C,D, E and F

Please answer C,D,E and F (as chegg policy, tutor should answer 4subpart questions) Thanks

1. This question is about option valuation [50 marks] You own a portfolio of three European call options and one European put option on the FM429 stock. All these options expire in one years time and have a strike price of 100. The annual risk-free rate is 5%. a) [10 marksl Draw the payoff diagram for the value of your portfolio of three calls and one put after one year as a function of the stock price at that time. Mark clearly on the figure the intercepts and slopes of all lines. b) [10 marks] FM429 currently sells for100 a share and, after one year, can either increase by 10% or fallby 10%. Assume that there is no arbitrage, compute: The current value of the European call on FM429. i) The current value of the European put on FM429, using put-call parity ii) The total value of your portfolio. c) 15 marks] Is the beta of the European call option on FM429 greater than, equal to, or lower than the beta of the FM429 stock? Explain. (Hint: You can use the binomial tree model to show that a call option is a portfolio of a stock and a risk- free bond.) d) (5 marks Suppose that you have been offered a European call option on FM429 for 28.56. Explain which trading strategy would generate a current arbitrage profit of 42.84. e) [10 marks] Assume that there is an increase in the volatility of FM429: if the stock increases in price, it will still increase by exactly 10 but if it falls, it wil fall by more than 10%. Everything else including the expiration date, current that strike price and interest rate are the same as in part Show mathematically the value of the European call option is higher than the value derived in part b). (Hint: You can show how this increase in volatility affects the risk-neutral probability and call value at each node.) [10 marks] Now assume that FM429's price can either increase by 10% or fall by 10% every six months and the annual risk-free interest rate is 10% with semi- annual compounding. Compute the current value of the European call on FM429. Page 2 of 5