2. (a) Explain the no-arbitrage valuation approach to valuing a European option using a one-step binomial tree. (b) Prove that early exercise is never optimal for an American call option on a non-dividend-paying stock, [2] (c) A stock price is currently $42. Over each of the next two four-month periods it is expected to go up by 10% or down by 15%. The risk free interest rate is 3% per annum with continuous compounding, (1) What is the value of a cight-month European put option on the underlying stock with a strike price of $41? [6] (ii) What is the value of a cight-month American put option on the underlying stock with the same strike price? (iii) Calculate the delta over each step for part 2(e)i. [3]