$($Financial Risk Management $)$

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

$G_{,}(y)=-[1+\frac{y}{}{]}^{-\frac{1}{}}$

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 $522$ price changes of an asset to fit the EV

distribution above. Suppose that there are $34$ scenarios in which the loss is

greater than $150.$ The fitted parameters of the above distribution are $=$

$29\mathrm{.}25$ and $=0\mathrm{.}35.$ What is the $1-$day VaR with a $99\%$ confidence limit$?$ What

is the corresponding value of the Expected Shortfall?