Any model on counterparty risk for derivative contracts needs to make an assumption on the close-out convention, that is the rule used to determine at which value a defaulted derivative transaction between two parties $A$ and $B$ is settled.
Broadly speaking, the literature is usually split between two different close-out assumptions: risk-free close-out, that is the defaulted contract is settled at its risk-free value neglecting any implied counterparty-related risk factors; or a substitution or risky close-out in which the settlement value includes counterparty-related risks "as computed from a third market player that is eager to become the counterparty of the survived party for the residual deal, replacing the defaulted one" (Brigo and Morini, 2010). From a modelling perspective, risk-free close-out is usually easier to deal with because it induces linear valuation PDEs, whereas risky close-out almost inescapably results in non-linear or semi-linear PDEs.
What is the actual practice among market practitioners when closing out a defaulted deal? What close-out assumption is usually made in counterparty models deployed in production environments?
While I am aware of what my institution does, I am wondering what the general practice is. Ideally, publicly available sources on this topic would be welcomed.
Brigo, Damiano and Morini, Massimo (2010). "Dangers of Bilateral Counterparty Risk: the fundamental impact of closeout conventions", available at SSRN: https://dx.doi.org/10.2139/ssrn.1709370.