Consider a two-period binomial model for a non-dividend-paying share whose current price is So= £100. Over each six-month period, the share price can either move up by a factor u 1.2 or down by a factor of d = 0.8. the risk-free rate is r = 5% per six-month period. (a) Prove that there is no arbitrage in the market. (b) Construct the binomial tree of share prices. (c) Calculate the price of a European call option written on the share with a strike price K = £100 and maturity of one year. [3 (d) Consider a modified call option based on the above parameters. In this case, the underlying asset price at maturity is the arithmetic average of share prices, denoted Ar, at times 0, 0.5 and 1 measured in years. That is, the payoff at maturity is given by max {AT-100, 0} . Calculate the initial price of this call option, assuming it can only be exercised at maturity.