A company is currently trading at $100 per share. After examining the stock, determined that in each 3 month period, its price will either increase to 25% or decrease by 20%. The interest rare is 3% every 3 months.

a) A six month Europrean call option on this company has an exercise price of $90. What is the value of this call option?

b) What is the value of a six month European put option on this company with an exercise price of $90?

c) Verify that put-call parity holds.

d) Now suppose that the company pays a dividend equal to $25 in three months. What is the value of a six month American call option on the company with an exercise price of $90? Would an individual ever want to exercise this option early?