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The 5% Value at Risk of a hypothetical profit-and-loss probability density function. Value at risk (VaR) is a measure of the risk of loss of investment/capital.It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day.
Many risk measures have hitherto been proposed, each having certain characteristics. The entropic value at risk (EVaR) is a coherent risk measure introduced by Ahmadi-Javid, [1] [2] which is an upper bound for the value at risk (VaR) and the conditional value at risk (CVaR), obtained from the Chernoff inequality.
Expected shortfall is considered a more useful risk measure than VaR because it is a coherent spectral measure of financial portfolio risk. It is calculated for a given quantile -level q {\displaystyle q} and is defined to be the mean loss of portfolio value given that a loss is occurring at or below the q {\displaystyle q} -quantile.
However, in this case the value at risk becomes equivalent to a mean-variance approach where the risk of a portfolio is measured by the variance of the portfolio's return. The Wang transform function (distortion function) for the Value at Risk is g ( x ) = 1 x ≥ 1 − α {\displaystyle g(x)=\mathbf {1} _{x\geq 1-\alpha }} .
Financial risk modeling: value at risk (parametric-and / or historical, CVaR, EVT), stress testing, "sensitivities" analysis (Greeks, duration, convexity, DV01, KRD, CS01, JTD) Corporate finance applications: [21] cash flow analytics, [22] corporate financing activity prediction problems, and risk analysis in capital investment
A core technique continues to be value at risk - applying both the parametric and "Historical" approaches, as well as Conditional value at risk and Extreme value theory - while this is supplemented with various forms of stress test, expected shortfall methodologies, economic capital analysis, direct analysis of the positions at the desk level ...
(ii) For Value at Risk, the traditional parametric and "Historical" approaches, are now supplemented [32] [27] with the more sophisticated Conditional value at risk / expected shortfall, Tail value at risk, and Extreme value theory.
There are many parametric copula families available, which usually have parameters that control the strength of dependence. ... Value-at-Risk forecasting and ...