ABSTRACT
In this part, we focus on counterparty risk embedded within credit derivatives (sometimes referring to this as counterparty credit risk). In the case of bilateral counterparty risk, combined with the related funding issue, the TVA equation is nonlinear (see Chapters 4 through 6). Moreover, in case of portfolio credit risk, the problem becomes highly dimensional due, in part, to the presence of multiple default indicator processes. As is well known (see e.g. Crépey (2013) or Guyon and Henry-Labordère (2012)), high-dimensional nonlinear problems are always a computational challenge. In this part, we focus on the study of unilateral counterparty risk, i.e. τb = +∞, τ = τc, in the case when funding is provided at the risk-free rate (cf. Sect. 3.2.4.2). This allows us to avoid the nonlinearities associated with the general funding issue.
