المدربThe risky discount factor of a name to is , the value of one unit paid at if the name has survived, with deterministic hazard rates and independent of rates. The risky annuity of a default swap is the value of one unit a year of premium paid while the name survives, plus the premium accrued to a default within each period.
أمثلة
Example 13.12 (A five-year bond on the curve)
A five-year 5% bond of the name (semi-annual coupons) is worth 107.08 per 100 on the riskless curve and 101.38 on the bootstrapped hazard curve. The risky discount factor to five years is 0.7604, against a riskless 0.8427. If the bond trades at 97.00, the flat hazard that reprices it corresponds to a default-swap spread of 220 basis points: the bond is 100 basis points cheaper than the default swap says, a negative basis of basis points (default swap minus bond-implied spread).
Example 13.15 (A protection position)
Long USD 10 million of five-year protection at the 100 coupon on the curve of Example 13.7: worth USD 88 133 (the risky annuity is 4.41), with a CS01 of USD 4 391 on the five-year quote and almost nothing elsewhere, and a jump-to-default gain of USD 5.91 million.