변동성지수의 미래예측력에 대한 연구 (The Predictability of Volatility Index in KOSPI200 Option Market)

서지정보

· 발행기관 : 한국금융학회
· 수록지 정보 : 금융연구 / 22권 / 3호 / 1 ~ 33페이지
· 저자명 : 엄영호, 지현준, 장운욱

초록

변동성지수는 옵션가격에 내재되어 있는 미래 변동성에 대한 기대를 지수화하여 표현한 것이며 미국, 독일 등의 증권거래소에서는 변동성지수의 발표뿐만 아니라 지수관련 파생상품도 거래되고 있다. 국내의 경우에는 아직까지 변동성지수를 공식적으로 발표하지 않고 있으나, 장외파생상품시장의 성장에 따른 변동성 헤지수요의 증가와 새로운 상품에 대한 수요의 증가 등으로 인해 변동성지수에 대한 관심이 크게 증가하고 있다. 변동성지수는 변동성에 대한 헤지기능과 함께 시장위험에 대한 지표의 기능을 할 수 있으며 미래 실제변동성에 대한 예측치의 역할을 할 수 있다.
미래 실제변동성에 대한 예측치로서 변동성지수 혹은 내재변동성의 유용성에 대한 기존연구들에서는 일별 자료를 이용하여 변동성지수가 실제변동성의 불편추정량은 아니지만 실제변동성에 대해 예측력을 갖는 것으로 설명하고 있다. 그러나 실제 2차적률에는 위험중립 2차적률 뿐만 아니라 고차적률까지 포함될 수 있다는 Bakshi, Kapadia and Madan(2003)의 연구를 고려할 경우 계량경제학적으로 중요변수 누락문제(omitted variable problem)가 발생할 수 있으며, 이는 변동성지수의 불편성(unbiasedness) 및 예측력 검증과정에 영향을 미칠 수 있다.
이에 본 연구에서는 1999년부터 2006년까지의 KOSPI200 지수옵션자료를 이용하여 변동성지수를 월별로 산정하고 실제변동성에 대한 예측력을 살펴보았다. 연구결과 측정오차를 고려하거나 고차적률을 고려할 경우 변동성지수의 실제변동성에 대한 불편성을 기각하지 못하고 실제변동성의 과거변수에 비해서도 높은 예측력을 나타냈다.

영어초록

Since the introduction of volatility indices, futures and options on the index have been traded in some derivative exchanges in the US and some European countries. Introducing similar volatility index is also now considered by the Korea Stock Exchange because of the increasing needs of hedge instruments in the fast-growing OTC markets. Furthermore, volatility indices measure market expectations of near term volatilities implied in stock index option prices. Thus, volatility index is not only important in hedging market volatility risk, but also useful in predicting future volatility and measuring market’s fear.
There have been many empirical tests about the predictability to the actual volatility and most of them were focused on the Black-Scholes implied volatility or the volatility index based on variance swap (hereafter VIX) or Black-Scholes implied volatility (hereafter VXO). Previous studies indicate that the volatility index or the Black-Scholes implied volatility has predictability to the future actual volatility though they are not unbiased estimators.
However, there might be some econometric problems in testing the predictability to the actual volatility. One of classical problems is the measurement error problem caused by low-liquidity or non-synchronous data and an over-lapping data problem mentioned by Christensen and Prabhala (1998). Also, Bakshi, Kapadia and Madan(2003) showed that higher moments of risk-neutral measure can affect to the actual volatility and in this case there may be an omitted-variable problem, which may result in the biasedness in the tests.
Besides these econometric problems, there are some measurement issues in estimating the actual volatility (the realized volatility based on intra-data and the sample standard deviation) and constructing the volatility index (VXO, VIX and splined VIX).
The purpose of this study is to empirically test whether volatility index is an unbiased estimator of the future actual volatility. Firstly, according to the result of Bakshi, Kapadia and Madan(2003), we test the predictability of the volatility index with the risk-neutral higher moments. Secondly, we test the predictability with considerations of measurement error problems. We use the data of specific time in trading hour to avoid non-synchronous problem and monthly data for using non-overlapping data. We use an instrumental variable regression method in estimating as well. Also for the robustness test of the results, we construct various volatility indices with respect to data types and numericlal methods and investigate their effects on the predictablility power. Finally, in the test we use the realized volatility of Andersen et al.(2001) as well as a sample standard deviation as the proxy for the future true realized volatility.
We test with the monthly volatility index constructed by the KOSPI200 index option data for the sample period covered from 1999 to 2006. The results indicate that the volatility index has predictability to the actual volatility and has higher predictability power than the historical volatility(past sample standard deviation). In case of the realized volatility, the volatility index is better than the past realized volatility in forecasting the actual volatility when considering measurement error.
The volatility index is an unbiased estimator when we take the measurement error or the omitted-variable problem into account, while it’s a biased estimator in general regression test. The VIX index is predictable to the actual volatility as much as the VXO index, but the former is less sensitive to data or construction method.
These results shows that the unbiasedness of the volatilty index to the actual volatility is not rejected when some econometric issues are considered and that the volatility index has higher predictability power than those of other volatility measures such as past actual volatilities.

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