Title: Discrete-time affine term structure models: an ARCH formulation

Authors: Alessandro Carta, Dean Fantazzini, Mario A. Maggi

Addresses: Department of Statistics, University of Warwick, CV4 97L, Coventry, UK. ' Moscow School of Economics, Moscow State University, 1, Building 61, Leninskie Gory, Moscow, Russia. ' Facolta di Economia, Universita' di Pavia, via San Felice, 5, 27100 Pavia, Italy

Abstract: Discrete-time affine term structure models can be expressed in AR(1)-ARCH form but it is not possible to get a non-negative variance equation only by restricting the parameters. In this paper, we use distribution assumption in order to assure the variance to be non-negative. We present a complete formulation for one-factor and multi-factor models with inverse Gaussian conditional innovations distribution. Moreover, we derive the log-likelihood functions and implement a two-factor empirical specification analysis, both with simulated and US interest rate data. We compare the estimation and forecasting results with a AR(1)-GARCH(1,1) model.

Keywords: ARCH; discrete-time ATSM; affine term structure models; maximum likelihood estimation; VAR; interest rates; financial risk.

DOI: 10.1504/IJRAM.2009.022203

International Journal of Risk Assessment and Management, 2009 Vol.11 No.1/2, pp.164 - 179

Published online: 22 Dec 2008 *

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