Numerical Solution of Nonlinear Schrodinger Approaches Using the Fourth-Order Runge-Kutta Method for Predicting Stock Pricing

Abstract

Stocks are a certificate that shows the book of ownership of a company. The certainties of stock price are important for investors. This study aims to predict changes in stock prices. The predicting model of the stock prices in this study uses the non-linear Schrodinger equation. Because this equation has no known analytical solution, so a numerical solution that calculated using the fourth-order Runge-Kutta method to determine the stock prices. This research will also develop an algorithm of numerical solutions in the fourth-order Runge-Kutta method. The analogy of parameters between the nonlinear Schrödinger equation with economic parameters that affect stock prices is obtained based on the hypothesis and the economic theory. The assumed main parameters influence stock prices include movement or growth in average stock prices that is volatility, strike price, speed of average stock returns, adaptive market potential, and current stock price. This present method has been validated to predict the real stock prices of two companies. The prediction results obtain the value of mean absolute percentage error (MAPE) of Astra Agro Lestari Tbk. (AALI) is 0.4633 % and Polychem Indonesia Tbk. (ADMG) is 3.48678 %. Based on these MAPE results, the non-linear Schrodinger equation has shown that good agreement with the real stock price.