Investments, tenth edition

  Option Pricing and Portfolio Theory 

 We’ve just seen that the option pricing model predicts that security risk characteristics can 

be unstable. For example, as the firm weakens, the risk of its debt can quickly accelerate. 

So, too, can equity risk change dramatically as the firm’s financial condition deteriorates. 

We know from the last chapter (Section 20.5) that equity in a levered firm is like a call 

option on the value of the firm. If firm value exceeds the value of the firm’s maturing debt, 

the firm can choose to pay off the debt, retaining the difference between firm value and the 

face value of its debt. If not, the firm can default on the loan, turning the firm over to its 

creditors, and the equity holders get nothing. In this sense, equity is a call option, and the 

firm’s total value is the underlying asset. 

 In Section 21.5, we saw that the  elasticity  of an option measures the sensitivity of its rate 

of return to the rate of return on the underlying asset. For example, if a call option’s elasticity 

is five, its rate of return will swing five times as widely as the rate of return on the underlying 

asset. This would imply that both the option’s beta and its standard deviation are five times the 

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Firm Value as Percent of Face Value of Debt

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alue of Put as % of Face

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alue of Debt