# BT2012.P2.06. Credit value adjustment (CVA)

Discussion in 'BT Part 2' started by David Harper CFA FRM, Apr 28, 2012.

1. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

Question:

6. From Acme Bank's perspective, the mid-market value, before adjusting for counterparty credit risk, of a interest rate swap (IRS) is -$11.0 million. Therefore, the IRS has a value of +$11.0 million to Acme's counterparty, BadCredit Corp. The present-valued expected exposure faced by Acme with respect to BadCredit, EE(BadCredit), is $30.0 million with expected loss rate of 12.0%. The present-valued expected exposure faced by BadCredit with respect to Acme, EE(Acme), is$20.0 million with expected loss rate of 8.0%. BadCredit Corp wants to exit the position and assigns the swap to GoodCredit Corp, who has an expected loss rate of only 4.0% (the expected exposure will remain the same). What is the transaction between Acme and BadCredit, in order to settle the assignment?

a. Acme receives $13.0 million from BadCredit Corp b. Acme receives$1.2 million from BadCredit Corp
c. Acme pays $2.4 million to BadCredit Corp d. Acme pays$5.2 million to BadCredit Corp

6. C. Acme pays $2.4 million to BadCredit Corp Before the assignment, the CVA adjustment = 20*8% - 30*12% = -$2 million, such that the IRS swap value (from Acme' perspective) is -$11 - 2 = -$13.0 million
After assignment, the CVA adjustment = 20*8% - 30*4% = $0.40 million; i.e., owing to lower counterparty exposure to GoodCredit Corp, the net value of the swap will increase to Acme. BadCredit Corp will need to receive$13.0 million (its value in the swap). GoodCredit corp will need to pay its value, in the swap, of $10.60 million; i.e.,$11.00 million + (30*40% - 2-*8%). Therefore, Acme pays BadCreditCorp the balance of $2.40 million. Put more simply, the assignment causes Acme's CVA adjustment to increase from -2.0 million [i.e., 20*8% - 30*12%] to +0.4 million [i.e., 20*8% - 30*4%], which increases the CVA-adjusted mid-market value by$2.4 million.

2. ### RK17New Member

Typo in first line of solution? Dave- hope you don't mind me pointing out these...
"..(from Acme' perspective) is -$11 - 2 = -$13.0 million"

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3. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

RK17, no of course not, I appreciate the help, thanks!

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4. ### slActive Member

It is not clear to me which of the loss rates represent the bank's loss rate and the counterparty's loss rate. Are we expected to infer it based on the expected exposure values?

"The present-valued expected exposure faced by Acme with respect to BadCredit, EE(BadCredit), is $30.0 million with expected loss rate of 12.0%" Since the EE represents the counterparty, the loss rate following it is represents the counterparty's loss rate? 5. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member Hi laxsum, I guess the question could have been expanded for further precision, as in: • "The present-valued expected exposure faced by Acme with respect to BadCredit, EE(BadCredit), is$30.0 million with expected loss rate, EL(BadCredit), of 12.0%"
or, since Canabarro use s() for loss rate so also:
• "The present-valued expected exposure faced by Acme with respect to BadCredit, EE(BadCredit), is $30.0 million with expected loss rate, s(BadCredit), of 12.0%" • Basically, Acme's CVA is reduced by the negative of EE(BadCredit)*EL(BadCredit), which is the expected exposure faced by Acme with respect to BadCredit, a future GAIN which represents a potential counterparty loss. So, the 12% expected loss naturally associates with the$30.0 million exposure. I could expand the question but i don't think it's necessary.

6. ### slActive Member

Thank you, David.

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7. ### jose.mejiaNew Member

Hi David,
I'm stuck with this question because I found a different answer = Acme pays $0.4 million to BadCredit Corp. I was reviewing the Canabarro reading and according to it the BadCredit Corp will need to receive$13.0 million (until here, no problem!).

GoodCredit corp will need to pay its value, in the swap, of $12.60 million; i.e.,$13.00 million + (30*4% - 20*8%), different to $10.6 million =$11.00 million + (30*4% - 20*8%). Therefore, Acme pays BadCreditCorp the balance of $0.40 million (not$2.4 million).

Note that, as Canabarro's reading, I use $13 million instead of$11 million for the above calculation, because it was the current status after the first CVA (I'm replicationg the reading example).

I don’t know, maybe I'm so confused with this . It would be great if you can help to clarify my ideas.

Thanks!

8. ### David Harper CFA FRMDavid Harper CFA FRM (test)Staff Member

Hi Jose,

Yes, but I think $10.6 is correct. Consistent with the Canabarro, the new net CVA is applied not to the CVA-adjusted$13.00 million, but to the original mid-market value of \$11.00 (i.e., BadCredit exits so we don't layer on additional CVA adjustment, we only net payments to make the new net CVA correct). Here is the Canabarro's procedure:
1. Mid market (unadjusted) value: A = -50, B = +50
2. Net CVA (from A's perspetive) = 200*2% - 100*5% = -1
3. CVA-adjusted MM value to A = -50 - 1 = -51
4. After assign from B to C, where EL(C) = 2%, such that after payments Net CVA (from A's perspective) = 200*2% - 100*2% = +2; i.e., just "switching in" C for B
5. After assign from B to C: CVA-adjusted MM value to A = -50 + 2 = -48
6. C pays +48 to B per matching value ; A pays 3 (to improve from -51 to -48) to B; B receives 51 to exit
Analogous to above:
2. Net CVA (from Acme's perspetive) = 20*8% - 30*12% = -2
3. CVA-adjusted MM value to Acme = -11 - 2 = -13
4. After assign from BadCredit to GoodCredit, where EL(G) = 4%, such that after payments Net CVA (from Acme's perspective) = 20*8% - 30*4% = +0.4
5. After assign from BadCredit to GoodCredit: CVA-adjusted MM value to Acme = -11 + 0.4 = -10.60 (to use -13 here would be to sort of "retain" BadCredit)
6. GoodCredit pays +10.60 to B per matching value ; Acme pays 2.4 (to improve from -13.0 to -10.6) to BadCredit; BadCredit receives 13.0 to exit
I hope that confirms, thanks and good luck tomorrow!

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Perfect!

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10. ### PLActive Member

hello david, when we calculate present value of exp. exposure faced by a wrt cpty b should we use risk neutral or actual distribution for market risk factor(ie historical simulation or risk neutral monte carlo simulation)?

11. ### BturtleNew MemberSubscriber

Hi David, i just cant seem to wrap my head around cva...
1. After assign from BadCredit to GoodCredit: CVA-adjusted MM value to Acme = -11 + 0.4 = -10.60 (to use -13 here would be to sort of "retain" BadCredit)
2. GoodCredit pays +10.60 to B per matching value ; Acme pays 2.4 (to improve from -13.0 to -10.6) to BadCredit; BadCredit receives 13.0 to exit
Why is it not Acme paying 10.60 and good credit paying 2.4 since CVA-adjusted MM value to Acme = -11 + 0.4 = -10.60 ?

12. ### ami44Active MemberSubscriber

Before the transaction GoodCredit had nothing, afterwards they have a swap worth 10.6, so they have to pay the 10.6 to someone.
Before the transaction Acme had a swap worth -13 afterwards they have a swap worth -10.6, they have to pay the difference of 2.4 to someone.
Before the transaction BadCredit had a swap worth 13 afterwards they have nothing, they need to receive the 13 difference from Acme and GoodCredit.

Last edited: Nov 11, 2015
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