The main objective of this work is to test whether some stochastic models typically used in financial markets could be applied to the COVID-19 pandemic. To this end we have implemented the ARIMAX and Cox-Ingersoll-Ross (CIR) models originally designed for interest rate pricing but transformed by us into a forecasting tool. For the latter, which we denoted CIR*, both the Euler-Maruyama method and the Milstein method were used. Forecasts obtained with the maximum likelihood method have been validated with 95% confidence intervals and with statistical measures of goodness of fit, such as the root mean square error (RMSE). We demonstrate that the accuracy of the obtained results is consistent with the observations and sufficiently accurate to the point that the proposed CIR* framework could be considered a valid alternative to the classical ARIMAX for modelling pandemics.