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A stock price is currently $50 per share. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. All the options below are on this stock. The continuously compounding risk-free interest rate is 5% per annum.
(a) What is the value of a six-month European call option that strikes at $51?
(b) What is the delta of the call option at the beginning and in three months?
(c) What is the value of a six-month European put option that strikes at $51?
(d) Do the European call and put values satisfy the put-call parity? Show your verification.
(e) If the put option were American, would it ever be optimal to exercise early at any of the nodes on the tree? What would be the value of the option?
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