The formula for price of a CDS is:
price of CDS (per $100 notional principal) = $100 - %upfront premium
Shouldn’t it be 100+%upfront premium? If there is a premium involved and the CDS spread is higher than CDS coupon, then you have to pay more. Why is there a minus sign instead of a plus sign?
The formula represents the seller’s point of view. The upfront payment is positive if the bond is riskier than the standard coupon premium payment, and negative otherwise. The positive upfront premium represents the PV of excess credit risk of the bond over the standard premium coupon, that the CDS buyer pays the seller BEFORE all the coupon payments. If the upfront payment is negative, this means the seller of the CDS pays it to the buyer BEFORE she starts paying the coupon premium. Recall, the coupon premium payment is 1% for any IG, 5% for any junk. Therefore, the upfront payment serves to level out the relative riskiness of the bond with respect to standard coupon premium payments