Risk-Free and Risky Close-Out Assumptions in Counterparty Models
Summary
The document explains that derivative counterparty-risk models must specify how a defaulted transaction is valued for settlement. It distinguishes risk-free close-out, which values the contract without counterparty-related risk factors, from substitution or risky close-out, which incorporates those risks into the replacement value for the surviving party.
The text describes a modeling trade-off: risk-free close-out generally leads to linear valuation partial differential equations, while risky close-out tends to produce nonlinear or semilinear equations. It asks which convention practitioners use in actual close-outs and production counterparty models, but does not answer that question or provide evidence about market practice. It cites work discussing the consequences of close-out conventions, so the passage serves as a framing of the modeling issue rather than a recommendation. The appropriate convention remains an open question in this document.
Key ideas
- Counterparty-risk models need a convention for settling defaulted derivative transactions.
- Risk-free close-out excludes counterparty-related risk factors from the settlement valuation.
- Risky or substitution close-out incorporates counterparty risk into the value of replacing the deal.
- Risk-free assumptions generally yield linear valuation PDEs, while risky close-out tends to create nonlinear or semilinear PDEs.
- The document asks about production practice but does not establish which convention practitioners generally use.
Tags
Full text
# Close-out in practice: default settlements and counterparty models # Close-out in practice: default settlements and counterparty models 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. References 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. Gregory, Jon and German, Ilya (2013). "Closing Out DVA", Asia Risk, 26(2), February.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.