logicpad
New Member
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.
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.