1. Answer three parts of this question. Your answers for each part should be no more than two pages long. (a) Both European put and call options can be used to provide portfolio insurance. Explain the strategies required for each option and show that they are equivalent. (b) American call options should never be exercised early. Critically evaluate this statement, providing proofs of your arguments where necessary. (c) Holding all other factors constant, what happens to the price of European put and call options when the price volatility of the underlying asset decreases? Fully explain your answer. (d) Describe how to construct an option trading strategy that will deliver a certain outcome at maturity. (e) In the Binomial Model of Option Pricing, the risk neutral probability of an upward movement in the underlying stock price will be different for two identical stocks if one pays a dividend and the other does not. Is this statement true, false or uncertain? Explain your answer fully.