Computational training study based on a stochastic model for the currency exchange rate prediction

Abstract

In this work, we propose a methodology to predict the exchange rate of a given currency based on a stochastic differential equation of the Black-Scholes type, which is used to train the model for a given period and thus obtain the average return and volatility parameters. The prediction is made by solving the stochastic differential equation obtained through a stochastic extension of the fourth-order Runge-Kutta method. The method is explicitly applied to the EUR-MXN exchange rate and pre-COVID and post-COVID experiments are carried out to quantify the jump effects on the currency price. The results show that jump effects in predictions can be smoothed by increasing the training time, although the possible deviation from actual values would increase. On the other hand, if a better prediction is desired, it is advisable to use prediction periods and training times that are small enough to avoid jumps or instabilities.