Discrete-time Affine Term Structure Models can be expressed in AR (1)-ARCH form, but it is not possible to get a non-negative vari- ance equations simply by restricting the parameters. In this paper we resort to a 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 Gamma conditional noise distribution. This way we get a well defined volatility process that avoids any prob- lem both in generating processes and in computing the conditional likelihoods of observations. The log-likelihood function is derived for one- and multi-factor specifications. Moreover, we implement a one-factor estimation both with simulated and US interest rate data. Finally, we compare the estimation results with a standard ATSM with Gaussian disturbances.
Discretete-time affine term structure models: an econometric formulation
FANTAZZINI, DEAN;MAGGI, MARIO ALESSANDRO
2005-01-01
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 vari- ance equations simply by restricting the parameters. In this paper we resort to a 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 Gamma conditional noise distribution. This way we get a well defined volatility process that avoids any prob- lem both in generating processes and in computing the conditional likelihoods of observations. The log-likelihood function is derived for one- and multi-factor specifications. Moreover, we implement a one-factor estimation both with simulated and US interest rate data. Finally, we compare the estimation results with a standard ATSM with Gaussian disturbances.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
