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Here is the fixed coupon for CDS index in John Hull's book Options, Futures and Other Derivatives 9th page 580.

Actually, I don't much understand the goal of this part, here is some of my understanding, I am not sure whether it is right.

Assume there is only one company in the index, the buyer of CDS will pay the coupon $c$ to seller every quarter until the default occurs.

Seller will pay the the protection $(1-R)B$ when the default occurs. As the definition of spread, seller equivalently pays the spread $s$ to buyer every quarter until the default occurs.

$D$ is the present value of paying $1$ every quarter until the default occurs. So the present value of this contract of notional principle $1$ is $$D\times (s-c)$$

which is the amount buyer should pay for the seller at beginning.

Are the above statements right? But why do we need the coupon $c?$ We can set $c=0$ to simply the process i.e there is only one cash flow from the seller during the contract.

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Coupons are there to reduce the counterparty risk between the seller and the buyer. If you didn't have that 500 bp coupon on a high yield bond the protection buyer would have to make a big payment upfront then wave it goodbye when the protection seller defaults. It also helps standardizing contracts (same quarterly payments whatever the spread you entered the contract at).

It's explained here http://economicsofcontempt.blogspot.hk/2009/01/upfront-cds-with-fixed-coupons.html

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  • $\begingroup$ thanks, is my understanding of the value of CDS index right? $\endgroup$
    – A.Oreo
    Commented Aug 30, 2017 at 10:40
  • $\begingroup$ No, the seller doesn't pay the spread to the buyer. The spread is just used to compute the initial cash outflow (and subsequently the mark-to-market). If the spread is 150 bps and the coupon is 100 bps, the initial price of the CDS is 50 bps * duration. $\endgroup$
    – Lliane
    Commented Aug 30, 2017 at 14:03
  • $\begingroup$ As mentionned in the book the regular quarterly payments are independent of the spread. $\endgroup$
    – Lliane
    Commented Aug 30, 2017 at 14:10
  • $\begingroup$ yeah,, I mean the seller only pays the protection when the default occurs, and the present value of this equals to pay the spread every quarter. $\endgroup$
    – A.Oreo
    Commented Aug 30, 2017 at 14:20
  • $\begingroup$ thank you for your help, I am recently reading credit products in John Hull's, maybe there are a lot of questions. $\endgroup$
    – A.Oreo
    Commented Aug 30, 2017 at 17:22

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