Investments, tenth edition

Hedging Bets on Mispriced Options 

 Suppose you believe that the standard deviation of IBM stock returns will be 35% over the 

next few weeks, but IBM put options are selling at a price consistent with a volatility of 

33%. Because the put’s implied volatility is less than your forecast of the stock volatility, 

you believe the option is underpriced. Using your assessment of volatility in an option-

pricing model like the Black-Scholes formula, you would estimate that the fair price for 

the puts exceeds the actual price. 

 Does this mean that you ought to buy put options? Perhaps it does, but by doing so, 

you risk losses if IBM stock performs well,  even if  you are correct about the volatility. You 

would like to separate your bet on volatility from the “attached” bet inherent in purchasing 

a put that IBM’s stock price will fall. In other words, you would like to speculate on the 

option mispricing by purchasing the put option, but hedge the resulting exposure to the 

performance of IBM stock. 

 The option  delta  can be interpreted as a hedge ratio that can be used for this purpose. 

The delta was defined as   

 

  Delta 5

Change in value of option

Change in value of stock

  

(21.5)  

Therefore, delta is the slope of the option-pricing curve. 

35

25

30

20

15

Elasticity

5

0

25

50

75

100

125

Stock Price

175

150

200

10