. 첫째, 국내지수옵션시장에서 내재변동성은 불안정한 장기기억과정을 가지고 있으며 실현변동성의 경우는 안정적인 장기기억과정도 가지고 있는 것으로 판단된다. 둘째, 이변량제약 GPH 추정치와 두 변동성 측정치를 이용한 회귀모형을 소폭 스펙트럴 최소자승추정법(Narrow Band Spectral Least Square)으로 추정한 결과, 두 변동성 측정치는 분수적 공적분관계가 성립하는 것으로 나타났다. 이것은 내재변동성이 실현변동성에 대해 장기적인 예측력이 존재한다는 것을 의미한다.
Abstract
This paper investigates whether or not there is a long-run predictability of option's implied volatility on the ex-post realized volatility in the KOSPI 200 index option market. It is known that if the option market is operated efficiently, Black-Sholes's option implied volatility will be a unbiased estimator for realized volatility. However, the predictive regression model used to test the predictablity has the problem with related to the existence of unobserved volatility risk premium and the measurement error from the nonsychronous trading. To tackle these problem in the regression estimation, we use estimation method in the frequency domain rather than in the time domain. Specifically, this study is based on the long memory model and the fractional conintegration of time series.The results of our study can be summarized as follows. First, the implied volatility is a nonstationary long memory process, but the realized volatility is a stationary or a nonstationary long memory process. Second, Using bivariate-restricted GPH estimator and NBLS method, we find that two measures of volatility are in the fractional cointegration relationship. This implies that implied volatility has a long-run predictability on the realized volatility.
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