P2.T6.306. Credit spreads and spread '01 (DVCS; Malz section 7.1)

[logicpad]

Thank you for providing sample questions, on official FRM 2013 practice exam, question 6, I couldn´t really find an example to solve this, estimating a CDS spread, which seems like a basic question not addressed here in the forum.



I had to figure it out, took a couple of hours and about 8 references on the web, till I put everything together. I wonder if you have an example like this, solved, or if there is a place in the Malz theory material provided (P.2 Credit - Malz - 7) that explains the logic of how to frame this question, with equations and an example, not just in general.



Question:

Valuing a 1 year CDS contract paying 75% of face value if bond defaults

Buyer pays premium, CDS spread, once a year at the end of the year

Risk neutral default probability is 5% per year

Risk free rate is 3% per year (you had to guess or assume continuous)

Defaults occur halfway through the year

Accrued premium occurs halfway through the year, right after default, if default

Estimate CDS spread.



a. 380 bp

b. 385 bp

c. 390 bp

d. 400 bp



logic: set the two legs of the contract equal, inital value of the contract is zero (

premium payment to protection seller (no default - premium leg) = payoff to protection buyer (default - contingent leg) - Accrued premium (for half the year there was no default and the protection buyer has to pay premium accordingly, and reduce its payoff from the seller by this amount)
I couldn´t find this equation with accrued premium or the logic of it anywhere in the material provided.



Setting this in equation form:

S (this is the spread variable we´re looking for) * (0.95 - no default) * (0.9704 - PV discount factor, continuous basis, 3%, premium is paid at end of year) = [(0.75 - payoff) * (1 - one dollar of face value) * (0.05 - prob default) * (0.9851 - PV 6 mths discount factor of 3% risk free rate, as default occurs half way through] - [(S/2 - half premium paid since default occurs half way through year) * (0.05 - prob default, this is an insight, the accrued premium occurs only if there´s default, so prob default applies to accrued premium paid as well as to the payoff to the buyer if default, which is more intuitive).



Solving for S gives:

0.95*0.9704*S = 0.75*1*0.05*0.9851 - [(S/2)*0.05*0.9851]

S = 0.0369 / [0.921 + (0.0492/2)] = 0.0390 = 390 basis points (answer is c)


In my view, there´s no way you can solve this from the theory given in the official books or with the material provided here, as there are no examples provided, nor is the logic explained. Any suggestions on where to look or how to approach or prepare for this question specifically? Thank you.

 

[ashanks]

Hi Logicpad,

The idea is basically on the same approach at highlighted in Malz Chap 7 for AIM 24.6 or even Malz Chapter 6 for AIM 18.6.

The swap pricing principle is basic and holds for pricing any kind of swap, and carries over from FRM 1. Just think of expected payments from either party's pespective and equate to zero.For example:

From protection sellers perspective, the following are the probability weighted (aka expected) payments, which we sum and add to zero.

95% no default:​

Expected value = 0.95*s* df(1) (positive since seller receives this payment; discounted by one period since received at end of period)​

5% default:​

Expected value = -0.05*0.75*df(0.5) + 0.05* s/2 * df(0.5)​

Hope that helps.

 

[logicpad]

Thank you ashanks, it does confirm the logic, swap pricing principle is a good starting point, but the application here is different, legs (fee and contingent) are default-based instead of interest-based (fixed-variable in IRS), and there´s both a negative and positive cash flow for the protection seller in the event of default, which makes this logic more complex than that of a regular swap, I would think, at least to come up with it. Once you see it written or explained, like anything, it´s a lot more simple.

I´m having some difficulty finding references here, applied references that is. Where do you get the reference numbers for AIMs by the way, backing what you´re saying (AIM 24.6 and AIM 18.6)?

In the frm books (Credit), AIMs are not numbered, just listed (Malz 7 is ch.8 in the frm credit book, p.187 has a generic description of CDS pricing logic, but no examples, p.178 defines CDS spread but there are no examples, counted 12 AIMs in the chapter, not 24 - Malz 6 is ch.7 in the credit book, counted 14 AIMs-learning outcomes, not 18), and in the garp listing of AIM statements, Malz 6,7 are listed under AIM 38. In the BT notes, the AIMS are not numbered, Malz 6 is p.68-85, and Malz 7 is p.87-92, and in the BT question-answer sets on Malz, Malz 6 is listed as P2.T6.300-305 and Malz 7 lists P2.T6.306-308. A bit of a notation mess I find, just finding what you´re looking for isn´t that easy.

Many thanks for the explanation, kind of you to drop by.

 

[ashanks]

Hi Logicpad,

Thanks for the post.

The generic principle for any derivative where no notional exchanges hands is that it prices to zero at the time of entering into it. PV(fixed leg) = PV(floating leg) is just replaced by Expected PV, where you think of expected as probabilistic expectation. For someone with a background in probability, the latter is like the zeroth law.

That said, I agree it's not exactly the same as a IR swap , and also under time and examination pressure it can even mess you up further. I guess my having taken an online course in Financial Engineering (https://www.coursera.org/course/fe) might have made it more 'obvious' to me than if I hadn't. If you enjoy pricing and that sort of quantitative stuff, I highly recommend you to take it when it runs again.

In general, I think such questions just need you to know three things

1] Expectation means probability weighted cash flow
2] Use discounting if there is a risk free rate
3] Which cash-flows to use as +ve and which -ve to work out a 'parity/equality' equation

Sorry about the notation - I was using what Kaplan Schweser uses. That said, you won't find anything more that what's already in Malz. I didn't realize that the official http://www.garp.org/frm/study-center/study-materials.aspx [look for "2013 AIM Statements" ] doesn't number them the way Kaplan Schweser does.

Also, no one is asking, but a friendly tip: in an exam where all questions carry the same marks - If I were getting a 387 and three options are 380, 385, 390 - I'd just leave it till the very end, instead of losing time to answer some other qualitative questions that might take half the time to solve.

Good luck and cheers!