The binomial model can be used to price unusual features of options. Consider the following scenario. A stock priced at $75 can go up by 20 percent or down by 10 percent per period for three periods. The risk-free rate is 8 percent. A European call option expiring in three periods has an exercise price of $70. The parties to the option agree, however, that the maximum payout of this option is $40.
Find the current value of the option. Then determine whether an American version of the option, also limited to a maximum payout of $40, would have any additional value over the European version.
Compare your answers to the value of the option if there were no limitation on the payoff.