solution

A stock follows a binomial process for two periods. At time t=0 the price is $100, and at time t=1 the stock price is either $120 or $90. If the time t=1 price is $120, the time t=2 price can be either $144 or $108. If the time t=1 price is $90, the time t=2 price is either $108 or $81. The riskless interest rate is 5% per period. An Americancalloption has an exercise price of $100.
a) Draw the binomial tree for this stock. Include the value at expiration in each of the final states of the American call option on the tree.
b) Calculate the value of the call option at time t=1 if the stock price is $120. What is the hedge ratio for the call?
c) Calculate the value of the call option at time t=1 if the stock price is $90. What is the hedge ratio for the call?
d) Calculate the value of the call option at time t=0. What is the hedge ratio for the call at time t=0?