Collateral, Margin Periods, and Bilateral Credit Exposure

Summary

The document explains why a party can have positive counterparty credit exposure even when its mark-to-market value is negative. If collateral held from the counterparty is insufficient relative to the negative mark-to-market, a counterparty default may leave the party unable to recover posted collateral. The answer expresses exposure as the positive part of mark-to-market minus the collateral balance, with the sign convention used in the example.

It also highlights the margin period of risk: after a counterparty defaults, collateral posting may stop while the portfolio value continues to change. Exposure calculations therefore commonly use a collateral balance from before the default-time valuation, such as the balance at the start of the margin period. The discussion assumes collateral is not segregated and does not detail legal enforceability, closeout netting, recovery, or how valuation changes are modeled, so the formula is an illustrative exposure definition rather than a full bilateral CVA/DVA framework.

Key ideas

• Negative mark-to-market does not guarantee zero counterparty exposure when collateral is held.
• Exposure is the positive part of mark-to-market less the relevant collateral balance under the stated sign convention.
• Nonsegregated collateral may be lost if the counterparty defaults.
• The margin period of risk creates exposure because collateral may stop updating while market values continue to move.

Tags

# Should one calculate CVA even when exposure is negative?


# Should one calculate CVA even when exposure is negative?












I have an example, where two companies have the bilateral nature of derivative contract. Companies have exchanged collateral a number of times, so at a certain point in time each sides holds some amount of collateral.

According to the literature, when exposure of company A is negative, it has to calculate DVA instead of CVA (and the opposite for company B).

Does this mean, that CVA = 0 for company A, even though company B holds some of it's collateral? If at that moment B defaults, A may still lose this posted collateral...

## Answer by byouness (score 1, accepted)

https://quant.stackexchange.com/a/44582

Indeed, if the collateral is not segregated, it could be lost if the counterpart defaults. So, the credit exposure should be computed taking into account the collateral balance $C(t)$:

$$ Exposure(t) = \max \left( MtM(t) - C(t) , 0 \right) $$

This means that, even if $MtM(t) < 0$, if $C(t) < MtM(t) < 0$, then you will have a strictly positive credit exposure.

Remark: Usually, the exposure is computed assuming that the counterparty default is happening and that it has stopped posting collateral in the past few days (called the margin period of risk or MPOR). So, if you want to keep things simple $C(t)$ above is actually the collateral balance as of $t - MPOR$.

This is to say that even if your collateral agreement is perfect (no threshold and no minimum transfer amount), you could still have a credit exposure coming from this lag.

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.