Options trading:

A stock price is currently 50. Over each of the next 3-months periods it is expected to go up by 7% or down by 6%. The risk-free interest rate is 6% per annum with continuous compounding.

(a) What is the value of a 6 months European call option with a strike price of 51?

(b) Compute the price of the 6 months European put option with a strike price of 51 using the put-call parity [Do not use a binomial tree]. Please give explanation.

(c) Compute the value of the European put option with a strike price of 51 using a two-step tree.

(d) Verify that the European call and European put prices satisfy put-call parity. Discuss using the results from previous answers.

(e) If the put option were American, would it ever be optimal to exercise it early at any of the nodes on the tree? lease give explanation.