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)