Investments, tenth edition

     5.   The Black-Scholes formula applies to options on stocks that pay no dividends. Dividend 

adjustments may be adequate to price European calls on dividend-paying stocks, but the proper 

treatment of American calls on dividend-paying stocks requires more complex formulas.  

     6.   Put options may be exercised early, whether the stock pays dividends or not. Therefore, 

 American puts generally are worth more than European puts.  

     7.   European put values can be derived from the call value and the put-call parity relationship. This 

technique cannot be applied to American puts for which early exercise is a possibility.  

     8.   The implied volatility of an option is the standard deviation of stock returns consistent with 

an option’s market price. It can be backed out of an option-pricing model by finding the stock 

volatility that makes the option’s value equal to its observed price.