Question 2. This is a continuation of Question 1.] You have a European call and put with values co and go at time 0, both with strike A and maturity 7, on a stock (S;). Risk-free rate r is negative in this question. (a) Which of the following is correct? (i] co - Po = So - Ke'f; or (ii) co - po = 50 - Kell; or (iii) co - Po = So - Kerr A carefully described, rigorous, proof of your answer is essential. 13 marks (b) Recall the 1-step binomial model for pricing a derivative and the notation used for it in lectures. (i) Follow through the argument used in lectures to see what, if any- thing, changes in a negative interest rate environment; specifically, for the value fo of the derivative at 0. 3 marks (ii) Using the intuition gained in Part (i), discuss what if anything changes as you generalise to an n-step binomial model. Do this just for a European call. No calculations are necessary. [2 marks] (c) As you know, letting n + co in the n-step binomial model gives the Black-Scholes formula for co and po. Using the intuition gained in (b), Parts (i) and (ii), state what you expect these formulae to be. Use standard notation. No calculations are necessary. [2 marks (d) Are the formulae you obtained in Part (c) consistent with the correct put-call parity formula in Part (a)? If not, why not? Prove your answer, and discuss. 4 marks SEE OVER