A mathematical model for stock price forecasting

Abstract

Many mathematical models of stochastic dynamical systems were based on the assumption that the drift and volatility coefficients were linear function of the solution. In this work, we arrive at the drift and the volatility by observing the dynamics of change in the selected stocks in a sufficiently small interval Δt . We assumed that only one change occurs within Δt = t _i+1 - t_i. During this time, a stock may gain one unit [+1], remain stable [0], or loss one unit [-1]. The likelihood of each change occurring were noted and the expectation (the drift) and the covariance (the volatility) of the change were computed leading to the formulation of the system of linear stochastic differential equations. To fit data to the model, changes in the prices of the stocks were studied for an average of 30 times. A simple checklist was used to determine the likelihood of each event of a loss, again or stable occurring. The drift and the volatility coefficients for the SDE were determined and the multi-dimensional Euler-Maruyama scheme for system of stochastic differential equations was used to simulated prices of the stocks for 1 < t < 30. The simulated prices was compared to the observed price and we observed that the simulated prices is sufficiently close to the observed price and there for suitable for forecasting the price of the stocks for a short time interval. 

Key words: stock price forecasting, system of linear stochastic differential equations, model, volatility coefficients, simulate, forecasting