Structural GARCH Code

This MATLAB package is used to estimate the Structural GJR-GARCH (SGJR) model from the Engle and Siriwardane paper Structural GARCH: The Volatility-Leverage Connection.

Running the Code

Clone this repository into your MATLAB working directory:

cd /home/user/projects/project/using/SGJR/
git clone [repository URI] ./sgjr  # creates an 'sgjr' directory in your working directory

Then, in your MATLAB code, add the SGJR directory to your path and reference it using the sgjr. prefix.

addpath(fullfile(pwd, 'sgjr'));
load(fullfile(pwd, 'sgjr', 'testData.mat'));
AIG_cell = struct2cell(AIG);
result = sgjr(AIG_cell{:}, zerocurve);

The call to the sgjr function will return an SGJR result object containing:

• parameters - A vector of parameters Structural-GARCH parameters of the form (omega, alpha, gamma, beta, phi)
• vcv - 5X5 QMLE Robust Variance-Covariance Matrix
• stdErrorsMLE - MLE standard errors
• stdErrorsQMLE - QMLE standard errors
• equityVariance - daily equity variance
• assetVariance - (T - burn_index) x 1 series of asset variances
• leverageMultiplier - (T - burn_index) x 1 series of leverage multiplier
• loglikelihood - log-likelihood at optimum
• BIC - Bayes Information Criterion
• numRuns - number of different starting parameters
• smoothedBvDebt - (T - burn_index) x 1 series of smoothed bvdebt
• mvEquity - (T - burn_index) x 1 series of market value of equity
• asset2Debt - (T - burn_index) x 1 series of B-S asset to debt series
• deltaImplied - (T - burn_index) x 1 series of B-S delta
• volatilityForecast - (T - burn_index) x 1 series of asset forecast vol
• tau - TODO - define
• gjr - Parameters from estimation of a GJR-GARCH regression on the returns provided

The burn_index parameter refers to the initial number of observations that are discarded when computing the likelihood function used for the optimization. This is done to minimize dependence on initial conditions.

Options

You can also pass in a forecastType option to specify either a 'Constant' or 'Dynamic' forecast ('Constant' is the default).

result = sgjr(AIG_cell{:}, zerocurve, forecastType, 'Dynamic');