1. A stock price is currently $55. Over each of the next two 5-month periods it is expected to go up by 7% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. The strike price is $56 for a 10-month European call.

a) What are the values for u, d, and p in a two-step binomial tree?

b) What is the value of the 10-month European call option given by a two-step binomial tree?

c) What is the value of the 10-month European put option on the same stock with a strike price of $56 given by a two-step binomial tree?

d) Verify that European call and European put option prices satisfy the put-call parity?

e) What is the value of the 10-month American call option on the same stock with a strike price of $56 given by a two-step binomial tree?

f) What is the value of the 10-month American put option on the same stock with a strike price of $56 given by a two-step binomial tree?

g) Verify that American call and American put option prices satisfy the put-call parity?