Question 4 (a) A stock is currently trading at $80. You hold a portfolio consisting of the following: Long 100 unit of stock Short 100 calls. Each with a strike price of $90 Long $100 puts. Each with strike price of $70 Suppose the delta of the 90-strike price call is 0.45, while the delta of the 70-strike put is -0.60. What is the aggregate delta of your portfolio? (2 marks) (b) Let a two-period binomial tree be given with the following parameters: S= 100, u=1.10. d =0.90 and R = 1.05. Consider a two-period American put option with a strike price of $90. Note that this put option is deep out of the money at inception (1) Calculate the risk-neutral probability (3 marks) (11) How do you know from examining the risk neutral probabilities on a binomial tree if the model is free from arbitrage? (2 marks) (111) Draw the tree of stock prices (3 marks) (iv) Explain about the binomial interest rate tree (5 marks) (c) A Future price is currently 60 and its volatility is 30Fi. The risk-free interest rate is 8fi per annum. Use a two-step binomial tree to calculate (1) the value of a six-month European call option on the futures with a strike price of 60? mark) (11) If the call were American, would it ever be worth exercising it early? (1 mark) [Total: 25 Marks] END OF QUESTION PAPER