Counterparty risk and funding: immersion and beyond

Abstract

In Crépey (2015, Part II), a basic reduced-form counterparty risk modeling approach was introduced, under a rather standard immersion hypothesis between a reference filtration and the filtration progressively enlarged by the default times of the two parties, also involving the continuity of some of the data at default time. This basic approach is too restrictive for application to credit derivatives, which are characterized by strong wrong-way risk, i.e. adverse dependence between the exposure and the credit riskiness of the counterparties, and gap risk, i.e. slippage between the portfolio and its collateral during the so called cure period that separates default from liquidation. This paper shows how a suitable extension of the basic approach can be devised so that it can be applied in dynamic copula models of counterparty risk on credit derivatives. More generally, this method is applicable in any marked default times intensity setup satisfying a suitable integrability condition. The integrability condition expresses that no mass is lost in a related measure change. The changed probability measure is not needed algorithmically. All one needs in practice is an explicit expression for the intensities of the marked default times.

CVA with Wrong-Way Risk in the Presence of Early Exercise

“…We further assume that trades are fully uncollateralized. 7 The underlying asset is lognormally distributed and represented by means of a Cox-Ross-Rubinstein binomial tree. We can thus apply the dynamic programing approach described above to price options on the tree and calibrate the function a(t) recursively via (7).…”

“…7 The underlying asset is lognormally distributed and represented by means of a Cox-Ross-Rubinstein binomial tree. We can thus apply the dynamic programing approach described above to price options on the tree and calibrate the function a(t) recursively via (7). This procedure turns out to be quite fast: the Matlab coded algorithm takes less than 0.1 second to run on a 3.06 GHz desktop PC with 4 GB RAM when n = m = 500.…”

“…2 where a possible underlying asset path is displayed along with the optimal exercise boundary 7 Here we are interested in analysing the full exposure profile as function of early exercise opportunities. On the other hand, more realistic collateralization schemes can be taken into account in a straightforward manner within the described framework.…”

“…Relevant contributions on alternative approaches to manage WWR include copulabased modeling as in [6], introduction of jumps at default as in [13], the backward stochastic differential equations framework developed in [7], and the stochastic hazard rate approach in [11]. In particular [11] introduces the idea to link the counterparty hazard rate to the portfolio value by means of an arbitrary monotone function.…”

Nonlinear Monte Carlo Schemes for Counterparty Risk on Credit Derivatives

“…But it is too restrictive for situations of strong dependence between the underlying exposure and the default risk of the two counterparties, such as counterparty risk on credit derivatives, which involves strong adverse dependence, called wrong-way risk (for some insights of related financial contexts, see Fujii and Takahashi [11], Brigo et al [2]). For this reason, an extended reduced-form modeling approach has been recently developed in Crépey and Song [4][5][6]. With credit derivatives, the problem is also very high-dimensional.…”