2. (a) In the Black-Scholes option pricing model, the underlying asset price evolves in continuous time and with continuous prices. What are the underlying assumptions that allow this? (b) A stock index is currently valued at 2500 points. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free rate is 5% per annum with continuous compounding and the dividend yield on the index is 2%. Each index point is worth $100. Using the binomial model of option pricing, compute the following: (i) The current price of a 1-year European call option written on the index with a strike price of 2250? (ii) The current price of a 1-year European put option written on the index with a strike price of 2250? (iii) Write down the Put-Call parity condition for these options and verify that it holds. (c) Sandra holds a stock portfolio worth 2.5 million and which has a beta of 0.5 with respect to the stock index used in part b. Sandra decides to hedge her portfolio using the put contract described in b (ii). (i) How many put contracts should Sandra trade to create the portfolio insurance? (ii) What are the cashflows at initiation and at maturity if the maturity value of the index is 2200? (iii) What is the value of the hedged position at maturity?