Abstract: The financial trading performance of any country rests mainly on the role of exchange rate, unambiguously the international trading activity. Thus, knowing the direction of exchange rates in future is one of the priorities of investors. For this purpose, the literature has several proposed models. One of them is geometric Brownian motion GBM model. Volatility or standard deviation is an important parameter, which has a direct effect on GBM model. In fact, there are many ways to compute volatility depending on historical data. This study compares the performance of four GBM models according to the way of computing volatility via forecasting exchange rates of EUR/USD, EUR/SAR and EUR/AUD. These models include GBM with constant volatility computed by three ways: first, simple volatility formula (GBM-S), second, log volatility formula (GBM-L), third, high-low-closed volatility formula (GBM-HLC), and finally GBM with stochastic volatility computed by deterministic functions σ(Yt) = Yt (GBM-STO). To evaluate the exchange rates forecasting methods, this study utilizes the mean square error (MSE). The results reveal that all models under study have high accuracy in forecasting exchange rates especially in stable markets. GBM-S has the highest performance with negligible difference of GBM-SV, while GBM-L introduces the lowest performance according to highest value of MSE.
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Keywords and phrases: geometric Brownian motion, exchange rate, stochastic volatility.
Received: January 23, 2022; Accepted: March 2, 2022; Published: April 18, 2022
How to cite this article: Mustafa Mansour and Mohammed Alhagyan, Forecast exchange rates of euro using geometric Brownian motion model according to four different ways to compute volatility, Advances and Applications in Statistics 76 (2022), 39-52. http://dx.doi.org/10.17654/0972361722035
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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