Please answer all questions and provide step by step solution for each question, provide explanation of the formulas used to obtain your spread-sheet outputs, plots, tables and spreadsheet data which are clearly la-belled (e.g., where appropriate include the question num-ber, title, parameter names, axis labels, clearly identified final solutions (e.g., if asked to calculate a premium, then do not just present a binomial tree which calculates the premium; instead clearly identify the answer with "The premium is $..."); all numerical results correct to at least four significant figures (unless otherwise specified). Use excel to answer some questions and show the PDF outputs of Excel.

[8 marks] . Consider a portfolio which consists of one European put and one short-sold European call option, together with one of the shares on which both the call and put are written. Both the call and the put have the same strike price, K, and expiry time, t = T. Show that this portfolio gives a guaranteed (i.e., risk-free) payoff at time t = T. How much would you (rationally) pay at some time 0