Lecture_7_CVA_201820180402201111

CVA
General Framework
CVA Definition 1
The Net Present Value of a derivative at time t is given by:
V(t) = E t [Π(t,T)]
where Π(t,T) represents (the sum of) all discounted cash flows between times T
and t. In the presence of counterparty risk, the sum of all discounted payoff terms
between t and T is denoted by Π D (t,T).
CVA is defined, according to Canabarro and Duffie (2004), as the difference
between the risk-free value and the risky value:
CVA := E t [Π(t,T)]−E t [Π D (t,T)] (1)
unilateral (asymmetric) CVA, if only the default of the counterparty is
considered
bilateral (symmetric CVA), if also the default of the investor is taken into
account.
Paola Mosconi 20541 – Lecture 10-11 20 / 86