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FRM Part II · FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment

A risk manager observes that a bond's credit spread has doubled from 100 bp to 200 bp while the assumed recovery rate stays at 50%. Under a constant-hazard reduced-form model, what is the change in the implied one-year conditional default probability, approximately?

With 50% recovery, hazard equals twice the spread: 2% rising to 4%. One-year default probabilities are therefore about 2.0% rising to about 3.9%, roughly doubling. Ignoring recovery would wrongly give 1% to 2%.

  1. AFrom about 2.0% to about 4.0%Correct
  2. BFrom about 1.0% to about 2.0%
  3. CFrom about 2.0% to about 3.0%
  4. DFrom about 1.0% to about 4.0%

Explanation

Hazard = spread/(1-R): 1.00%/0.5 = 2.0% and 2.00%/0.5 = 4.0%. One-year default probabilities are about 1-exp(-0.02)=1.98% and 1-exp(-0.04)=3.92%, so roughly 2% to 4%. The 1% to 2% option ignores recovery.

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