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FRM Part II · FRM Exam Part II · Credit Risk

In the Merton model, a firm has asset value of 140 and zero-coupon debt with face value 100 due in one year. The risk-neutral probability of default is 10%. The risk-free rate is zero for simplicity. Equity is viewed as a call option on assets. Which statement about the effect of an increase in asset volatility, holding asset value and debt constant, is correct?

Equity rises and debt falls. In the Merton model equity is a call option on firm assets, and higher asset volatility increases option value. With total asset value held constant, the gain to equity holders comes at the expense of debt holders, whose claim is effectively short a put.

  1. AEquity value rises and debt value fallsCorrect
  2. BEquity value falls and debt value rises
  3. CBoth equity and debt values rise
  4. DBoth equity and debt values fall

Explanation

Equity is a call on assets with strike equal to debt face value, so higher volatility raises its value. Since assets are fixed, the total value is unchanged, so risky debt value (assets minus equity) falls. Shareholders gain at creditors' expense.

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