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Answer: The company's PD is 5.20%, and a limitation of the Merton model is that it is costly, especially for smaller firms, to continuously calibrate PD on historical series of actual defaults.
## Explanation **Correct Answer: C** Using the Merton model, the probability of default (PD) is calculated as: $$PD = N\left(\frac{\ln(F) - \ln(V) - \mu(T - t) + \left(\frac{\sigma^2}{2}\right)(T - t)}{\sigma\sqrt{T - t}}\right) = -1.626$$ Where: - V = CAD 400,000,000 (company's asset value) - F = CAD 300,000,000 (face value of debt) - σ = 0.25 (volatility) - μ = 0.15 (expected return) - T-t = 1 (time to maturity) The company's PD = N(-1.626) = 5.20% (Using Excel: PD = NORMSDIST(-1.626) = 0.051975) **Limitation of Merton Model:** The Merton model has several limitations: - It is applicable to liquid, publicly traded names only - There is continuous need for calibration of PD on historical series of actual defaults - This analytical maintenance requirement is costly for smaller organizations - The model relies on continually changing movements in market prices, volatility, and interest rates **Why other options are incorrect:** - **A**: 3.03% is incorrect - this results from subtracting instead of adding the last term in the formula - **B**: 4.04% is incorrect and the limitation description is inaccurate - **D**: 12.49% is incorrect and the limitation description is misleading
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A credit risk analyst at a bank is using the Merton's model to estimate the probability of default (PD) of a non-dividend-paying company. The company's debt consists of only long-term zero-coupon bonds. The analyst gathers the following information:
| Parameter | Value |
|---|---|
| Value of the company's assets | CAD 400 million |
| Face value of the company's debt | CAD 300 million |
| Expected rate of return of the value of company's assets | 15% |
| Instantaneous volatility of the value of company's assets | 25% |
| Annual interest rate | 3% |
| Remaining time to maturity for the company's debt | 1 year |
What is the PD of the company and a limitation of using the Merton model to predict default of the company?
A
The company's PD is 3.03%, and a limitation of the Merton model is that it cannot be applied to debt holdings maturing in more than 1 year.
B
The company's PD is 4.04%, and a limitation of the Merton model is that it only applies under the assumption that the value of the firm is normally distributed.
C
The company's PD is 5.20%, and a limitation of the Merton model is that it is costly, especially for smaller firms, to continuously calibrate PD on historical series of actual defaults.
D
The company's PD is 12.49%, and a limitation of the Merton model is that it is not capable of continuously calibrating PD due to continually changing movements in interest rates and market prices.