Sep 18

Beta distribution for loss given default (LGD) – 7 min screencast

by David Harper, CFA, FRM, CIPM

FRM |

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A brief explanation of the beta distribution which is commonly used to model loss given default (LGD; 1-recovery rate).  I show the EditGrid/excel model (on the member page) by illustrating a beta distribution for a junior-type obligation (recovery = 25%, LGD = 75% like Basel II foundation approach) and a senior-type obligation (45% LGD per Basel II).

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For FRM candidates, please note:

  • Whereas point estimates are typical for probability of default (PD), the LGD is harder to estimate. LGD therefore deserves to be characterized by a distribution owing to its random nature (most importantly, wide dispersions in LGD statistics).
  • Its strengths are: we can bound by [0,1], it is flexible and it only requires the two parameters. Alpha gives the “center” while beta gives the “shape” (tail fatness)
  • Its key weakness is that it can only be unimodal (a single hump). Recovery data is often bimodal, which includes the ideas of high densities near zero (no recovery) and 100% (full recovery)

Screencast:

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