Stochastic modeling of currency exchange rates with novel validation techniques

To properly manage market risk industrial companies use tools based on value-at-risk, which requires proper modeling of future risk factors dynamics. One of the major challenges faced by this technique applied to modeling currency exchange rates is the choice of an appropriate model for simulation of the future paths. In order to fit the data, it should reflect its properties including heavier than Gaussian tail distributions, stabilizing volatility and mean reversion in long term horizon. In this paper, we propose to apply the Chan–Karolyi–Longstaff–Sanders (CKLS) model for the description of currency exchange rates data. This model was introduced for describing the evolution of the short interest rate and could be considered as the natural extension of the classical Ornstein–Uhlenbeck process. The standard version of CKLS process was based on the Brownian motion (BM). However, it can be easily extended to any class of distributions. Since the financial data of interest exhibit non-Gaussian behavior, we modified the CKLS model to use skewed generalized Student’s t-distribution (SGT). In this paper, we apply the generalized method of moments to estimate the parameters of the CKLS/SGT process. The accuracy and behavior of the estimators are analyzed using Monte Carlo simulations. Further, we propose a new validation and selection technique. We apply the CKLS/SGT and GBM models to two currency exchange rates and compare their performance.