CDS Pricer
Price a credit default swap year by year from a constant hazard rate: probabilities of survival and default, expected loss, the protection and premium legs, the par spread and the upfront payment against a standard coupon.
Learning focus: a CDS is fairly priced when the present value of expected default losses (the protection leg) equals the present value of premiums paid while the reference entity survives (the premium leg); any gap from the standard coupon is settled upfront.
| Year | Hazard | Survival to year end | POD (conditional) | POD (from today) | Loss given default | Expected loss | DF | PV of expected loss | Premium PV per 1% coupon |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 2.00% | 98.0000% | 2.0000% | 2.0000% | 6,000,000.00 | 120,000.00 | 0.9709 | 116,504.85 | 95,145.63 |
| 2 | 2.00% | 96.0400% | 2.0000% | 1.9600% | 6,000,000.00 | 117,600.00 | 0.9426 | 110,849.28 | 90,526.91 |
| 3 | 2.00% | 94.1192% | 2.0000% | 1.9208% | 6,000,000.00 | 115,248.00 | 0.9151 | 105,468.25 | 86,132.40 |
| 4 | 2.00% | 92.2368% | 2.0000% | 1.8824% | 6,000,000.00 | 112,943.04 | 0.8885 | 100,348.43 | 81,951.22 |
| 5 | 2.00% | 90.3921% | 2.0000% | 1.8447% | 6,000,000.00 | 110,684.18 | 0.8626 | 95,477.15 | 77,973.00 |
| Total | 9.6079% | 576,475.22 | 528,647.95 | 431,729.16 |
The PV of expected loss column sums to the protection leg. The last column sums to the premium leg at a 1% coupon, so the par spread is the first total divided by the second, times 1%. Premiums are paid at year end only while the reference entity survives; this version leaves out the premium accrued between the last payment and a default, which would raise the premium leg slightly.
With a constant hazard rate, survival falls by the same proportion each year. Survival and cumulative default are complements, so each year they add to 100%.