A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding.
a) What is the value of a six-month European call option with a strike price of $51?
b) For the situation considered in the earlier problem, what is the value of a six-month European put option with a strike price of $51? Verify that the European call and European put prices satisfy put–call parity.
c) If the put option in the earlier problem was American, would it ever be optimal to exercise it early at any of the nodes on the tree? Find the value of this American put option.