Stochastic interest rate modelling with continuous-time GARCH(1,1) model

There is a massive amount of study deals with the stochastic modelling of the interest rates. The first approach to specify the interest rate movements as continuoustime Ito process was introduced by Merton in 1973. But his approach had many shortcomings including possibility of negative interest rates. In his seminal work in 1977, Vasicek developed Merton’s model by introducing mean-reverting characteristics of the data. Vasicek model is an Ornstein-Uhlenbeck type of process but this model do not eliminate the possibility of generating negative interest rates either. Moreover, it is not an adequate model for the interest rates because it does not corporate the conditional volatility characteristics of the data. (Anderson and Lund, 1997). In order to deal with these drawbacks Cox, Ingersoll, and Ross (1985) introduced their square-root model in the general equilibrium context. Mean-reverting and ’level effect’ characteristics of the CIR model helped in eliminating the possibility of negative interest rates and represent the conditional heteroskedasticty characteristics of the data.