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

3.3 The choice of the copula function
Let consider two markets (for example the equity market and the
bond market). We are interested in the probability that the loss in
one market is greater than its value-at-risk given that the loss in the
second market is already greater than its value-at-risk:
λ (α) = Pr {ϑ 2 > VaR 2 (α) | ϑ 1 > VaR 1 (α)}
= Pr { ϑ 2 > F −1
2 (α) | ϑ 1 > F −1 }
1 (α)
= Pr {F 2 (ϑ 2 ) > α, F 1 (ϑ 1 ) > α}
Pr {F 1 (ϑ 1 ) > α}
1 − 2α + C (α, α)
=
1 − α
λ (α) depends on the copula, but not on the margins.
Modelling dependence in finance using copulas
An open field for risk management 3-10