본 연구는 2004년 1월부터 2011년 12월까지의 일간자료를 활용하고, 또 그 기간을 금융위기 전, 금융위기 중, 그리고 금융위기 후로 구분한 후, 각 기간마다의 국내 지수옵션시장 내재변동성 특성이 어떻게 다른지를 관찰하였다. 우선 변동성스마일 현상과 관련 전체적으로는 원월물의 경우 변동성스마일의 형태가 좌우대칭의 형태에 가까우나 만기가 짧아짐에 따라 DITM에서 변동성이 크게 나타나는 비대칭 형태로 Sneer 현상이 나타나는 것을 확인할 수 있었다. 그리고 이런 현상은 금융위기 중에도 확인되고 있다. 다만 금융위기 중의 변동성은 금융위기 전후 기간에 비하여 전체적으로 높아져 있다는 것이 금융위기 기간과 그렇지 않은 기간 사이의 중요한 차이였다. 한편, 금융위기 중이거나 금융위기 전후 구분 없이 변동성 기간구조의 경우 만기까지의 기간이 줄어듦에 따라 변동성은 모두 커졌다. 특히 모든 기간 중 최근월물이 되면서 ATM에서 거리가 먼 DITM, DOTM의 변동성이 큰 폭으로 증가했다. 그런데 금융위기 중일 때와 금융위기 기간이 아닐 때의 차이도 함께 관찰됐다. 하나는 금융위기 중이 아닐 때에는 대부분의 경우에서 풋옵션의 변동성이 콜옵션의 변동성보다 약간 높았었다. 하지만, 금융위기 중에는 콜옵션의 DITM이 풋옵션의 DOTM에 비해, 또 콜옵션의 ITM이 풋옵션의 OTM에 비해 특히 근월물의 경우 그 반대의 현상이 나타났다. 또 하나의 중요한 차이는 금융위기가 아닌 기간 중의 DITM과 DOTM 기간구조가 비교적 완만한 지수함수의 모양을 보이고 있는데 반해, 금융위기 중의 그것은 결코 완만하지 않은 지그재그 형태의 복잡한 모양을 띠었다. 금융위기 전, 중, 후 기간의 콜옵션과 풋옵션의 결정계수에 대한 주요인 분석결과 Eigenvalue 값이 1보다 큰 주요인의 숫자가 금융위기 전, 중, 후 기간과 상관없이 모두 3개인 것으로 나타났다. 하지만 그 내용을 살펴보면 금융위기 기간이 국내 KOSPI 지수옵션에 구조적인 영향을 주었다라고 해석할만한 변화를 감지할 수 있었다.
Unlike active research on behaviors of implied volatilities in other countries, we are lack of systematic study on Korean option markets in this area. Recently, however, Ok and Lee (2010) studied behaviors of implied volatilities in terms of KOSPI200 index option market. Although their findings are interesting, their data set was not large enough to include the period of 2008 global credit crisis. One of the notable features during the crisis is that volatilities tend to be magnified, which has to be transferred into notable price changes in option markets. In this regard, Kang(2013) has found by analyzing KOSPI200 index options that zero-beta ATM straddle in Korea generates negative abnormal returns, which are not statistically significant. This result contrasts with empirical findings in other countries. Choi and Lee(2014), however, subsequently have noted that Kang’s result comes from the fact that he included the period of 2008 global credit crisis. By excluding this period, Choi and Lee (2014) showed that zero-beta ATM straddle in Korea generates perfectly consistent result with those of other countries. Being motivated by this result, we further investigate Ok and Lee (2010) by extending the period that certainly includes 2008 global crisis, as well as separating the duration of period into one that belongs to the crisis, and the other that does not.
Using daily data from Jan. 2004 to Dec. 2011, this study has analyzed behaviors of implied volatilities. In so doing, we have divided the period into three, that is, period before the credit crisis, period during the crisis, and period after the crisis. First of all, we have noticed volatility smiles for options that have relatively longer terms to maturity. For options with shorter terms to maturity, however, volatility sneers seem more prevalent. This phenomenon was noted even during the crisis. As expected, overall volatilities during the crisis were higher than those of before and after the crisis. Regarding the volatility term structure, implied volatilities increase as the term to maturity becomes shorter, regardless of whether the data are before, during, and after the crisis. Especially, volatilities of DITM, DOTM for the nearest maturities have increased the most. Nevertheless, there were significant differences between before-after the crisis and during the crisis. One is the fact that volatilities of put tend to be a bit higher than those of call during before-after the crisis, while the opposite is true during the crisis. The other is the fact that the volatility term structure has a smoothing exponential form during before-after the crisis, whereas it has a complicated zigzag form during the crisis. According to the principal component analysis, we have found that there exist 3 eigenvalues whose values happen to be greater than 1, regardless of the period. And yet, we have noted that in the case of put option, the 4th biggest eigenvalues during the crisis was very close to 1, while it was far away from 1 before-and-after the crisis. Also, by looking at component charts, there appear structural impacts on implied volatilities during the crisis that last even after the crisis. Based on these analysis, we can conclude that behaviors of implied volatilities during the crisis were different from those before-after the crisis, and during the crisis, there was a structural change. As a result, we need a caution in analyzing KOSPI200 option market when we include the period during the crisis.