Sep 12

Cumulative probability of default – 8 min screencast

by David Harper, CFA, FRM, CIPM

FRM |

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This is a helpful exercise for an FRM candidate because we need to apply three steps (each itself testable; from Saunders Chapter 11) to get the answer.

To help you follow in this screencast, I color-coded the three steps…

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We are given two spot rate term structures (spot rates for Treasuries and for risky corporate bond). The question is, what is the 2-year cumulative probability of default (PD)?

  1. Compute 1-year forward rates. I follow Saunders with annual compounding but I briefly show how to similarly use continuous compounding (which John Hull uses, but which is not the FRM assigned approach). This has previously caused confusion. Neither is wrong.
  2. Compute marginal probability of defaults
  3. Compute the 2-year cumulative probability of default

Here is the practice question:

  • Treasury (riskless asset) spot rates are 4% (1 year spot) and 5% (2 year spot)
  • Corporate bond spot rates are 5% (1 year spot) and 7% (2 year spot)
  • What is the corporate bond's 2-year cumulative probability of default?

Screencast with the answer:

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