Journal of Computational Finance

Analytic derivatives of asymmetric Garch models

George F. Levy


The model parameters of a Garch process can be estimated by using numerical optimization to maximize the log-likelihood. However, widely used optimization techniques (such as Newton methods) require information concerning the derivatives of the log-likelihood. This paper presents computer algorithms that compute the analytic derivatives of asymmetric regression-Garch(p,q) processes, with series shocks from either a Gaussian distribution or a Student’s t-distribution. Initial estimates and pre-observed values for the Garch model parameters are also discussed. Monte Carlo simulation results are presented which compare the results obtained using both analytic and numeric derivatives. It is found that the numeric derivatives are faster but provide less accurate parameter estimates for short Garch sequences.

To continue reading...

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an indvidual account here: