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FRM Part I · FRM Exam Part I · Measuring Credit Risk

Holding all other Merton model inputs constant, the volatility of a firm's assets increases. Which outcome is correct?

Equity value rises, risky debt value falls, and default probability rises. Equity is a call on assets and gains from higher volatility, while lenders are effectively short a put whose value increases, reducing the value of the debt and widening the spread.

  1. AEquity value rises, risky debt value falls, and the default probability risesCorrect
  2. BEquity value falls, risky debt value rises, and the default probability rises
  3. CEquity value rises, risky debt value rises, and the default probability falls
  4. DEquity value falls, risky debt value falls, and the default probability falls

Explanation

Equity is a call on assets, and a call's value increases with volatility. Debt equals the risk-free bond minus a put, and the put's value also rises with volatility, so risky debt falls. Greater volatility also raises the chance that assets end below the debt face value, so default probability rises.

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