We consider joint estimation of conditional Value-at-Risk (VaR) at several levels, in the framework of general conditional heteroskedastic models. The volatility is estimated by Quasi-Maximum Likelihood (QML) in a first step, and the residuals are used to estimate the innovations quantiles in a...

In the Basel regulation the required capital of a financial institution is based on conditional measures of the risk of its future equity value such as Value-at-Risk, or Expected Shortfall. In Basel 2 the uncertainty on this equity value is captured by means of changes in asset prices (market...

We provide a rigorous proof of granularity adjustment (GA) formulas to evaluate loss distributions and risk measures (value-at-risk) in the case of heterogenous portfolios, multiple systematic factors and random recoveries. As a significant improvement with respect to the literature, we detail...

As international financial integration gathers pace, interconnectivity has increased tremendously among financial institutions, financial markets and financial systems, a phenomenon to which the recent global financial crisis perhaps provided the best testimony. The interconnectivity among...

Standard risk measures, such as the Value-at-Risk (VaR), or the Expected Shortfall, have to be estimated and their estimated counterparts are subject to estimation uncertainty. Replacing, in the theoretical formulas, the true parameter value by an estimator based on n observations of the Profit...

This paper assesses systemic linkages among banks in Hong Kong using the risk measure "CoVaR" derived from quantile regression. The CoVaR measure captures the co-movements of banks¡¯ default risk by taking into account their nonlinear relationship when the banks are in distress. Based on...

This paper estimates macroeconomic credit risk of banks¡¦ loan portfolio based on a class of mixture vector autoregressive models. Such class of models can differentiate distributions of default rates and macroeconomic conditions for different market situations and can capture their dynamics...