The effects of incorporating memory and stochastic volatility into GBM to forecast exchange rates of Euro

The performance of financial trading in any country depends significantly on the role of exchange rate, specifically the activity of international trading. Thus, one of the priority of stakeholders is knowing the direction of exchange rates in future. For this reason, many models in literature are proposed. Geometric Brownian motion GBM model is one of them. This paper studies the affection of incorporating memories and stochastic volatility SV assumption on EUR by forecasting exchange rates of EUR/USD, EUR/SAR and EUR/AUD. The forecasting done depending on three models including GBM (no memory), geometric fractional Brownian motion GFBM (one source of memory) and GFBM perturbed by SV that obeys fractional Orenstein-Uhlenbeck process (two sources of memory). The findings show that GFBM perturbed by SV has the best performance according to the smallest value of mean square error MSE. This result shows the positive effects to incorporate two sources of memory and SV assumption into GBM and thus it can apply in forecasting future prices of exchange rates of for EUR/SAR, EUR/USD and EUR/AUD.