변동성지수의 미래예측력에 대한 연구

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.