Continuous - time Interest Rate Differential Models

In continuous time, UIP is a stochastic differential equation. The solution of this differential equation, provides the log of exchange rate as a nonlinear function of the exogenous interest differential. In this sense, understanding dynamic properties of the interest rates differential is a natural starting point to understand exchange rate dynamics. Due to this reason we empirically examine various continuous-time models for the interest differential to check whether the model can produce many nonstandard features in the data and to compare performance of the models. If the interest rate differential model can generate empirical features of the data, this features can be transferred into the exchange rate solution in the process of the solving stochastic differential equation. Models we consider are mean-reverting, regulated Brownian motion, and regulated jump-diffusion model. To investigate the properties of the model and to examine its ability to explain the data we compare moments and other key features of the pseudo-data generated by the models and actual data. For this, we simulate the model by setting the parameters of the continuous-time model to point estimates obtained by the simulated method of moments (SMM). All models are able to generate high degree of persistence with high values of the autocorrelation coefficients. Median values of the simulated volatility are very similar to the volatility from the data and all models produce strong ARCH effects in interest rate differential. Out of the models, simple mean-reverting model performed reasonably well.