CDS price formulas

CFA Level II Portfolio Management
#1

I think there is a big problem in CDS price formulas

We have: Upfront premium ≈ (Credit spread – Fixed coupon) × Duration

So, if the credit spread changes, the different is: Upfront premium 2 - Upfront premium 1 = (Credit spread 2 - Credit spread 1) x Duration = Change in spread in bps × Duration (1)

We also have % Change in CDS price = Change in spread in bps × Duration (2)

and Price of CDS in currency per 100 par = 100 – Upfront premium % (3)

I’m so confuse about % Change in CDS price meaning. The usual thinking of % Change in CDS price: (CDS price 2 - CDS price 1)/ (CDS price 1). So there is a conflict between formula 2 and combination of formula 1 + 3, u****se example 7 in curriculum:

An investor buys $10 million of five-year CDS protection, and the CDS contract has a duration of four years. The company’s credit spread was originally 500 bps and widens to 800 bps.

The percentage price change is estimated as the change in spread (300 bps) multiplied by the duration (4) or 12%.

If I use formula 1 + 3, the CDS price is 84 and 72 respectively (if fixed coupon = 1%) . And the percentage price change is 14.28% (>< 12%. ) But if fixed coupon = 5%, CDS price is 100 and 88, percentage price change is eactly 12%

Someone can explain that ?

#2

Need some help :slight_smile:

#3

Your use of formula 1 & formula 3 etc is confusing. I belive the question is assuming that the CDS is a 5% so it would be priced at par if its credit spread was 500bps. You would then just need to take the change in yield X duration aka 3% * 4 = 12%

If a companies credit spread was that high to begin with you would never be issuing a CDS at 1%, 1% CDS is for much more creditworthy borrowers