Continuous time modeling of interest rates: An empirical study on the Turkish short rate

We proposed a continuous time ARMA known as CARMA(p,q) model for modeling the interest rate dynamics. CARMA(p,q) models have an advantage over their discrete time counterparts that they allow using Ito formulas and provide closed-form solutions for bond and bond option prices. We demonstrate the capabilities of CARMA(p,q) models by using Turkish short rate. The Turkish Republic Central Bank’s benchmark bond prices are used to calculate short-term interest rates between the period of 15.07.2006 and 15.07.2008. ARMA(1,1) model and CARMA(1,0) model are chosen as best suitable models in modeling the Turkish short rate.