Please answer these questions completely (At Least 4 questions as chegg policy said)

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 marks] 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 for 100 a share and, after one year, can either increase by 10% or fall by 10%. Assume that there is no arbitrage, compute: i) The current value of the European call on FM429. ii) The current value of the European put on FM429, using put-call parity. iii) 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 will fall by more than 10%. Everything else including the expiration date, current stock price, and interest rate e the same as in part b). Show mathematically that 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