Stochastic interest rate volatility modeling with a continuous-time GARCH(1, 1) model

In this work, we develop a continuous-time GARCH(1, 1) (COGARCH(1, 1)) model driven by a NIG-Lévy process in order to analyze the volatility characteristics of Turkish interest rates. To our knowledge, this is the first work considering NIG-COGARCH modeling of interest rate data that utilizes the indirect inference method for parameter estimation. The discrete-time GARCH(1, 1) model has been used as a skeleton for building the NIG-COGARCH(1, 1) model. Daily interest rates on the Turkish two-year maturity treasury bond for the period between 02/01/2006 and 31/12/2010 have been used for the analysis. The empirical results show that the NIG-COGARCH(1, 1) model successfully captures the volatility clustering and heavy-tailed behavior of the interest rate returns and yields better in-sample estimations for conditional volatility in terms of forecast error statistics than the discrete-time model.