Title: Term structure modelling with quadratic CARMA processes

Authors: Zhigang Tong

Addresses: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

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.

Keywords: term structure; interest rates; continuous time autoregressive and moving average; CARMA; quadratic modelling; Kalman filter; continuous time models; bond prices; bond yields; forecasting.

DOI: 10.1504/IJBD.2016.081373

International Journal of Bonds and Derivatives, 2016 Vol.2 No.4, pp.285 - 303

Received: 14 Jan 2016
Accepted: 18 Jan 2016

Published online: 06 Jan 2017 *

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