The price of CDS refers to the CDS spread or upfront payment given a particular coupon rate for a contract. Unlike conventional derivatives where the underlying is actively traded, the underlying of a CDS, that is, the credit quality, is not traded.

Basic Pricing Concepts

Probability of default: the degree of likelihood that the borrower will fail to make scheduled principal and interest payments.

Hazard rate: the probability of default at any point in time (t), given that no default has occurred prior to that time. It is a conditional probability of default.

Loss given default: the loss if a default occurs.

Expected loss = Loss given default x Probability of default

A CDS is comprised of a premium leg and a payment leg (contingent leg).

To calculate the value of protection leg, we need to consider:

• The probability of each payment,
• The timing of each payment, and
• The discount rate.

To calculate the value of premium leg, we need to consider various hazard rates.

The CDS premium is determined by the no-arbitrage condition. Any different in the two series results in an upfront payment from the party having the greater present value to the counterparty.

Upfront payment = PV of protection leg - PV of premium leg

The Credit Curve

The credit spread of a bond is the rate in excess of LIBOR paid to investors to compensate them for assuming credit risk.

credit spread ≈ probability of default x loss given default

The credit curve is a curve that graphically exhibits credit spreads for a range of maturities of a company's debt. It is essentially determined by the CDS rates.

The hazard rate is a key factor that affects the shape of credit curve.

• A constant hazard rate -> A flat credit curve.
• Greater hazard rates in later years -> An upward-sloping credit curve.
• Greater hazard rates in early years -> A downward-sloping credit curve.

CDS Pricing Conventions

Upfront premium = PV of the credit spread - PV of the fixed coupon
= (credit spread - fixed coupon) x duration of the CDS

or:
PV of the credit spread = Upfront premium + PV of the fixed coupon
Credit spread ≈ (Upfront premium/Duration) + Fixed coupon
Upfront premium % = 100 - Price of CDS in currency per 100 par

Valuation Changes in CDS during Their Lives

Like other financial instruments, the value of a CDS changes over time in response to changes in various factors such as duration, reference entity's credit quality, probability of default, the expected loss given default, and the shape of the credit curve, etc. The new market value of the CDS reflects gains and losses to the two parties.

Profit for the protection buyer = Change in spread in bps x Duration x Notional %Change in CDS price = Change in spread in bps x Duration

Monetizing Gains and Losses

• The protection buyer gains if the company's credit spread increases.
• The protection seller gains if the company's credit spread decreases (i.e., credit quality improves).

Either party can enter into offsetting CDS to monetize gains or losses of the original CDS contract. Another way to realize a profit or loss on a CDS is to exercise the CDS when a credit event occurs.