Question 1: Does that mean upfront premium is equal to CDS Price? Exhibit 26, shows the same equation for upfront premium.
Next, if we look at BB example 27. If you look near the end of solution, the CFA text uses (the equation that is marked incorrect in the errata):
10 year CDS price per 100 = [1 + ((1 - 1.75%) x 8.68)] = 93.4
9 year CDS price per 100 = [1 + ((1 - 1.66%) x 7.91)] = 94.78
Question 2: I’m assuming this incorrect this uses the crossed equation (second equation I listed in the message).
Using the correct equations (i think the correct one – the top equation) CDS prices are:
10 year CDS price per 100 = [(1 - 1.75%) x 8.68)] = -6.51
and rolling forward one year.
9 year CDS per price 100 = [(1 - 1.66%) x 7.91)] = -5.22?
Question 3: Is negative CDS prices ok? That does not seem right.
Question 4: The CDS price is increasing. I read in an article that CDS prices increase when the probability of default increases. But here, the credit spread decreases and the CDS price increases. How can I understand this. Why the CDS price increases with declining spread?
S2000, I wrote a similar question in a thread that you replied to but the thread was not specifically related to this BB27. I think this will help many people because this is very, very confusing so I started a new thread. Thanks anybody who can shed light. I’m absolutely breaking my head.
The CDS premium formula is (CDS spread - fixed coupon) * effective duration of the CDS.
To be sure not to be wrong in the calculation consider that the CDS Credit protection buyer of the swap has to pay a premium (a positive or negative one). Paying a negative premium is receiving the absolute number.
So if the fixed coupon the long party to the swap had to pay is higher than the CDS spread he pays relatively more than he should and must receive the difference: [ (CDS spread -fixed coupon) * effective duration of the spread] aka the CDS PREMIUM.
Now imagine you want to buy something. The lower the better.
In the finance world there is no free lunch. If you profit from a cash inflow (the absolute number of the difference (CDS spread - fixed coupon)* EffDur) before buying your CDS you must pay a higher price to cancel out this advantage.
From the perspective of the buyer if the coupon income is less than the spread, he must pay to the credit seller the difference because he receives (the spread) relatively (to par) more than he has to pay.
So this advantage has must to be offset by a higher price he has to pay to enter the swap.
As a conclusion the price of a CDS = 1- (CDS spread -fixed coupon) * effective duration of the CDS.
You notice here that if the CDS spread is higher than the coupon the buyer must pay the difference between what he receives (the spread) and the coupon (what it pays) because he receive more than par.
So he will have to pay a lesser price to offset this negative difference he must pay for. (Cds spread -coupon) > 0 effective duration > 0 so price < 1.
If you understand the mechanism you just have to remember the components in the premium formula.
Hope this helps .
NB: the first formula you mention in your post is the formula for the CDS premium and the second formula has the wrong (+) instead of the (-) sign.
If you take their formula for the CDS price it means if CDS spread is higher than fixed coupon, not only the protection buyer will have to pay the difference between the CDS spread and the fixed coupon to the credit protection seller but he will have to pay a higher price at the initiation of the swap. He would pay 2 times the premium.