  Risk measure forecast and model have been developed in order to not only
provide better forecast but also preserve its (empirical) property especially
coherent property. Whilst the widely used risk measure of Value-at-Risk (VaR)
has shown its performance and benefit in many applications, it is in fact not a
coherent risk measure. Conditional VaR (CoVaR), defined as mean of losses
beyond VaR, is one of alternative risk measures that satisfies coherent
property. There has been several extensions of CoVaR such as Modified CoVaR
(MCoVaR) and Copula CoVaR (CCoVaR). In this paper, we propose another risk
measure, called Dependent CoVaR (DCoVaR), for a target loss that depends on
another random loss, including model parameter treated as random loss. It is
found that our DCoVaR outperforms than both MCoVaR and CCoVaR. Numerical
simulation is carried out to illustrate the proposed DCoVaR. In addition, we do
an empirical study of financial returns data to compute the DCoVaR forecast for
heteroscedastic process.
