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In the current paper, we proposed a method to estimate value-at-risk (VaR) for the model with
GARCH effect when the distribution of independent innovations of the residuals of the GARCH
model has a mixture of generalized hyperbolic secant distribution (GHSD), with two tailed ge-
neralized Pareto distributions (GPD), and estimating the parameters of the GHSD and the GPD
distributions by the Bayesian inference approch.
This approach has two steps : The first step is the estimation of the variability (volatility) followed
by the GARCH model using the maximum likelihood method. The second step is used to take
into account the uncertainties in the parameters, including the a priori information to estimate
the parameters of the hyperbolic secant distribution (GHSD) and (GPD) distributions to obtain
the a posteriori distribution of the parameters. We apply the mixture model to the innovations
obtained from the residuals to derive the value-at-risk (VaR) estimates.
