Exercise 1: Pricing American options (14 Marks) Let us assume that todays stock price is 40 and it is expected either to increase by 10% or to decrease by 10% every period over the next three 3-months periods (three-period Binomial tree). Also, suppose that the continuously compounded risk-free rate of interest is 4% per annum.

(a) Find the price of a 9-month European call option with strike price 45, written on a non-dividend paying stock. (2Marks)

(b) By checking the values at all nodes, find the price of a 9-month American call option with strike price 45, written on a non-dividend paying stock. Is an early exercise optimal? (6Marks)

(c) Find the price of a 9-month American put option with strike price 45, written on a non-dividend paying stock. Is an early exercise optimal?