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Is a fully collateralized interest rate swap considered free of counterparty credit risk? Or close to risk free? Therefore discounted by the rate that best proxies the risk-free rate (which is the OIS-rate)? And then you have the fair value, no more adjustments?

For a swap that is not collateralized, or not fully collateralized, the practice is to derive the risk-free value by OIS-discounting, and then perform any applicable value adjustments (CVA, DVA, FVA)?

Or is practice divided on uncollateralized swaps? Do some people adjust for credit risk directly, by using a discount rate other than OIS?

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1. Discount

Yes, usually, people discount using the risk free rate, and then adjust for the counterparty credit risk (CVA), funding cost (FVA), and so on.

2. Collateral

The Margin period of risk:

In the case of default, the counterparty will usually stop posting collateral for a given period of time before being closed-out. This period is called the margin period of risk: $MPOR$.

As a result, for credit exposures computation, the collateral used is computed based on market values that are lagged by $MPOR$: $$Collateral(t, \omega) = f(MtM(t - MPOR, \omega))$$

CCR for collateralized trades

The above, combined with the fact that collateral agreements are not perfect (thresholds, minimum transfer amounts, etc.), implies that a swap that is subject to variation margin can still have some counterparty credit risk.

However, if the swap is subject both to initial margin and variation margin then nothing will be left in terms of counterparty credit risk.

In this case the CCR is essentially replaced by other costs (e.g. the initial margin gives rises to a new adjustment called the MVA to account for funding costs of this IM).

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    $\begingroup$ I just want to add that the discounting is done at OIS (Fed Funds) because in a perfect csa with cash being posted, it actually specifies interest to be paid on the variation margin at Fed Funds. $\endgroup$
    – dm63
    May 21, 2018 at 11:04
  • $\begingroup$ Usually, the discount is done at OIS, assuming a perfect CSA. Any divergence of the CSA from this perfect case (e.g. cheapest to deliver, etc.) will give rise to yet another adjustment: the ColVA. $\endgroup$
    – byouness
    May 21, 2018 at 12:30
  • $\begingroup$ @profesarrmariorty, thanks for the beer :) I'd take an "accept" instead for now if this answers your question to help other people having the same question find this answer quickly :) $\endgroup$
    – byouness
    May 21, 2018 at 12:31
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The pre-crisis concept of a risk-free rate was either government securities or LIBOR-based swap rates. As LIBOR is unsecured bank borrowing-lending rate, this was clearly an approximation too far.

Counterparty credit adjustments for a bank, and post-crisis discounting: The value is derived by discounting at the overnight (OIS) rate, and then apply xVA adjustments, including to margin (@byouness).

You may find that non-bank institutions, especially those that are permitted to measure credit risk and supply capital using a framework that diverges from BCBS i.e. SII, use a discount rate other than LIBOR or OIS.

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