Sep 17

Expected default frequency (EDF, PD) with Merton Model – 9 min screencast

by David Harper, CFA, FRM, CIPM

FRM |

A graphical and Excel-based review of the Merton model for estimating probability of default…

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For FRM candidates, a few notes:

  • This Merton model for PD/EDF is not option pricing. Option pricing can be used to solve for (i) the firm’s asset value and (ii) the asset volatility. Those become inputs into this exercise. After we use option-pricing theory to get asset value and volatility, the calculation of EDF under the Merton model is a mechanical formula and some statistics (standard normal distribution)
  • At the end, to estimate the expected default frequency (EDF), we use N(-distance to default). In other words, PD  = N(-d2) = NORMSDIST(-d2). This is the same N(d2) found in the Black-Scholes except for two differences.

    First, instead of strike price, we use the default point or default threshold; e.g., short-term liabilities plus one-half long-term liabilities.

    Second, and this is the important difference, Black-Scholes OPM uses a riskless rate; but this Merton model uses the expected return (growth) on the firm’s assets. That’s because this is not option pricing, risk-neutral valuation is not being used!
  • KMV does not take the final step; KMV does not conclude that PD = NORMSDIST(-DD). To use N() or NORMSDIST() it to assume normality. The KMV EDF will be greater than N(-d2) due to “heavier tails” implied by their non-parametric approach. In brief, KMV EDF > N(-d2).

Screencast:

Comments

  1. kolzhas2008 20 Sep 2008

    quick remark, it should be sigma squared not sigma sub 2, right?

  2. David Harper, CFA, FRM, CIPM 21 Sep 2008

    Yes absolutely correct. As the rate is “eroded” by one half the variance, the numerator should be sigma^2. Thank you for correcting this! David

  3. Tjahyadi 18 Nov 2008

    How to find the volatility ?
    Thanks

  4. Tjahyadi 18 Nov 2008

    How to find the asset volatility ?

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