Ito's Calculus for Stock Price Prediction for the Johannesburg Stock Exchange Market

Abstract

The Johannesburg Stock Exchange is positioned as the leading African stock market and listed among the top twenty in the world, considering market capitalization. Price prediction remains at the center of concerns for stock markets in Africa and the world. Ito's calculus has extended the calculation methods to stochastic processes, Brownian motion, and stochastic differential equations with some relevant applications in mathematical finance. This work aims to present a rigorous mathematical justification for the models used by financial practitioners for pricing derivatives and managing risk. Additionally, this research will develop mathematical models, background of pricing models with comprehensive proofs, and test their reliability with historical data collected from the Johannesburg Stock Exchange for future decision-making.