CFA Level II ExamFixed IncomeHard
A credit analyst is using a structural credit model, such as the Merton model, to assess the default probability of a company. The analyst estimates the company's asset value, asset volatility, and the face value of its debt. Which of the following assumptions is fundamental to the application of the Merton model?
- AThe company's asset value follows a normal distribution.
- BThe company's default event is an exogenous, unpredictable shock.
- CThe company's equity can be viewed as a call option on its assets.
- DThe company's debt is a perpetual bond.
Show answer & explanationAnswer & explanation
Correct answer: C. The company's equity can be viewed as a call option on its assets.
A fundamental assumption of the Merton model is that the equity of a company can be modeled as a call option on the company's total assets, with the exercise price equal to the face value of its debt and the expiration date being the debt's maturity. Default occurs if the asset value is less than the debt value at maturity.
Why the other options are wrong
- A. The Merton model typically assumes that the company's asset value follows a geometric Brownian motion, implying that the log of asset value is normally distributed, not the asset value itself.
- B. This describes a characteristic of reduced-form models, not structural models like Merton, where default is endogenous (determined by asset value relative to debt).
- D. The model assumes debt has a specific maturity, not that it is perpetual.
Merton Model Assumptions
The Merton model (a structural credit model) views a company's equity as a call option on its assets and its debt as a risk-free bond minus a put option on its assets. Default occurs if asset value falls below the debt's face value at maturity.
- Company assets follow a geometric Brownian motion (log-normal distribution).
- Equity is a call option on assets; debt is a put option on assets.
- Default is endogenous, occurring when asset value < debt value at maturity.
- Debt is a single zero-coupon bond.
Memory trick: Equity's a call, on assets, standing tall.