Investments, tenth edition

 Figure 21.15 

Implied volatility of the S&P 500 index as a 

function of exercise price 

  Source: Mark Rubinstein, “Implied Binomial Trees,”  Journal of Finance  (July 

1994), pp. 771–818. 

     1.   Option values may be viewed as the sum of intrinsic value plus time or “volatility” value. The 

volatility value is the right to choose not to exercise if the stock price moves against the holder. 

Thus the option holder cannot lose more than the cost of the option regardless of stock price 

performance.  

    2.   Call options are more valuable when the exercise price is lower, when the stock price is higher, 

when the interest rate is higher, when the time to expiration is greater, when the stock’s volatility 

is greater, and when dividends are lower.  

    3.   Call options must sell for at least the stock price less the present value of the exercise price and 

dividends to be paid before expiration. This implies that a call option on a non-dividend-paying 

stock may be sold for more than the proceeds from immediate exercise. Thus European calls are 

worth as much as American calls on stocks that pay no dividends, because the right to exercise the 

American call early has no value.