1. (a) Define the following terms: i. Arbitrage-free; and ii. The efficient market hypothesis. (2 marks) (b) For each of the following: define the term, give a mathematical expression for the pay-off at expiry and sketch the pay-off diagram, assuming that there are transaction costs, for both the holder and the seller: i. European call option; and ii. European put option. (6 marks) (c) Let P(0) be the current price of a risky asset. Prove that a consequence of a risk-averse market is that P(0)