Abstract
A Value-at-Risk (VaR) forecast may be calculated for the case of a random loss alone and/or of a random loss that depends on another random loss. In both cases, the VaR forecast is obtained by employing its (conditional) probability distribution of loss data, specifically the quantile of loss distribution. In practice, we have an estimative VaR forecast in which the distribution parameter vector is replaced by its estimator. In this paper, the quantile-based estimative VaR forecast for dependent random losses is explored through a simulation approach. It is found that the estimative VaR forecast is more accurate when a copula is employed. Furthermore, the stronger the dependence of a random loss to the target loss, in linear correlation, the larger/smaller the conditional mean/variance. In any dependence measure, generally, stronger and negative dependence gives a higher forecast. When there is a tail dependence, the use of upper and lower tail dependence provides a better forecast instead of the single correlation coefficient.
Highlights
A Value-at-Risk (VaR) forecast is crucial as a main reference for banking and insurance industries in assessing their financial risk performance as well as in allocating their capital
Forecasting VaR, in general, requires the quantile of the loss distribution; later, we name this as the quantile-based VaR forecast which will be described in Section 2 through simulation
We aim to explore the VaR forecast in a different direction for a random loss that depends on another random loss, i.e., forecasting VaR for dependent losses
Summary
A Value-at-Risk (VaR) forecast is crucial as a main reference for banking and insurance industries in assessing their financial risk performance as well as in allocating their capital. We visualize such estimative VaR forecasts along with their coverage probability via distribution function and probability function.
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