A stock price is currently trading at $100 and the annually compounded risk-free interest rate is 5%. In one year, the stock price will either be $110 or $95. If in one year the stock price is $110, the stock price will either be $121 or $104.5 one year after then. If in one year the stock price is $95, the stock price will either be $104.5 or $90.25 one year after then. (a) (b) Assuming that there is no arbitrage in the market and the interest rate stays constant throughout the whole investment period. If there is a derivative on the market that has payoff max($1.5 - 100,0), where S is the stock price in two years, use a two-step binomial tree to find the price of this derivative. [15 marks] If in one year the stock price is $110, the risk-free rate is 6% one year after then. If in one year the stock price is $95, the risk-free rate is 4% one year after then. Find the current price of a call on the underlying stock with strike price $108 and 2-year maturity. (c) [12 marks] If the call option described in part (b) is an American call option, explain whether you would early exercise the call option. [4 marks]