31.

The price of a stock today is $30. After every 6 months, it can either go up by a factor U = 1.25 or go down by a factor D = 0.75. The interest rate is 9% per annum, continuously compounded. Consider an American call with a strike price of $32 and time to maturity of 1 year. Build a two-period binomial tree to find the price of the American call. What is the replicating portfolio today of the American call?

a.

Buy 0.5683 shares and borrow $13.16

b.

Buy 0.5613 shares and borrow $12.07

c.

Buy 0.5052 shares and borrow $16.22

d.

Buy 0.4872 shares and borrow $17.93

e.

Buy 0.5364 shares and borrow $16.85