CoachThe credit triangle is the rule of thumb of Proposition 13.4, used to read a hazard rate from a spread (and back) in the head.
Examples
Example 13.7 (An investment-grade curve)
Par spreads of 60, 75, 90, 120, 135 and 150 basis points at one, two, three, five, seven and ten years (illustrative), recovery 40%, on chapter 1’s SOFR curve, bootstrap to hazards of 1.00%, 1.51%, 2.04%, 2.86%, 3.03% and 3.32% on the successive intervals (Figure 13.2). The credit triangle gives 1.00%, 1.25%, 1.50%, 2.00%, 2.25% and 2.50%: the average hazard to each maturity, where the bootstrap gives the forward hazard on each interval. The probability of default is 0.995% over one year, 9.76% over five and 23.1% over ten (Figure 13.3).