$($Financial Risk Management $)$

Numerical methods and copulas:

a$.$ A financial analyst has a portfolio of $n$ securities$.$ She is modelling the

dependence between their returns using a Gaussian copula.

i$.$ Explain what process she has to follow in her analysis.

ii$.$ What is tail dependence? Also, is the Gaussian copula good to model

this kind of dependence?

iii. What is the main problem that she faces in terms of the number of

parameters of the model? How can factor models reduce this problem?

b$.$ A bank has a large portfolio of loans of a given type. The one$-$year probability

of default on each loan is $1\mathrm{.}9\%$ and the copula correlation of the Gaussian

copula used by the bank is $0\mathrm{.}45.$ If the bank has an exposure of $10$ million to

the portfolio, and the loss given default for each loan is $35\%,$ calculate the

$99\mathrm{.}5\%$ one$-$year credit VaR using Vasiciek's model.