Investigating the Performance of Stochastic Processes in Modeling the Savings Deposits

One of the most important actions on risk management is to obtain correct and rigorous information from the nature of the time series which are known as risk drivers. In this paper we introduce a model for interest free deposits using stochastic processes. To this end we use the geometric Brownian motion, jump-diffusion, Cox- Ingersol-Ross and mean-reversion models. Also to develop the approach we decompose the volatility of the time series into deterministic and stochastic parts and model the stochastic part only. The deterministic part is the sum of trend line and periodic cycles. We observe that after estimation of parameters and model calibration, the results are consistent with initial expectations which are as follows: The performance of the models increases with separation of deterministic and stochastic parts. Although at the same time the phenomenon of mean reversion and heavy tail is approved, but, Cox-Ingersol-Ross model show a better behavior than jump-diffusion model. Finally the man-reversion and Jump-diffusion models have better performance than other models.