Problem $5\mathrm{.}1$

Apply the control variate method to the two American options in Problem $3\mathrm{.}5,$ using the European option as control variate, in order to obtain an improved estimate for the American option prices.

Use the same option and market parameters as in Problem $3\mathrm{.}5.$ Recall that for the control variate method one has to complute the European option prices both using the binomial tree method, and exactly using the BlackScholes formula. $($The exact rosults were obtained in Problem $4\mathrm{.}2.)$