$($Financial Risk Management $)$

The Generalised Pareto $($cumulative$)$ distribution given by

$\frac{G{G}_{}(yy)}{{}^0}=1-01+{}^0$

is sometimes used in the context of Extreme Value Theory $($EVT$)$ to calculate VaR.

a$.$ Briefly explain what is the EVT approach to calculate VaR.

b$.$ For a given portfolio we use $482$ price changes of an asset to fit the EV

distribution above. Suppose that there are $36$ scenarios in which the loss is

greater than $184.$ The fitted parameters of the above distribution are $=34\mathrm{.}53$

and $=0\mathrm{.}38.$ What is the $1-$day VaR with a $97\%$ confidence limit$?$ What is the

corresponding value of the Expected Shortfall?