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# CVA Questions

#### Ekin4112

##### New Member
Subscriber
Hi,

I don't see many CVA questions in GARP's practice exams. I was wondering what would be a typical question that would come up in the exam? Can someone give me an example please? (Would problems in the BT mock exams relevant?)

Also, in the book the CVA formula = spread * EPE; however I see CVA = EE * spread. Which one is correct?

There is also a formula where CVA = (1-Rec) * sum( Discount Factor(t) * EE(t) * PD(t)); Would we need to apply this formula in the exam?

I think in terms of credit risk concepts, this topic is a bit weak for me.

I hope someone can help!

Thanks,

#### ShaktiRathore

##### Well-Known Member
Subscriber
Hi
Some questions as cva calculation for two counterpartys as A and B would come the formula cva=Ea*sa-Eb*sb where Ea and Eb are exposures faced by A and B wrt each other and sa and sb are their mean loss rates,this type of question is highly common involving two counterparties where you would be asked to calculate cva or exposures.
Rest assure both formulas are correct epe is nothin but average of EE over time,the first version would give avg cva over time and next one at point of time,direct application of formula can come.
Thanks

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Thanks a lot!

#### WhizzKidd

##### Member
Hi @David Harper CFA FRM

With regard to CVA, it is to my understanding more than just a calculation. Can you point me to a document to explain a trading desk may manage CVA and DVA. Or something that explains the concept an an intuitive, but layman fashion?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
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Hi @HTHNIK Yes, xVA (CVA) is more than a calculation. I would recommend the entire book but Chapter 18 of Jon Gregory's The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital (get here at http://amzn.to/2gOGAyE) is on xVA management; this is the 3rd edition of the same text that has been assigned in the FRM to counterparty risk for years. Jon Gregory's page is here http://www.cvacentral.com/ (also the older edition is here at https://www.bionicturtle.com/forum/...it-value-adjustment-2nd-ed-by-jon-gregory.37/). I hope that helps!

#### WhizzKidd

##### Member
Thanks @David Harper CFA FRM,

I have started reading up, but this is something that baffles me, when pricing a derivative, the price is:

Price Contract=Default free (risk-free) price + DVA - CVA

I don't understand why this is, if as a bank we are pricing a contract for a client, why would I subtract CVA and add DVA? CVA prices the risk of the counterparty defaulting (vv for DVA), so I would charge more for the risk of default. So why don't we add CVA instead (increase the price for the risk of default)?

http://frank-oertel-math.de/CCR_CVA_Basel_III_Dialogue_Damiano_Brigo_Nov_2011.pdf

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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
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Hi @HTHNIK Thanks for attaching the paper, it is interesting and--as you suggest--it is fully consistent with the FRM syllabus (ie, Gregory ) in giving the following equation:
"Q: So every party will compute the final price as [writes on a notebook] DEFAULT RISK FREE PRICE + DVA - CVA ?
A: Indeed. In our example when the bank does the calculation, Price To Bank = DEFAULT RISK FREE PRICE to Bank + DVA Bank - CVA Bank, whereas when the corporate does the calculation one has a similar formula. Now, since
DEFAULT RISK FREE PRICE to Bank = - DEFAULT RISK FREE PRICE to Corporate
VA Bank = CVA Corporate
DVA Corporate = CVA Bank

we get that eventually

Price To Bank = - Price To Corporate
so that both parties agree on the price, or, we could say, there is money conservation.

We could call Bilateral Valuation Adjustment (BVA) to one party the difference DVA - CVA as seen from that party,
BVA = DVA - CVA
Clearly BVA to Bank = - BVA to corporate." -- page 22

Re: "... I would charge more for the risk of default." Well, I think the perspective is: a higher risk of default (and/or greater exposure) lowers the price the client will pay. The essential relationships are:
• unilateral: risky_value = risk_free_value - CVA
• bilateral: risky_value = risk_free_value - CVA + DVA = risk_free_value + BVA, where BVA = DVA - CVA
Imagine an option (on an asset) with a risk-free price of $10.00. You are going to buy the asset from me, so I will be the short and you will be the long. The$10.00 price assumes I will not default. Now, add an assumption: there is 25% that I will default on my obligation to pay you the intrinsic value at maturity. Are you willing to pay more, or do you insist on paying less, knowing that as your counterparty, I may default on your unrealized gain? CVA subtracts from price, just as you insist on paying less than the risk-free $10.00 amount. Specifically, you insist on a price in the amount of$10.00 - CVA. I hope that clarifies!

#### WhizzKidd

##### Member
Thanks David, that does make more sense. I was thinking about it from a price I would charge the counterparty as opposed to the price that I would pay on the transaction.

So it's basically how much would I pay for a contract knowing that I am exposed to the counter party defaulting.

#### WhizzKidd

##### Member
@David Harper CFA FRM On the DVA subject, am I correct in saying that (for our example), DVA is added to the price because as a counterparty you would need to be compensated for the risk of me defaulting. Hence, I pay a higher price, because DVA is the risk of me defaulting.

Taking it further, in that banks want to increase DVA because it is a profit to them (i.e., DVA is increased through right way risk deals), why would I want to increase DVA if it means that I am paying more on my derivative transactions? What benefit is drawn from this?

#### ami44

##### Well-Known Member
Subscriber
@David Harper CFA FRM On the DVA subject, am I correct in saying that (for our example), DVA is added to the price because as a counterparty you would need to be compensated for the risk of me defaulting. Hence, I pay a higher price, because DVA is the risk of me defaulting.
That is exactly right.

Taking it further, in that banks want to increase DVA because it is a profit to them (i.e., DVA is increased through right way risk deals), why would I want to increase DVA if it means that I am paying more on my derivative transactions? What benefit is drawn from this?

Indeed, if your credit spread increases your derivative portfolio often gains value through DVA. The same is true for issued debt. Bonds you might have issued at 100 might be worth less if your credit deteriorates, which means the absolute value of your debt is shrinking.

What does that mean? Increase of your credit spread might be good for your balance sheet, at least for the derivatives and issued debts that are measured at market value. The down side is, that your only move might be to shrink your business. Because as you mentioned new derivatives and new issuing of debt will be expensive, but buying back bonds or terminating existing derivatives leaves you with a profit. These profit is real. Imagine you can buy back a bond at 50, because people think you are on the brink of bankruptcy. Since you issued at 100 you realize a pretty nice profit. But you probably have to shrink your balance (i.e. sell some assets) because issuing new debt will be very expensive or even impossible. The same goes for derivatives, if people think you might default soon, they might be willing to terminate existing derivatives at a good price for you. But they will be less willing to enter into new contracts, or at least they will demand huge premiums.

That means if your credit deteriorates there will come a point were you have to shrink your business until your credit recovers. Of course that doesn't always work out for a multitude of reasons.

Also, in my opinion you can see here the pitfalls of having a view soleyly on fair values or market prices. If you buy back a bond at 50 and issue a new one at 100 you realized a huge profit, if you value your position with market prices. The fact that the rate on the new bond is much worse than on the old one is not adequatly reflected in the prices. You need a measure like projected net interest income to see, that your deal was actually not a good one.

#### WhizzKidd

##### Member
*Please ignore the previous comment, I was trying to figure out how the quotes work.

Thanks @ami44 ,

Indeed, if your credit spread increases your derivative portfolio often gains value through DVA. The same is true for issued debt. Bonds you might have issued at 100 might be worth less if your credit deteriorates, which means the absolute value of your debt is shrinking.

Why does our derivative portfolio increase in value as our credit spread increases though? I understand that the price of (new) derivative transactions will go up, but why would the value of the existing ones go up (and be seen as valuable on our books)?

Because as you mentioned new derivatives and new issuing of debt will be expensive, but buying back bonds or terminating existing derivatives leaves you with a profit. These profit is real. Imagine you can buy back a bond at 50, because people think you are on the brink of bankruptcy. Since you issued at 100 you realize a pretty nice profit. But you probably have to shrink your balance (i.e. sell some assets) because issuing new debt will be very expensive or even impossible. The same goes for derivatives, if people think you might default soon, they might be willing to terminate existing derivatives at a good price for you.

From my previous question I am trying to understand why DVA implies value. Are you saying the only way to realise DVA as profit is to hedge it?

In this case, buy our own bonds back at a discount from the market and because of the lower price we realise a gain relative to what we initially issued them at. Basically, shrinking our debt is beneficial. And derivatives are difficult as we would have to unwind them to realise a profit (I still don't fully understand this point), but what about selling CDSs on our name? I read that selling CDSs on yourself can also hedge DVA, but I fail to see how this is equivalent to buying our bonds back or how it reduces our debt in the market?

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#### ami44

##### Well-Known Member
Subscriber
Why does our derivative portfolio increase in value as our credit spread increases though? I understand that the price of (new) derivative transactions will go up, but why would the value of the existing ones go up (and be seen as valuable on our books)?

If you terminate a derivative before maturity the party with negative present value has to pay the other party this value as compensation (termination fee).
The present value is normally calculated with taking DVA and CVA into account. Of course the actual amount of the termination fee is determined by negotiation of the counterparties because normally neither counterparty has a right to terminate the contract unilaterally. But at least the starting point of the negotiation is the present value.

Concerning the DVA the rational is the following:
if the derivative has a negative present value for you than it has a positive value for your counterparty. The more your counterparty believes you might default the more it fears it might loose that value and the more they would accept a discount on that fee, because with it they loose that uncertainty.

Imagine an extreme case that everybody knows you will be bankrupt tomorrow. Your counterparty expects to get the amount of the LGD times the present value from the bancruptcy proceedings. Just to avoid these lengthy process they might be happy to get a fee of that amount now.

Back to your original question, your derivative portfolio is worth the present value including DVA and CVA, because if you would terminate all your derivatives immediatly, this is what you will get (in theory).

I will look at the rest of your post later.

#### ami44

##### Well-Known Member
Subscriber
From my previous question I am trying to understand why DVA implies value. Are you saying the only way to realise DVA as profit is to hedge it?
I did not talk about hedging, i hope that is clear with my previous post.

In this case, buy our own bonds back at a discount from the market and because of the lower price we realise a gain relative to what we initially issued them at. Basically, shrinking our debt is beneficial. And derivatives are difficult as we would have to unwind them to realise a profit (I still don't fully understand this point), but what about selling CDSs on our name? I read that selling CDSs on yourself can also hedge DVA, but I fail to see how this is equivalent to buying our bonds back or how it reduces our debt in the market?

I think a cds on yourself issued by yourself is essentially worthless. It might theoretically be worth something if your LGD is greater than zero, but I doubt that this is an instrument that is used by anybody anywhere.

My point with the buying back of bonds and derivatives is, that you can realize a profit from an increase of your credit spread, but only if you do not have to substitute the bought back derivative or bond with the same. E.g. if you terminate your swap and realize the DVA as profit, you will loose that profit if you have to contract a new, similar swap to substitute the old one.

#### Daniel26

##### New Member
To make it as simple as possible and to give you another practical example where is no upfront payment like in a long option position:

1) Suppose you are a Swap Dealer at a Banks Swap Desk. We assume there is no DVA. A client with lets say a BB rating wants to enter into a fixed rate payer swap. There is no CSA in place. To make the deal favorable for your desk you have to consider CVA. CVA desk will usually quote you the CVA charge as a running spread on the fixed leg of the swap (or as a simple present value) you want to execute. Therefore you have to add the CVA charge to the rate the client has to pay.

2) The Deal is already executed. To get the value of your position you can take the risk free value (which is the MTM of the swap you have entered into discounted at market rates. And remember: you have already adjusted it by a CVA charge while executing the trade) and subtract the current CVA which might have changed due to a spread increase for example.

CVA desk will charge you with the CVA and therefore guarantee you as a dealer that you will not "have to take care" of credit risk.

#### nansverma

##### Member
I have a basic question on CVA : Is it calculated on Profit/Loss value or the future value (which is unknown and hence we take expected value) ? Gregory talks about exposure and replacement cost which seems to be the expected future value and not loss value. Some examples for FRM exam just have +/- MTM values. I am not clear what is the cost to a counterparty - is it just the loss or the entire future value ? Thank you for clarifying.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @nansverma I would characterize CVA as the mark-to-market (MTM) price of counterparty risk. Without obsessing over particulars, CVA is given by CVA = LGD*EE(profile)*Discount_function*PD, so you have a series of future-dated credit exposures that are discounted to a present value (and the loss given default is assumed). As Gregory discusses in 14.2.7 (see below), there is a class real-world versus risk-neutral decision/controversy around calibrating the exposure distribution and the default probabilities, but I don't think this needs to change our view about the basic idea that CVA is a forward looking (via the expected exposure profile) estimate of the loss net of recovery (i.e., variation on classic EAD*PD*LGD) which is discounted to a present value which can be thusly added/subtracted to the MTM default-free value of the position:
"Gregory 14.2.7 Risk-neutrality: In Chapter 10, we discussed in detail how to quantify exposure, which covers the EE term in Equation 14.4. Section 10.4 discussed the difference between real-world and risk-neutral exposure quantification. In general, CVA is computed with risk-neutral (market-implied) parameters where practical. Such an approach is relevant for pricing, since it defines the price with respect to hedging instruments and supports the exit price concept required by accounting standards (Section 2.1 in Chapter 2). Of course, certain parameters cannot be risk-neutral, since they are not observed in the market (e.g. correlations), or may require interpolation or extrapolation assumptions (e.g. volatilities). Risk-neutral parameters such as volatilities may generally be higher than their real-world equivalents (e.g. historical estimates).

A more controversial issue is the reference to default probability in Equation 14.4. Risk-neutral default probabilities were discussed and defined in Chapter 12. As for exposure, the use of risk-neutral parameters is relevant for pricing purposes. However, the use of risk-neutral default probabilities may be questioned for a number of reasons:
• risk-neutral default probabilities are significantly higher than their real-world equivalents (Section 12.2.1);
• default can, in general, not be hedged, since most counterparties do not have liquid single-name credit default swaps referencing them; and
• the business model of banks is generally to “warehouse” credit risk, and they are therefore only exposed to real-world default risk.
The above arguments are somewhat academic, as most banks (and many other institutions) are required to use credit spreads when reporting CVA. There are, however, cases where historical default probabilities may be used in CVA calculations today:
• smaller regional banks with less significant derivatives businesses who may argue that their exit price would be with a local competitor who would also price the CVA with historical default probabilities; and
• regions such as Japan where banks are not subject to IFS 13 accounting standards.
In situations such as the above, which are increasingly rare, banks may see CVA as an actuarial reserve and not a risk-neutral exit price."

I hope your exam went well!

#### nansverma

##### Member
Hi @nansverma I would characterize CVA as the mark-to-market (MTM) price of counterparty risk. Without obsessing over particulars, CVA is given by CVA = LGD*EE(profile)*Discount_function*PD, so you have a series of future-dated credit exposures that are discounted to a present value (and the loss given default is assumed). As Gregory discusses in 14.2.7 (see below), there is a class real-world versus risk-neutral decision/controversy around calibrating the exposure distribution and the default probabilities, but I don't think this needs to change our view about the basic idea that CVA is a forward looking (via the expected exposure profile) estimate of the loss net of recovery (i.e., variation on classic EAD*PD*LGD) which is discounted to a present value which can be thusly added/subtracted to the MTM default-free value of the position:

I hope your exam went well!
Thanks David. Exam was fine, lets see ! Though besides exam, I am still more interested in learning how things work on ground

#### danghara

##### Member
Subscriber
Hi David,

Could you please explain why in default, CVA converge to exposure of transaction, WHICH MAY BE ZERO?

I will be so appreciate if you explain the figure in the attached file,too.

thanks

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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
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Hi @danghara First, please note that any bilateral derivative contract always must have one counterparty who has zero credit exposure, right? Exposure = max(value, 0). If you and me enter into an interest rate swap, the initial value will be zero (aka, par transaction). Whichever way the rate moves, up or down, one of us will go in-the-money (unrealized gain) with credit exposure and the other will go out-of-the money with zero credit exposure because their value is negative.

Okay but above, your underlined text appears to be directly referencing the "jump" to zero on the chart right-hand side. The chart is firstly illustrating that CVA is an increasing function of the counterparty's credit spread. This is basic CVA: counterparty risk increases as the counterparty's default probability increases (aka, their credit spread increases). Gregory is also showing a huge sudden increase in the spread (aka, jump to default) which is basically assuming default. If the assumption is a par transaction (i.e., initial value is zero)--think: you and I just entered into an interest rate swap--and you suddenly default, then exposure is zero because initial value is zero. Don't get me wrong, I don't like this chart, I think it's confusing and Gregory (IMO) goes a bit overboard in this section. For example, what is 100,000 bps? Isn't that 1,000%?! I hope that's helpful!