Modelling the term structure of implied volatility stock options on the JSE Limited

Abstract: This paper models the implied volatility skew of the JSE Top 40 options, with the aim of producing useful forecasts for option traders based on weekly historical data over a 388 week period. The comovements of implied volatility for 51 rates moneyness, ranging from out-of-the money to in-themoney are statistically investigated. The dissertation demonstrates that the 51 rates of moneyness can be reduced to fewer dimensions of three uncorrelated variables known as principal components. These variables account for the trend, slop and curvature of the implied volatility skew, which on average, explain more than 99% of the movements of the implied volatility skew across the study sample. Instead of forecasting the volatility skew using the 51 rates of moneyness, the three principal components are forecasted using ARMA models, and results of forecasts are transformed to forecasted implied volatility. The out-of-sample accuracy of these models is tested against actual observed figures, and was found to correctly predict both the sign and magnitude 57.5% of the time. To illustrate the applicability of this research, an example was used to show the benefit of such forecast. The approach used in the research is easily transferable to the term structure as well, which can potentially give a better understanding of the entire implied volatility surface.M.Com. (Financial Economics in Economics and Econometrics