Stochastic differential equation approach for daily gold prices in Sri Lanka

Abstract

In our day to day life, predictability of gold prices is significant in many domains such as economic, financial and political environment. The objectives of this research are to study the behavior of the gold price in Sri Lanka, to forecast the daily gold prices making use of four Stochastic Differential Equation (SDE) models, Brownian motion, Geometric Brownian motion, Cox-Ingersoll-Ross (CIR) model and Vasicek model and compare the results with an ARIMA (2,1,2) model which is used to forecast the Sri Lankan gold prices in a previous research. The daily gold prices per troy ounce in Sri Lanka are obtained from 01st of October 2015 to 14th of October 2016 from the website http://www.cbsl.gov.lk/htm/english/_cei/er/g_1.asp on 1st of November, 2016. The gold prices from 01st of October 2015 to 07th of October 2016 are used to estimate the parameters of the four models and the parameter estimation is done using maximum likelihood estimation method. The gold prices from 10th of October 2016 to 14th of October 2016 are used to forecast the gold price. By taking the gold price on 10th of October 2016 as the initial value, daily gold prices from 11th of October 2016 to 14th of October 2016 are forecasted. Numerical approximations are carried out using Euler-Maruyama approximation method and the Monte Carlo simulation technique is used to simulate the daily gold prices. After evaluating forecasting accuracy of estimated models and existing ARIMA (2,1,2) model by root mean square error (RMSE) and mean absolute percentage error (MAPE), it turns out that the Vasicek model has the minimum RMSE and MAPE values for the given data set. The price of the gold may change rapidly because of some economic factors such as inflation, currency exchange rates etc. In these situations the best SDE model to forecast the daily gold price in Sri Lanka may be changed to another model. Hence this method is suitable for short runs only.