The Relationship of Volatility with Stock Index Option Returns and Prices - Tabassum, Saima (2020)
This paper attempts to identify different kinds of volatilities such as backward looking which includes realized volatility and conditional volatility and forward looking which includes implied volatility. As the report deals with time series data hence the Dickey-Fuller unit root and Engle-Granger cointegration tests are done to check for the stationarity and long term impacts of the data. I have conducted a study attempting to model the relationship between these mentioned volatilities of S&P 500 index stock option with their values and returns using the multiple and simple regression with robust standard error for considering the heteroskedasticity. The Pearson correlation analysis has been done to investigate the correlation between the volatilities, prices, returns and vega index. The paper also tried to portrait the real world scenario of using high-frequency data including its advantages and limitations. I have found that the realized and conditional volatilities of S&P 500 stock index option, have a negative relation with the first difference of historical daily prices and have a positive relation with the first difference of its daily returns at 1% significant level from 2010 to 2019 whereas the first difference of implied volatility has a negative relation with the first difference of its prices and have a positive relation with the first difference of its returns at 1% significance level. Again, I also observed that the vega index of currently trading S&P 500 stock option index has a statistically negative relation with its return at 1% significance level.