MODIFICATION OF HESTON’S MODEL FOR STOCK MARKET
Abstract
This research work is centred on the return on investment that informs investors and entrepreneurs on general performance of a company. The research problem was a modification of an existing model. This was done by incorporating rate of reinvestment of return and return on investment that follow random process. In addition to the modification, the existing model was extended from a two to four compartment stochastic differential equation. Formulation of a four- compartment stock market model was based on a four dimensional geometric Brownian motion. The compartments were that of stock price, stock price volatility, return on investment and return on investment volatility compartment. The solution of a four-compartment stock market model was proved to exist and also unique. The Octave programming language was used to implement the simplified stochastic Runge-Kutta
(SSR-K) scheme. Data were collected from Nigerian Stock Exchange (NSE) for the period of 2007 -2014 to validate the model formulated. It was found that, the stock price, stock price volatility, return on investment and return on investment volatility
follow random (stochastic) process. The correlation between the empirical stock price on the other hand and the corresponding computed values on the other hand from the model formulation was found to be significant as the significant value was zero
(0).The absolute error of the empirical return on investment and the corresponding computed values from the model formulation was found to be zero(0). Implying that, the computed results agreed very well with the empirical values. In addition, results
showed that stock price increases when return on investment decreases. We concluded that return on investment was considered to be the best index to use to study the general performance of companies rather than stock price.
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