Common Factors and Local Factors in Variance Risks: Evidence from S&P500 and KOSPI200 Index Options

This paper conducts a factor analysis using the implied variances of S&P 500 index options and KOSPI 200 index options. After estimating the factors that influence variance risks, we rotate the factors to decompose them into a common factor and local factors. The results show that 10~12 percent of variance risks in both markets is explained by the common factor and 65 percent of S&P 500 implied variances and 70 percent of KOSPI 200 implied variances are explained by each local factor, which is in contrast to the results for bond markets that the most variation of interest rates could be explained by a common factor. To figure out the source of common and local factors, additionally, we adopt the regression models that incorporate the risk-neutral (RN) variance, skewness, and kurtosis as explanatory variables. Approximately, the common factor is mainly determined by the RN variance of the S&P 500 index and RN higher moments of the KOSPI 200 index. In contrast, the S&P 500 local factor is influenced by the RN variance of the S&P 500 index and the KOSPI 200 local factor is explained by the RN higher moment of the KOSPI 200 index.