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HOW DO YOU VALUE A CREDIT DEFAULT SWAP?
March 2011
4 min read
Author: Pierre Wernert
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Warren Buffet once called these products ‘weapons of mass destruction’, how do
credit default swaps work?
--------------------------------------------------------------------------------
MULTI-BILLIONAIRE WARREN BUFFET ONCE CALLED THESE PRODUCTS 'WEAPONS OF MASS
DESTRUCTION', BECAUSE HE THOUGHT THEY WERE PARTLY RESPONSIBLE FOR CAUSING THE
CREDIT CRUNCH. DESPITE THIS REMARK, THERE IS STILL A BUOYANT TRADE IN CREDIT
DEFAULT SWAPS. HERE WE DISCUSS HOW THEY WORK, AND HOW THEY ARE VALUED.
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.
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