Question 5 (16 marks) Consider a derivative written on a stock where the derivative's terminal payoff is depicted as follows: Payoff B A K K2 K; ST Assume that the distribution of terminal stock price (St) is lognormal. The maturity of this derivative is at time T. You should assume that both sloped lines are at a 45 degree angle to the horizontal Required: a) The payoff to this derivative can be replicated as a package involving one or more zero-coupon bonds and call options. Write down the component pieces of this package, being explicit with respect to long/short positions, face value of bonds and strike price of call options. [4 marks] b) Write down the construction cost of the package from part (a). [4 marks) c) Determine the payoff to the derivative and derive an analytic formula to price the above exotic derivative using building blocks. Clearly define all constants you may use. Show all working. [8 marks] NB: NB: You must write your entire answer in the answer booklet, not in this question booklet. The formulae for Black-Scholes call and put options are given on the formula sheet. Question 5 (16 marks) Consider a derivative written on a stock where the derivative's terminal payoff is depicted as follows: Payoff B A K K2 K; ST Assume that the distribution of terminal stock price (St) is lognormal. The maturity of this derivative is at time T. You should assume that both sloped lines are at a 45 degree angle to the horizontal Required: a) The payoff to this derivative can be replicated as a package involving one or more zero-coupon bonds and call options. Write down the component pieces of this package, being explicit with respect to long/short positions, face value of bonds and strike price of call options. [4 marks] b) Write down the construction cost of the package from part (a). [4 marks) c) Determine the payoff to the derivative and derive an analytic formula to price the above exotic derivative using building blocks. Clearly define all constants you may use. Show all working. [8 marks] NB: NB: You must write your entire answer in the answer booklet, not in this question booklet. The formulae for Black-Scholes call and put options are given on the formula sheet