How do you value a credit default swap?

A credit default swap, or CDS, is effectively an insurance product whereby the consequences of a bankruptcy (default) of a reference party are transferred in return for a periodic payment. Take, for example, a party that wishes to purchase or has already purchased a bond, but is keen to avoid the (further) risk that the seller will go bankrupt. By concluding a CDS, any loss sustained in the case of default is compensated, or paid off, in return for a periodic payment; the premium for the CDS.

The CDS is valued in much the same way as its cousin, the interest rate swap. In an interest rate swap, the exchange of fixed and variable interest cash flows is valued by estimating the amount of the future cash flows in advance. These cash flows are then discounted at the market interest rate applicable at that time and added up. In the case of a CDS, two types of cash flow are also exchanged. Firstly, a series of cash flows from the risk seller to the risk buyer, including the periodic payment of the premium. These cash flows are then exchanged for a (possible) cash flow from risk buyer to risk seller in the event of a default. The periodic payment ceases immediately if that bankruptcy actually takes place.

rating transition matrix

The greatest uncertainty in valuing a CDS is the moment of bankruptcy. This is generally determined by means of probability distribution and modeled on the basis of the ‘probability of default’ (PD). This probability can be obtained in the market by combining the rating of the bond with the rating transition matrix. These ratings are prepared by rating agencies. A triple-A rating is considered to denote ‘virtually risk-free’, a D rating means that a default event has already occurred. The matrix then indicates how great the probability is that a reference party will migrate from one rating to another.

Table 1 is a fictitious example of a rating transition matrix:

In order to illustrate the valuation of the CDS, we give an example of a credit default swap with the following assumptions:

• the term is two years,
• in case of bankruptcy, the loss is equal to the entire principal,
• the reference party’s current rating is BBB,
• we take the (fictitious) rating transition matrix from table 1, and
• the premium on the CDS is 4% of the principal.

Table 2 shows the probability distribution when calculating the moment of default:

Explanation of table 2:
In year 1, the probability of default (the probability of migration from rating BBB to D) is: 5%. Taking into account this probability of default in that first year, the robability of bankruptcy in year 2 is 95%, multiplied by the following two-stage default probabilities:

• constant year 1 (BBB), followed by bankruptcy (70% x 5%),
• downgrade to CCC, followed by bankruptcy (20% x 20%), and
• upgrade to AAA, followed by bankruptcy (15% x1%).

The anticipated cash flows that are payable are equal to the premium in the first year (4) and 95% of the premium in the second year (95% x 4=3.8). The anticipated cash flows that are receivable are equal to 5% of the principal (5) in the first year and 7% of the principal in the second year (7).

Assuming an interest rate of 2% per year, the following calculations apply:

The market value of the CDS is positive because the discounted present value of the premium payments is lower than the anticipated payments in the case of bankruptcy.