Application of Geometric Brownian motion in prediction of gold price and currency rate

Variables such as exchange rates and gold prices has a great importance for economic actors therefore the aim of this study were determined as prediction of U.S Dollar exchange rate and gold coin price in Iran Market. Forecasting has been done by Geometric Brownian Motion model that is considered as one of the stochastic differential equations. Data were collected and analyzed in the period from the beginning of 1392 until the end of 1395. also forecasting prices for each under study time series has been done in various forecasting horizons involved 7, 14, 21, 30, 60, 90, 180 and 360 day time period. The results show that Geometric Brownian Motion model can simulate the prices of gold coin and exchange rate highly accurate in accordance with the criteria of mean absolute percentage error. Also The other results obtained from this study is that According to ten different prediction accuracy criteria, By increasing the forecast horizon, ability of the GBM model in simulation and forecasting exchange rates and the price of gold coin decreases.