the linear approach to dynamic programming by using ideas from approximation theory to avoid inefficient discretization …

We propose a new measure of time-varying tail risk that is directly estimable from the cross section of returns. We … exploit firm-level price crashes every month to identify common fluctuations in tail risk across stocks. Our tail measure is … significantly correlated with tail risk measures extracted from S&P 500 index options, but is available for a longer sample since it …

We propose a measure for systemic risk: CoVaR, the value at risk (VaR) of the financial system conditional on … institutions being under distress. We define an institution's contribution to systemic risk as the difference between CoVaR … leverage, size, and maturity mismatch predict systemic risk contribution. We also provide out of sample forecasts of a …

Value at Risk has become the standard measure of market risk employed by financial institutions for both internal and … methodologies developed so far give satisfactory solutions. Interpreting Value at Risk as a quantile of future portfolio values … assumptions invoked by existing methodologies (such as normality or i.i.d. returns). The Conditional Value at Risk or CAViaR model …