AssessmentQ1

Option Calculations and Model AssessmentQ1(a) A share in Noname Pty Ltd is currently priced at $8.25. It will go up by 10% or down by 5% over each of the the next two years. The continuous risk free rate is 4% p.a.(i) Calculate qu and qd. (6 Marks)(ii) Calculate the price of a call option on the share, with a Strike (or Exercise) price of $8 and time to expiry of two years. (10 Marks)(b) (i) At time t=1, for each of the two future possible scenarios (ie up and down), determine the number of units of a share (bought) and bond (sold) you have to hold to create the same payoff as the option (at time t=2); (10 Marks)(ii) show that the payoffs from the stock/bond combination are the same as for the option; and (7 Marks)(iii)explain how, and why, you can use this to show that the price of the call option is the same as you obtained above. (7 Marks)Q2 A European call option to buy a share in Noname Pty Ltd is currently priced at $1.00. The Exercise Price is $8.00, the time to expiry is 2 years and the continuous risk free interest rate is 4%p.a. The current share price is $8.25 and the historical standard deviation of the stock, , is 15% per annum. Based on the above information, d1 = 0.628249, d2 = 0.416117, N(d1) is 0.735079 and N(d2) is 0.661338. Assume that there are no transactions costs, investors can borrow and lend at the risk free rate, and the contract size is one share per option. [Note that although some parameters are the same, the answer will be different to Q1]i. What is the intrinsic value of the option? 2.5 Marks)ii. What is the time value of the option? (2.5 Marks)iii. Draw a pay off diagram for the option (as per page 369 of the text book) (2.5 Marks)iv.Use the Black Scholes model to determine the theoretical price for a European call option. (7.5 Marks)v. Calculate the theoretical price for a European put option (7.5 Marks)Q3 Evaluate and critique the advantages and disadvantages of the use of models, including their assumptions .(10 Marks)Q4 Value at RiskYou are working as a fund manager for one of the big four banks. You are managing a portfolio of $250m and have been asked by the Risk department to estimate the probability that you could lose $25m by the end of the :a) month; (3 Marks)b) quarter; (3 Marks)c) year. (2 Marks)They have told you to assume your returns arenormally distributed for the purpose of preparing the estimate. Your recent results show average return of 12% and a standard deviation of returns of 20%.For their Value At Risk (‘VAR’) reports they have asked you to quantify the maximum loss of funds that could occur by the end of the year:a) (with 1% probability; and (6 Marks)b) with 2.5% probability. (6 Marks)Q5Calculate 95% Confidence Intervals for a stock that isnormally distributed with mean of 9% and standard deviation of 25%. Apply this confidence interval each year, to obtain the minimum and maximum price for the stock after five years. Assume the initial price is $7.50. (10 Marks)