KOSPI 200 주가지수옵션 추정변동성의 실현변동성 설명력에 관한 비교연구

Abstract

옵션변동성을 계산하기 위해서 블랙-숄즈모형을 이용한다. 그러나 블랙-숄즈 내재변동성은 미래변동성에 대한 불편추정치이지만 실제 예측에는 편의가 존재하는 것으로 알려져 있다. 본 연구에서는 일정한 모형 없이 변동성을 계산하는 모델-프리 내재변동성을 도출한다[Britten-Jones and Neuberger(2000)]. 이는 이전의 연구들처럼 정해진 모형을 기준으로 내재변동성을 계산하는 것이 아니라 다양한 만기의 옵션에 내재된 변동성을 적분하여 계산하는 것이다. 미래변동성에 대한 효율적인 추정방법을 분석하기 위해서 본 연구에서는 일정시점을 기준으로 실현변동성을 미래변동성이라 가정하고, 블랙-숄즈내재변동성과 모델-프리내재변동성 및 과거변동성의 예측력을 비교한다.

The estimation of future volatility(FV) is important for asset pricing, portfolio decision and risk management. Various methods are suggested to forecast the future volatility. Volatility estimated from past data is called historical volatility(HV), and that calculated from the option price is called implied volatility(IV). For the computation of IV, any option pricing model is used. Black-Scholes implied volatility(BSIV) is computed from the well-known Black-Scholes formula. The formula is fitted with market observed data and it is solved for the only unknown variable, i.e., volatility. BSIV is generally found to be better than the historical volatility in forecasting the future volatility. However, BSIV has a few drawbacks. One is that the model is not much successful in fitting the option prices, and it is not guaranteed the model is correct one. Second, the usual tradition in using the BSIV is that only at-the-money options are used. It is well-known that IV's of in-the-money or out-of-the-money options are much different from those estimated from near-the-money options. It is so called volatility smile phenomena. BSIV literatures are ignoring the information contained in in-the-money or out-of-the-money options. In this regard, a new model is confronted with Korean market data. Britten-Jones and Neuberger(2000) derive a formula for volatility which is a function of option prices. Since the formula is derived without using any option pricing model, volatility estimated from the formula is called model-free implied volatility(MFIV). MFIV overcomes the two drawbacks of BSIV. Firstly, since it is independent of any model, it is free from the issue of model fitness for market price. Secondly, it exploits all available market prices and informationally efficient. Jiang and Tian(2005) show that the MFIV is estimable with market observed option prices. They show that, with the S&P index options(SPX), MFIV is superior to HV or BSIV in forecasting the future volatility. In this thesis, the performance of MFIV is compared with that of the other volatilities with KOSPI 200 index options. To estimate the performance of estimated volatilities, realized volatility(RV) is regressed on various combinations of volatilities. Regression results confirm the findings similar to those of Jiang and Tian(2005). In KOSPI 200 index options, MFIV, BSIV and HV have some predictive power for realized volatility. However, none of them is surely said to be an unbiased estimator for RV. Among those three estimators, MFIV is closest to the unbiased estimator. When the forecasting performances are compared, MFIV is better than any other estimated volatilities. The hypothesis that MFIV contains all informations for realized volatility and the other volatilities are redundant is not rejected in any cases. In Jiang and Tian(2005), this hypothesis is not rejected in regressions with log volatilities. Therefore, in Korea, MFIV can be a better predictor for future volatility than that of the United States.