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

4.2 The pricing of credit derivatives
In multi-asset options, the risk is a market risk (because of the
volatility of the asset prices). In credit derivatives, the risk is a credit
risk (because of the default of the counterparties).
A default is generally described by a survival function
S (t) = Pr {T > t}. Let ˘C be a survival copula. A multivariate survival
function S can be defined as follows
S (t 1 , . . . , t N ) = ˘C (S 1 (t 1 ) , . . . , S N (t N ))
where (S 1 , . . . , S N ) are the marginal survival functions. Nelsen [1999]
notices that “ ˘C couples the joint survival function to its univariate
margins in a manner completely analogous to the way in which a
copula connects the joint distribution function to its margins”.
⇒ Introducing dependence between defaultable securities can then be
done using the copula framework (see [21] and [25]).
Modelling dependence in finance using copulas
New pricing methods with copulas 4-9