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# P2.T6.212. Merton-based default probabilities

#### Suzanne Evans

##### Well-Known Member
Because this set is part of a fresh global topic review (T6) these questions try to approximate the difficulty level FRM exam questions; i.e., not too deep. For a more detailed discussion of the Merton model for credit risk, please see "Merton model, a summary of the issues" in David's Notebook at http://www.bionicturtle.com/forum/threads/merton-model-a-summary-of-the-issues.5646/

Questions:

212.1. The asset value of a firm is currently $24.00 million but expected to grow to$27.27 million at the end of one year, at which time it's only debt matures with a face value of $15.00 million. The firm's asset volatility is 18.0%. Which is nearest to the firm's lognormal distance to default (DD) at the one year forward horizon? a. 1.00 b. 1.92 c. 2.50 d. 3.15 212.2. Each of the following is true about the KMV model EXCEPT which is false? a. Unlike Merton, which assume the default threshold is total debt, KMV's default threshold falls between short-term and total (short-term + long-term) debt b. Similar to the Merton model, the KMV approach requires an estimate of asset volatility and future asset value in order to calculate distance to default as a number of standard deviations c. Similar to the Merton model, the KMV approach models distance to default (DD) = (asset market value - default threshold)/(asset market value * asset volatility) d. Similar to the Merton model, the KMV approach assumes the future asset value is lognormal such that asset (log) returns are normal with EDF ~= N(DD) 212.3. Analyst Greg is employing the Merton model to both value a firm's equity and estimate a default probability. He has collected the following information: • The firm's default threshold one year forward is$10.00 million; e.g., face value of short-term debt is $10.00 million • The firm current asset value is$12.75 million with an expected return of +8.0% per annum with continuous compounding
• The volatility of the firm's assets is 9.60%
• The risk-free rate is 2.0%
His exercise includes two components: one, valuation of the firm's equity market value by treating equity as a call option on the firm's assets; two, estimate of default probability by calculation of a forward distance to default. Greg makes two assumptions:

I. An increase in the risk-free rate will increase an estimate of the firm's current equity market value, and
II. An increase in the risk-free rate will decrease the estimated default probability
Which of Greg's two assumptions is correct?

a. Neither
b. I. only
c. II. only
d. Both

#### Suzanne Evans

##### Well-Known Member
@[email protected],

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