Merton model [practice, credit]
by David Harper, CFA, FRM, CIPM
The Merton model is a classic in credit risk. If you are interested in a few resources from last year: here is a 10-minute video I recorded last year to introduce the role of d2 in the Merton model for credit risk; and another with a bit more context (including how Merton is a so-called structural type of model) - David
[source FRM sample 2009 Full Exam 1] Question Full E1.08: You don’t have access to KMV’s data. Your boss wants you to tell him your estimate of the probability of default of a credit. To do so, you use the Merton Model because the credit you are considering has no systematic risk. In Merton’s Model, the distance to default (DD) and the expected default frequency (EDF) are:
a. positively and linearly related
b. negatively and linearly related
c. positively and non-linearly related
d. negatively and non-linearly related
my adds [some of these are tough]
- E1.08e. Explain the Merton Model in a few brief sentences.
- E1.08f. Cite two differences between Merton Model and Moody's KMV.
- E1.08g. Cite a few variables that would decrease the EDF?
- E1.08h. Cite a disadvantage of this approach (i.e., equity-based model of default prediction).
- E1.08i. [hard] The question implies that the Merton Model requires, or wants, an assumption that the credit has no systematic risk. Is this true?
- E1.08j. [hard] As the relationship between DD & EDF is non-linear, can we be more specific: what is the distribution of DD? Reconcile this distribution with the lognormal property of stock prices.
- E1.08k. The answer says the risk-neutral probability of default (PD) = 1 – N(d2). But de Servigny says PD = N(-d2). Which is correct?
- E1.08l. If the distance to default (DD) is 2.0, what is Merton's implied risk-neutral probability of default (PD)?
- E1.08m. [hard] Under risk-neutral valuation, can we assume this PD applies in the real world?
My answers here in forum or here in wiki.
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