Basic pricing concepts:
Example: Assume that the hazard rate for a 10 year bond is 2% each year. The probability of no default in 10 years is (0.98) × (0.98) … (0.98) = (0.98)10 = 0.817. Thus, the probability of default is 1 – 0.817 = 0.183, or 18.3%.
Pricing a CDS means determining the CDS spread or upfront payment given a particular coupon rate for a contract.
The upfront payment of a CDS is calculated as the difference in the present value of the protection leg and the present value of the premium leg.
Upfront payment = present value of protection leg – present value of premium leg
Protection leg is the payment from the credit protection seller to the buyer when a default occurs. Premium leg is a series of payments from the protection buyer to the protection seller until default occurs. The party with the greater present value makes a payment to the counterparty.
CDS prices are often quoted as credit spreads. The convention in the CDS market for the fixed payments made from the CDS buyer to the CDS seller is to use standardized coupons of 1% for investment-grade debt and 5% for high-yield debt. If the credit spread of the reference obligation is different from these rates, then an upfront payment is made from one party to the other.
Credit spread ≈ (Upfront premium/Duration) + Fixed coupon
PV of credit spread = Upfront premium + PV of fixed coupon
Upfront premium ≈ (Credit spread – Fixed coupon) x Duration
The change in the value of CDS after inception can be calculated as:
Profit for the buyer of protection ≈ Change in spread in bps * Duration * Amount