What is the convention regarding mtm for collateral

amin · Post by **amin** » Sat Apr 07, 2012 3:23 pm

I have to calculate CVA with collateral, margining and inclusive of funding and investment cost of a derivative in a monte carlo simulation setup.

For the purpose of collateral margining, I have to figure out the mark to market of the derivative on the simulation grid along all paths. My question is what is the convention regarding this mark to market. When we mtm for collateral margining, do we consider the possibility of future default of either party in this mtm or we consider clean nondefaultable price for mtm that would be used for calculation of collateral.

silverside · Post by **silverside** » Sat Apr 07, 2012 5:27 pm

very good question

I remember reading an interesting paper a month or two ago which discussed this, I think it talked about different approaches and possibly the model used by BofA ? maybe it was on the risk.com or W sites ?

or possibly the MtM calculation may be specified in the CSA similarly to how cash-settled swaption value is calculated ??

amin · Post by **amin** » Sat Apr 07, 2012 6:26 pm

You mean risk.net or defaultrisk.com?

amin · Post by **amin** » Sat Apr 07, 2012 6:46 pm

For other members at NP who might be working on a similar problem, I give my strategy for CVA calculationas.

For calculation of CVA of Bermudan IR exotics in stoch vol heston model along with funding and investment costs and collateral. My strategy goes like this:

1. I simulate the exotic product in SV LMM model. Reduced form models are used with jump to default. CIR process is used to model stochastic default intensity.

2. I used backward LS monte carlo algorithm to calculate the price of the product at all points along the simulation grid. All cash flows are also calculated from original simulation.

3. I move backward along the simulation grid from terminal date or default of either counterparty and calculate collateral along the simulation grid from the price of exotic product calculated from step 2. Collateral and other derivative cash flows are discounted with appropriate discount rate. This continues till we reach the start date.

4. We do another sweep of LS monte carlo on the cash flows in step three to find out Bermudan price.

5. CVA can be found as a difference between default and no default case.

I would welcome comments on this and would also appreciate if somebody could help with the original question regarding how to calculate MTM.

amin · Post by **amin** » Mon Apr 09, 2012 11:15 pm

I made some changes to above since there was a mistake in step three that I corrected. The way it is different from others is that step three does not require dynamic programming and only requires discounting backward one date at a time and we continue to aggregate cash flows towards start date with appropriate discount factors.

amin · Post by **amin** » Tue Apr 10, 2012 3:22 pm

thinking again, it seems that if we mtm remaining deal with the same clauses for collateral and default as in the original deal, we will have to combine 2 and 3 as in Brigo and Fries. mtm for collateral will not be simply with market risk but would include credit risk and future collateral. Any views?

amin · Post by **amin** » Tue Apr 10, 2012 7:27 pm

OK guys, I know for sure. I asked a market player and usual convention is that we do not consider default in mtm for collateral. We do consider future default while calculating mtm in case of default closeout calculations.

polysena · Post by **polysena** » Tue Apr 10, 2012 8:08 pm

It seems correct not sure 100% but I guess I read something similar in Jon Gregory's book Counterparty Crdit Risk first or second chapter along these lines. Poly

Nonius · Post by **Nonius** » Wed Apr 25, 2012 12:45 am

Lot of similar questions on this cva ish topic. This is unchartered waters but I've always held that cva for derivatives under CSA amounts to pricing a) variance on derivatives + b) doing the usual on the credit component. CSA turns mtm exposure into mtm VARIATION exposure. Mtm is replaced by Vol of mtm. I should write it up.

Worrying about collateral value is a red herring....replace the collat with repo + cash. I'm being cryptic.

EverQuestFinancial · Post by **EverQuestFinancial** » Wed Aug 22, 2012 9:23 am

I don’t know what the convention is but think about it this way. The market value of the netting set for the purposes of determining collateral transfers must be agreed by both parties, otherwise there is no way to determine how much collateral shall be posted and by whom. This implies that the credit risk of both parties must be taken into account. That is, I have to take the both the CVA and my own DVA (which is the CVA as seen from the other party’s perspective).

Interestingly, the market value calculated for determining collateral transfers does not necessarily coincide with the market value calculated at close-out. This is because the ISDA documentation is ambiguous concerning how close-out values shall be calculated. Roughly speaking the agreement lets the surviving part decide if its own the credit quality should be taken into account (i.e. if the surviving part’s DVA should be taken into account on close-out in the same way as it is taken into account for determining collateral transfers). This is advantageous for the surviving bank as it would always choose the close-out calculation method that is most beneficial to itself. The consequence of this is that if the surviving bank is a creditor it would be undercollateralized. By contrast, if the surviving bank is debtor it would have posted the exact amount of collateral (assuming that the full market value is collateralized exactly).

Generally speaking, close-out value can be determined in two different ways.

Risk-free close-out. This approach ignores the credit risk of the surviving party and simply discounts the future expected payments of the residual derivative contract using a risk free rate. This was an obvious choice when one of the counterparties in a deal can be considered risk-free as was generally the case with banks before the financial crisis. Since risk-free close-out ignores all credit risk the DVA of the defaulting party and the CVA of the surviving party would collapse to zero.

Transfer/Substitution. Since no party is considered risk free any longer a different approach is normally used that takes the surviving counterparty’s credit quality into account. This is done by assuming that the derivative contract is transferred from the defaulted party to a third party. This third party would naturally take the credit quality of the surviving counterparty into account when valuing the derivative. However, the legal documentation does not prescribe that the credit quality of the surviving party should be taken into account rather it says that it might. This ambiguity makes it unclear to know in beforehand how the close-out value is actually going to be determined.

There are thus different ways of determining close-out values and the surviving party has some leeway in choosing the most beneficial the calculation method. Importantly, what is the most beneficial calculation method depends on if the defaulting bank is in- or out-of-the-money on its netting set. That is, if the defaulting bank is a net debtor or creditor.

If the defaulting bank is a debtor (i.e. it has to pay money to the surviving bank) then risk-free close-out is most beneficial the surviving part as the amount it would receive would be higher than if its own credit quality also would be taken into account. Since the risk-free close-out is higher than when both the CVA and the DVA is taken into account it means that the surviving bank is undercollateralised at default (because the value of the netting set increases as its own DVA is dropped).

However, if the defaulting bank is a net creditor (i.e. the surviving bank must pay to the bankruptcy estate) then transfer/substitution close-out is most beneficial for the surviving as its liability to the defaulted bank would be lowered by the inclusion of its own DVA. When transfer/substitution close-out is applied the close-out value is equal to the market value that is calculated in order to determine collateral transfer.

To sum up, both CVA and DVA should be taken into account when modelling collateral flows but this may not coincide with the credit exposure if either party defaults.