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FRM Part II · FRM Exam Part II · Fundamentals of Credit Risk

In a Merton model, a firm's equity is viewed as a European call option on firm assets with strike equal to the face value of zero-coupon debt. Firm asset value is 150, debt face value is 100 due in one year. Holding other inputs constant, which change would most clearly increase the value of equity and decrease the value of risky debt?

An increase in asset volatility raises equity value because equity is a call option on firm assets, and it lowers risky debt value because debt holders are short a put on those assets. Wealth shifts from creditors to shareholders when asset risk rises.

  1. AA decrease in asset volatility
  2. BAn increase in asset volatilityCorrect
  3. CA decrease in the debt face value
  4. DA fall in the risk-free rate

Explanation

Equity is a call option, so its value rises with asset volatility (higher vega). Since assets plus nothing else equal debt plus equity, the debt value falls by the same amount; debt holders are effectively short a put. Lower volatility or lower debt face value would raise debt value instead.

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