Modelling implied volatility in South African stock options: a comparison of statistical and machine learning methods

Abstract

The Black-Scholes model is used to derive the price of an option. Two of the underlying assumptions is that of constant volatility and normality in stock price returns. Volatility is often modelled using various statistical and machine learning methods. This research focused on the use of GARCH, EGARCH, APARCH and LSTM models to predict the volatility underlying the All Share Index, a South African stock index. Exploratory data analysis indicated that the ALSI exhibited the leverage effect, long memory properties and asymmetry in its returns and that the traditional models such as ARCH and GARCH may not be sufficient to model stock price volatility. These models will therefore be used as benchmark models against the APARCH, EGARCH and LSTM models. The ARMA(3,3)-EGARCH(1,1) model outperformed the other models considered. While LSTM models can add value in the estimation of stock price volatility, they are highly sensitive to the selected hyperparameters and architecture used.