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# GARP.FRM.PQ.P22016 GARP PQ - Question 5 - CDS (garp16-p2-5)

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
HI @RushilChulani From the perspective of today, each year's future spread payment, S, will either be made or not (by the protection buyer). The probability it will be made is (1-PD)^n and the probability it will not is 1 - (1-PD)^n where these two probabilities add to 1005, such that the expected future (FV not PV) payment is a weighted average of these two outcomes: S*(1-PD)^n + zero*[1 - (1-PD)^n] = S*(1-PD)^n. I would remind you that, if default occurs it occurs only once on one of the years (e.g., either year 1 or year 2), default cannot occur on both year 1 and year 2. However, survival can occur on all five years. I hope that helps!

#### Tereza

##### Member
Hello, I would like to ask, would you have some variation for this question to practice for the exam?

#### greaterman

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

Why the Premium leg = [0.5 * 7% default * d(0.5)] + [93% survival *d(1.0)] ?
d(0.5) already discount the Rf rate by half as "halfway through", why 0.5 "half one more"?

Thanks.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @greaterman Because the first term captures the outcome of a default (i.e., triggering a payout by the protection seller according to the CDS) and GARP (following Hull's approach) assumes "defaults can occur only halfway through the year and that the accrued premium is paid immediately after a default." So it's a model assumption that, if an accrued premium is paid (due to a default), then it will be one-half the spread. I hope that's helpful,

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