Term structure modelling with quadratic CARMA processes
by Zhigang Tong
International Journal of Bonds and Derivatives (IJBD), Vol. 2, No. 4, 2016

Abstract: In this paper, we develop a continuous time term structure of interest rates model which generalises the quadratic models. We model the underlying state variables as continuous time autoregressive and moving average (CARMA) processes and the short rate is a quadratic function of state variables. We derive the analytical solutions to bond prices and yields. We estimate the new quadratic model through the Kalman filter. Our empirical work shows that the quadratic CARMA model improves the performance of both linear CARMA models and standard quadratic models significantly in terms of in-sample model fit and out-of-sample forecasting power.

Online publication date: Fri, 06-Jan-2017

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