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

a) A six month European call option on Cassiopeia 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 Cassiopeia with an exercise price of $90?

c) Verify that put-call parity holds.

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