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For a swap thats fully collateralised once a day, i suppose that the cva measures risk only for the intraday chance of counterparty default? Surely thats tiny enough to be neglible, or am i missing something?

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Collateral imperfections: the CVA cover the expected exposure in the event that the counterparty defaults. When the trade is collateralized and subject to variation margin. This exposure will come only from the imperfection of the collateral. Because posting and receiving collateral actually has a cost, usually the collateral agreement will be a threshold amount (bellow which no collateral is posted / received), and a minimum transfer amount.

The Margin period of risk: Also, when computing the CVA, you are concerned with the case where the counterparty defaults, and in this case before the default, the counterparty would usually stop posting collateral for a given period (called margin period of risk), usually around 10 days. In this period, the value of the swap can move with the market and diverge from the collateral balance.

The initial margin: The IM is supposed to cover these market values moves during the MPOR, it's a quantile like PFE, but it not the same as PFE is a quantile of the credit exposure = max(MV(t), 0) whereas the initial margin is a quantile of the market value variation over the margin period of risk = MV(t + MPOR) - MV(t).

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I would say it is negligible, the only times have ever had to compute that on standalone ISDAs (with just one albeit large swap) it's really honestly been very small perhaps a few tens of k for a 500mm swap over 15 years from distant memory, even if you say for example that your period of risk is greater than a day (let's say you have a massive swap, a major deriv cprty defaults, whole market is same way around so you can't replace your market risk hedge as quickly as you'd like - inconceivable in vanilla swaps but bear in mind regulatory hedge replacement windows typically assume 7 days or similar).

This is even in the context of wrong way credit rates correlation - if you model credit intensity and rates as correlated brownians you just aren't going to get a material one day move. As a caveat I would say however if you have a large long dated swap book that is very one way vs a counterparty (let's say you are receiving fixed and assume low rates <-> wide credit), then obviously it will add up. So as in many problems, it's worth looking at with conservative assumptions on period of risk and correlation, to allow you decide if you can afford to ignore it on your portfolio. Regulators as mentioned do demand a marghin period of risk, but unless am wrong for certain banks, this does not generally make it into economic CVA calculations and hedging decisions.

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  • $\begingroup$ the vast Mjority of swaps are traded fully collateralised, so where is tge demand for cva calculations coming from? $\endgroup$
    – Randor
    Dec 15, 2016 at 20:53
  • $\begingroup$ In full generality: Gap risk. Basically full collateralisation is not necessarily a guarantee of zero default risk. However as per above,m in this case it is most likely negligible, unless, as I say, you have a very large long dated wrong way exposure to a systemically important counterparty, then, just like a regulator demands a non unit margin period of risk, there is some default risk on a fully margined product - you do have to replace your hedge before the market moves $\endgroup$
    – Mehness
    Dec 15, 2016 at 21:01
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    $\begingroup$ It's also why exchanges have initial margin etc... and CSAs may not have zero thresholds. $\endgroup$
    – Mehness
    Dec 15, 2016 at 21:03
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    $\begingroup$ Any trading desk that was around on the weekend of the Lehman default went through these processes (ahem, yours truly included), namely when to replace the hedge (worse in credit space, all fully collateralised but in many cases correlated and hence gap risky exposures). However again, you are asking is it ok to ignore gap risk, on your example, in most cases it probably is, if you have a multi billion wrong way book vs a counterparty, then it's sth you might want to think about. $\endgroup$
    – Mehness
    Dec 15, 2016 at 21:07
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i think that cva is meant to cover Expected credit losses and PFE x% covers Unexpected credit losses and so gap risk would be more covered by PFE

i think initial margin for ccp cleared trades is more like a charge for PFE than for cva

So, i still dont really fully get where the demand for cva is coming from

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  • $\begingroup$ hmm - Expected and Unexpected are regulatory distinctions. PFE is obviously a tail measure, which is not the same as an expected shortfall, as priced by a model in collateral vs MTM. For an extreme example, consider a daily margined CDS where you buy protection from on an entity, from that entity itself. You would obviously price the wrong way risk on that, which is not the same as PFE at all. WWR should be part of a CVA calc if deemed important. Although PFE derived thresholds do cover and provide protection against WWR, that is not the same as saying PFE and expected WWR are the same. $\endgroup$
    – Mehness
    Dec 15, 2016 at 21:46
  • $\begingroup$ actually put another way the presence or absence of collateral makes no difference to a modelled correlated price process. The correlation, if wrong way, creates gap risk. If there were zero collateral, you would call this CVA, if you now put collateral in, you don't immediately discard the correlation effect and call it PFE or sth, it's still part of the CVA calc, you just have collateral which means its impact is rendered, in most cases, negligible. $\endgroup$
    – Mehness
    Dec 15, 2016 at 21:49
  • $\begingroup$ eu.wiley.com/WileyCDA/WileyTitle/productCd-047074846X.html Brigo's excellent book on collateral and CVA has good mentions and reference to WWR in CVA calcs. Definitely not to be conflated with PFE, if you are trying to price CVA - PFE is, more for trying to protect against it. Correlation can create gap risk even in the presence of daily margining, it's no more complicated than that really. $\endgroup$
    – Mehness
    Dec 15, 2016 at 22:10

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