# Fixed coupon for CDS index

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.