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b) A stock price is currently 40. Over each of the next two three- month periods, it is expected to go up by 10% or down by 10%. The risk-free interest rate is 12% per annum with continuous compounding. Calculate the price of a six-month American Put option with strike price 42 using the binomial method. Demonstrate your methods. (13 marks) c) A European put option has an exercise price of 105. It has one year to expiration. The underlying stock does not pay any dividends and has a current price of 100. This price has a 50% chance of increasing to 110 and a 50% chance of decreasing to 90. The risk-free rate of interest is 1% p.a. Calculate the price of the put option using the two-state stock price model applying the replicating portfolio method. (8 marks) d) Show what happens to the price of a call option in the Black-Scholes model when Ndi) and N(da) tend to 1. How is this different from when Nd) and Nida) tend to 02. What is the interpretation therefore of Nid) and Nida)