(b) Consider a European call and a European put on the same underlying non- dividend paying stock. Both options have one month to maturity, and a strike price of 100. The underlying stock can take one of two values at the maturity date, either 130 or 80. The price of the call is 16.36 and the price of the put is 7.27. (1) What is the implied one-month risk-free interest rate? (ii) What is the implied current price of the underlying stock? (c) Consider a two-period binomial model (t = 0, 1, 2), with a risky non-dividend paying stock, FML, which is currently trading for 3.50. In each period, the stock can go up by 30% or down by 10%. The risk-free interest rate is 4% in the first period and 2% in the second period. A European option in the market with underlying stock FML has the following payoff function at the maturity date t = 2: (5 marks) (4 marks) max (ST-Smin, 0) where S, is the price of FML at the maturity date t = 2 and Smin is the minimum stock price FML takes during the life of the option i.e., the minimum stock price FML realises on the path from t = 0 to t = 2. What is the value today of this option? (7 marks)