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This is my first post on this forum (which I regularly consult for all the valuable information's in it).

On question 5, I fail to understand why couldn't we simply use the formula:

PD = Hazard Rate = Spread / (1-R). Using this would give a Spread of exactly 560 bps.

Could someone tell me what is wrong in my rationale?

Thank you very much.

Kind regards,

Hi @Arnaudc Welcome to the forum! This CDS question is essentially similar to https://www.bionicturtle.com/forum/threads/2013-garp-practice-exam-p2-question-6.7039/

As with that problem, this approximation would work except the CDS has a mechanical feature difference from the bond, under the assumptions given at least. Specifically, from what I can tell the following typical assumption explains almost the entire different between your approximation and the more exact answer given: "Assuming defaults can only occur halfway through the year and that the accrued premium is paid immediately after a default."

To see why, imagine there was no accrual paid upon default. Then the solution would be given by:

Premium leg = [0.5*0%*d(0.5)] + [100%*d(1.0)] and Payoff leg = same = 80% * 7% * d(0.5), such that

0.975895*S = 0.05465, and S = 560.1 (versus your 560 approximation!).

To recap,

As with that problem, this approximation would work except the CDS has a mechanical feature difference from the bond, under the assumptions given at least. Specifically, from what I can tell the following typical assumption explains almost the entire different between your approximation and the more exact answer given: "Assuming defaults can only occur halfway through the year and that the accrued premium is paid immediately after a default."

To see why, imagine there was no accrual paid upon default. Then the solution would be given by:

Premium leg = [0.5*0%*d(0.5)] + [100%*d(1.0)] and Payoff leg = same = 80% * 7% * d(0.5), such that

0.975895*S = 0.05465, and S = 560.1 (versus your 560 approximation!).

To recap,

- Instead of Premium leg = [0.5*
**0%***d(0.5)] + [**100%***d(1.0)] - The CDS assumes: Premium leg = [0.5 *
**7% default*** d(0.5)] + [**93% survival***d(1.0)]

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@David Harper CFA FRM ,

Thank you very much for your time answering my question. You made a point by stressing the importance of assumptions to assess which models could/should be used.

I still have a point needed to be clarified.

The reason why you assume 100% of premium payment seems related to the fact that you are certain you would receive the premium at the end of 1 year? Is it because default or non default, in any cases, the premium is paid at the end of the year 1?

In this case I understand and a higher spread is intuitive as a default half year means we would receive only half of the premium we were promised.

EDIT:

Actually the "simplified formula" is based on the assumption that the spread should equal your EL% (PD x LGD). In my case, 7% x 80% = 5.60%. Absent any convention of discounting / in between period default, the spread should be equal to EL% (as it equals paying leg with contingent leg)

Again, thank you for your time, I really appreciate what you are doing for the community of learners we are.

Thank you very much for your time answering my question. You made a point by stressing the importance of assumptions to assess which models could/should be used.

I still have a point needed to be clarified.

The reason why you assume 100% of premium payment seems related to the fact that you are certain you would receive the premium at the end of 1 year? Is it because default or non default, in any cases, the premium is paid at the end of the year 1?

In this case I understand and a higher spread is intuitive as a default half year means we would receive only half of the premium we were promised.

EDIT:

Actually the "simplified formula" is based on the assumption that the spread should equal your EL% (PD x LGD). In my case, 7% x 80% = 5.60%. Absent any convention of discounting / in between period default, the spread should be equal to EL% (as it equals paying leg with contingent leg)

Again, thank you for your time, I really appreciate what you are doing for the community of learners we are.

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- pv[Premium leg] = pv[Contingent Payoff] is technically exact, and probability-adjusted translates in this case into
- pv[7% prob of 0.5 accrued premium + 93% prob of full premium] = pv[7% prob of 80% payoff]; but, if we just "eliminate the unique CDS feature" and assume the premium is paid regardless then
- pv[100% prob of full premium] = pv[7% prob of 80% payoff], which is, just as you say, equivalent to spread = EL = LGD*PD. A potential confusion, for me at least, is the 80%: is the 80% recovery or LGD? It is the CDS recovery but LGD to the protection seller, so i think it's easy to select the wrong 20%/80% here. But we're pricing the CDS, and so the spread is compensation for the 80% that will be paid by the protection seller. Thank for helping me think it through!

Thank you for confirming / clarifying!

Regarding the LGD confusion, I think an easy way not to get it wrong is to understand the LGD as the loss an investor would suffer an a specific instrument without taking into account CDS protection. (then this LGD is simply plugged into CDS valuation formula's.

Thanks again.

Kind regards,

can someone please qn 5- the calculation of the CDS spread. Thanks!

Please note that I moved your question here (from the 2016 GARP Error thread), where this question has been discussed already.

Thank you,

Nicole

@Srilakshmi Let us know if the above doesn't already answer it for you? Thanks @Nicole Seaman !

Thanks,

Rushil

But the difference on the payment side is that the

Hi @David Harper CFA FRM, Thank you for responding! I yet am bothered by the fact that we don't consider the survival for just the specific year. So for example, why isn't it 0.9802 * 0.9512 for year 1, [1-(0.9802-9608)] * 0.9048 for year 2, ...., [1-(0.9231-9048)] * 0.7788 for year 5. Won't that be the probability of survival with that specific year and not probability of survival since year 1?

(I used Hull's Ninth edition as reference and so the numbers are different. The idea is {1-[Prob of survival (n-1) - Prob of survival (n)]} for year "n")

Rushil

Hi @RushilChulani I think I do understand why that's not obviously intuitive. After all, it's different than how the contingent payoff is treated which may be more intuitive in contrast. After all, the contingent payoff probabilities are unconditional (aka, joint) default probabilities which means they are mutually exclusive and naturally additive; for example, the year 5 payoff pd is only 1.84% because it is a joint probability given by 92.2% cumulative probability thru the end of year 4 (the prior year) * 2.0% conditional probability. On this payoff side, perhaps it is more intuitive because the 2.0% is a conditional PD such that we don't perceive the double-counting.

But the difference on the payment side is that the*protection buyer pays the spread every year* as long as the reference survives (as opposed to the protection seller who only pays once, if at all); i.e., if the reference never defaults, there will be five (not one!) spread payments. If there were only one spread payment at the end of five years, we would be double-counting. But in this case of a "stream of spreads" we are merely weighting the stream of payments by their probability of occurring. Let A(t) be the annuity factor; i.e., the sum of discount factors, which is 4.317. Imagine that survival is guaranteed, in which case five (5) spreads are paid with a present value = 4.317*S. Implicitly that would be to assign 100% to each of the five cumulative probabilities because each spread is guaranteed: S*100%*0.951 + S*100%*0.905 ... S*100%*0.729. Notice how that isn't double-counting? So these probabilities are just weighting each year's spread payment. I hope that's helpful!

(I used Hull's Ninth edition as reference and so the numbers are different. The idea is {1-[Prob of survival (n-1) - Prob of survival (n)]} for year "n")

Rushil

But the difference on the payment side is that the

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