Empirical Studies On The Volatility Of Shangzheng 50ETF Options

In the BS option pricing model, the volatility is assumed to be constant, and it does not vary with the remaining duration and exercise price during the entire period of validity. However, the descriptive statistical analysis on the time series of Shangzheng 50ETF daily yields suggests that the time series have significant volatility clustering and the historical volatility shows obvious characteristics of mean reverting, which reflected more intuitively in the volatility cone.Statistical characteristics above indicate that the time series of daily yields may exist autocorrelation and autoregressive conditional heteroskedasticity, and there may be a long-term average for its historical volatility. The empirical studies based on the GARCH model make clear that the historical volatility have significant heteroskedasticity. The regression coefficients of ARCH and GARCH are 5.03% and 94.49% respectively, the long-term historical volatility is around 33.02%. The estimated variance equation of GARCH model can be modified to forecast the future historical volatility and the term structure of the volatility. It turns out that the fitting effect of the long term historical volatility is better than the short term and the forecasting accuracy will rise when lengthening the period of volatility. Though the fitting effect of term structure seems not very ideal, the modified variance equation can explain well how sensitive is the volatility term structure to the current volatility.In addition, the descriptive statistical analysis on the implied volatility surface showes the following results:as the maturity approaching, the implied volatility will rocket and show right upper skew along with the rise of the exercise price; simultaneously, the skewness will becomes sharper with the shrinkage of the remaining duration. Comparing the implied distribution with the standard normal distribution, it turns out that the right part thick-tail of the implied distribution is an important factor to the skew of implied volatility.