Question 2. {This is a continuation of Question 1.] You have a European call and put with values on and 33,) at time 0, both with strike H and maturity T, on a. stool-z (St). Risk-free rate r is negative in this question. (a) 1Winch of the following is correct? (i) capn=SgKe"r; or (ii) on pr_. = 5.3 Kel'lT; or {iii} cc. pa = 3.1 R's'1'. A carefully described, rigorous, proof of your answer is essential. [3 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; specically, for the value In of the derivative at U. [3 marks] (ii) Using the intuition gained in Part {i}, discuss what if anything changes as you generalise to an art-step binomial model. Do this just for a European call. No calculations are necessary. [2 marks] {c} As you know, letting it i- on in the nstep binomial model giv the Black-Scholars formula for cc. and 394}. Using the intuition gained in (h), Parts (i) and (ii), state what you respect 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 putscall parity formula in Part (a)? If not, why not? Prove your answer, and discuss. [4 marks]