Modelling dependence in finance using copulas - Thierry Roncalli's ...

Let consider an example of equity portfolio with a long position in
the security S t . We define the loss variable as follows: ϑ = S t+1 − S t .
We assume two distributions: ϑ ∼ N (0, 1) and ϑ ∼ t 4 .
Rating Regulatory BBB A AA AAA
α 99% 99.75% 99.9% 99.95% 99.97%
Return time 100 days 400 days 4 years 8 years 13 years
Φ −1 (α) 2.33 2.81 3.09 3.29 3.43
t −1
4
(α) 3.75 5.60 7.17 8.61 9.83
Let consider now a portfolio with different securities. The
Capital-at-Risk will be influenced by
• the assumption on the distributions of individual risk factors;
• and by the assumption on the dependence between the different
risk factors.
Modelling dependence in finance using copulas
An open field for risk management 3-3