How do you calculate the tail risk at variance (TVaR)?

How do you calculate the TVaR?

First of all, you need to have a sequence of values, usually losses $f_L$. It can be the output of a simulation in which case you have just a vector of thousand of losses in dollar, for example. So you just find the loss that corresponds to the say, 95% quantile, $l(95\%)$ then keep all loss values equal or higher than $l(95\%)$, and just take the average of those remaining values. In mathemtical terms:

$$ \text{TVaR} = \frac{1}{n} \int_{\text{VaR(95%)}}^\infty f_L dL$$

where $n$ indicates the number of loss values that are inexcess of the quantile $l(95\%)$.

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