주가지수 옵션 횡단면 정보의 미래 기대변동성 예측력에 관한 연구

It is often said that investors’ expectation about market volatility and risk premium is reflected in stock index option price (implied volatility), precisely speaking, cross-sectional information of stock index option market. For example, it is well-known that “Volatility smile” or “volatility skew” is one of the phenomena which can represent investors’ expectation or risk premium related to market uncertainties. However, abnormalities may exist in the market as well. Some authors have been argued about “overvaluation puzzle of put option price.” Broadie, Chernov, and Johannes (2009), Bondarenko (2014) have claimed that it is hard to explain every dimension of overvaluation phenomenon of put option price under the existing theoretical models, because these cross-sectional unprecedented phenomena are reflecting demands of abnormal premium for market volatility and uncertainty, and thus the excessive volatility skew or unusual volatility shape sporadically occurs. This study puts a concern about information implied in cross-sectional abnormalities rather than it investigates the abnormalities themselves. Many articles have demonstrated that when investors demand abnormal premium or have extremely biased expectation over economic uncertainty, prices of related options tend to be extremely overvalued or undervalued. Based on this empirical tendency, we can infer that a situation where investors’ overvaluation (undervaluation) of put options deepens might lead to decrease (increase) in market volatility for the future with a high possibilities. Accordingly, using this inference, we can predict volatility (price of options) if we can know when we observe overvaluation or undervaluation. Therefore, our goal is to examine the prediction power of the inflection point of the future expected market volatility using cross-sectional information of the KOSPI 200 options. To this end, we first use probit model to test for the prediction power of the cross-sectional information of the options. The implied volatility of at-the-money option is used as a proxy variable for the expected market volatility in the model. We use two independent variables sets which can be obtained from cross-sectional stock index options. The one of the set is kurtosis and skewness which are higher moments of the implied risk neutral probability density, and the other set is slope and curvature of volatility curve which are main concerns of this study. Second, we present virtual investment strategies using the VKOSPI, the daily volatility index provided by KRX, to examine the effectiveness of the investment strategy of expected volatility based on our prediction model. Our prediction tests are two-folded in terms of dependent variables. The first one is min/max method measured by peaks and troughs of expected volatility and another one is up/down method measured by expected volatility’s % change of volatility at each time interval. And then, each method is categorized into 4 sub-tests by differing independent variables, such as implied higher moments and pairs of information of volatility curves. Thus, we test the 8 sub-models of prediction in total and compare their prediction power of the cross-sectional information of the options. The results show us that first, the expected volatility seems to be near the trough (peak) when skewness or slope is getting higher (lower) and kurtosis or curvature is getting higher. Second, the prediction power of our model is strong enough to capture the expected volatility located in the near-troughs and the near-peak area. Third, prediction power is improved when the implied kurtosis or curvature is added to the model, rather than only using skewness or slope. Fourth, prediction power is relatively high when information of volatility curve, rather than implied risk neutral probability density, is used. Since slope and curvature of volatility curve are more related to the information of deep-out-of-the-money option, it can be interpreted that they are useful to predict the inflection point of expected volatility with higher prediction power. Moreover, Our empirical findings mentioned in the above works well in out-of-sample prediction as well as in-sample prediction. Using the probability obtained from the prediction model with slope and curvature of volatility curve, we found that the strategy that virtually invest in VKOSPI index outperforms others. Surprisingly, the 2008 financial crisis at which the volatility is soared up, and subsequent period at which volatility trend shows decreasing are also well captured from out-of-sample prediction. Therefore, we can conclude that our prediction model is a useful strategy of defensive investment in the practical portfolio point of view.