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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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