Factors Affecting CDS Pricing
What you'll learn
- LOS 27.cExplain the principles underlying and factors that influence the market’s pricing of CDS.
The factors that influence the pricing of CDS (i.e., CDS spread) include the probability of default, the loss given default, and the coupon rate on the swap. The CDS spread is higher for higher probability of default and for higher loss given default. For this discussion, we will focus on single name CDS.
However, the principles apply to index CDS as well.
Earlier, we showed the calculation of CVA, which is the present value of expected loss. CVA, therefore, would be the best estimate of the value of the hedging instrument to cover the risk of the protection seller.
Probability of default (POD) is the likelihood of default by the reference entity in a given year. However, because the CDS typically covers a multi year horizon, the probability of default is not constant; the probability of default usually increases over time. Hence, the probability of default in any given year assumes that no default has occurred in the preceding years.
We call the probability of default given that it has not already occurred the conditional probability of default or hazard rate. The credit risk of a reference obligation and hence the cost of protection is proportional to the hazard rate. The POD in any year is equal to the probability of survival at the end of the prior year multiplied by the hazard rate of that year.
Consider a five year senior CDS on Xeon Corp. Xeon’s hazard rate is 2% and increases by 1% per year.
Compute the survival rate in five years.
Solution
The hazard rates for the five years are: 2%, 3%, 4%, 5%, and 6%.
For a single period CDS, ignoring the time value of money, we can estimate the CDS premium as:
For example, if the recovery rate is 50% and POD is 3%, CDS spread = 0.5 × 0.03 = 0.015 or 150 bps.
The cash payments made by the protection buyer on the CDS (i.e., the coupon payments) cease when there is a default (i.e., when the CDS terminates). Hence, the expected value of the coupon payments also depends on the hazard rate.
The payments made by the protection buyer to the seller are the premium leg. On the other side of the contract, the protection seller must make a payment to the protection buyer in case of a default; these contingent payments make up the protection leg.
The difference between the present value of the premium leg and the present value of the protection leg determines the upfront payment.
We can approximate the upfront premium as the difference between the CDS spread and the CDS coupon rate, multiplied by the duration of the CDS. Again, the CDS spread is the compensation for bearing the credit risk of the reference obligation.
We can also quote the CDS price as:
Aki Mutaro, bond portfolio manager for a regional bank, is considering buying protection on one of the bank’s high yield holdings: Alpha, Inc., bonds. Ten year CDS on Alpha bonds have a coupon rate of 5% while the 10 year Alpha CDS spread is 3.5%. The duration of the CDS is 7.
Calculate the approximate upfront premium and price of a 10 year Alpha Inc., CDS.
Solution
Hence, the protection seller would pay (approximately) 10.5% of the notional to the protection buyer upfront because the CDS coupon is higher than the credit spread.
Valuation After Inception of CDS
At inception of a CDS, the CDS spread (and the upfront premium) is computed based on the credit quality of the reference entity. After inception, the credit quality of the reference entity (or the credit risk premium in the overall market) may change. This will lead to the underlying CDS having a nonzero value.
For example, if the credit spread declines, the protection seller, having locked in a higher credit spread at initiation, would gain.
The change in value of a CDS after inception can be approximated by the change in spread multiplied by the duration of the CDS:
or
Note that the protection buyer is short credit risk and hence benefits (i.e., profit is positive) when credit spreads widen.
The protection buyer (or seller) can unwind an existing CDS exposure (prior to expiration or default) by entering into an offsetting transaction. For example, a protection buyer can remove his exposure to the CDS by selling protection with the same terms as the original CDS and maturity equal to the remaining maturity on the existing CDS. The difference between the upfront premium paid and received should be (approximately) equal to the profit for the protection buyer.
This process of capturing value from an in the money CDS exposure is called monetizing the gain.