Practice exam
Microsoft Word - ECON3760 - Final Exam - W2020 1 DEPARTMENT OF ECONOMICS AND FINANCE Lang School of Business and Economics University of Guelph ECON*3760 Fundamentals of Derivatives FINAL EXAMINATION Professor Nikola Gradojevic April 20, 2020 Instructions This take-home exam will last for 72 HOURS, from: 12:00pm (noon on April 20) - 12:00pm (noon on April 23). Answer ALL 4 questions. The questions carry equal weight (25%) and together count for 100%. Please email your typewritten solutions to the TA – Mate Bors [
[email protected]] by 12:00pm (noon) on April 23. Any literature sources you use must be referenced on the last page of the exam. Late exams will not be considered! GOOD LUCK! 2 Question 1 Micca Metals, Inc. is a specialty materials and metals company located in Detroit, Michigan. The company specializes in specific precious metals and materials which are used in a variety of pigment applications in many other industries including cosmetics, appliances, and a variety of high tinsel metal fabricating equipment. Micca just purchased a shipment of phosphates from Morocco for 6,000,000, dirhams, payable in six months. Six-month call options on 6,000,000 dirhams at an exercise price of 10.00 dirhams per dollar are available from Bank Al-Maghrub at a premium of 2%. Six-month put options on 6,000,000 dirhams at an exercise price of 10.00 dirhams per dollar are available at a premium of 3%. Compare and contrast alternative ways that Micca might hedge its foreign exchange transaction exposure. Assumptions Values Shipment of phosphates from Morocco, Moroccan dirhams 6,000,000 Micca's cost of capital (WACC) 14.000% Spot exchange rate, dirhams/$ 10.00 Six-month forward rate, dirhams/$ 10.40 Options on Moroccan dirhams: Call Option Put Option Strike price, dirhams/$ 10.00 10.00 Option premium (percent) 2.000% 3.000% United States Morocco Six-month interest rate for borrowing (per annum) 6.000% 8.000% Six-month interest rate for investing (per annum) 5.000% 7.000% a) What are the costs and risk of each alternative? (15 MARKS) b) What is the optimal strategy if Micca wishes to take a “reasonable risk”? Explain. (10 MARKS) 3 Question 2 Consider a call option written on a non-dividend-paying stock when the current stock price is $35, the exercise price is $30, the risk-free interest rate is 5% per annum, the volatility is 35% per annum, and the time to maturity is 4 months. a) What is the price of a European call option written on the stock? (10 MARKS) b) What is the price of an American call option written on the stock? (5 MARKS) c) Assume that the stock will pay a dividend in 2 months. The expected dividend is 60 cents. What is the price of a European call option written on the dividend-paying stock? (10 MARKS) Important: Please show all your steps to the solution. Question 3 Consider the following options portfolio. You write a January maturity call option on Canadian Pacific with exercise price 60. You write a January Canadian Pacific put option with exercise price 55. a) Graph the payoff of this portfolio at option expiration as a function of Canadian Pacific’s stock price at that time. (10 MARKS) b) What will be the profit/loss on this position if Canadian Pacific is selling at 57 on the option maturity date? What if Canadian Pacific is selling at 65? Use the figure below (and bid/ask prices) to answer these questions. (15 MARKS) 4 Question 4 The three-period binomial interest rate tree provided below gives one-period interest rates and prices of zero-coupon bonds. Starting at t = 0, you are provided with the one-period interest rate and prices of zero-coupon bonds with maturities of one period, two periods, three periods, and four periods. At t=1, you are provided with the one-period interest rate and prices of zero-coupon bonds with maturities of one period, two periods, and three periods. At t=2, you are provided with the one-period interest rate and prices of zero-coupon bonds with maturities of one period and two periods. At t=3, you are provided with the one-period interest rate and prices of zero-coupon bonds with maturity of one period. Calculate the price of a two-period floor (depicted below by a rectangle) with an exercise rate of 9 percent. The underlying is the one-period rate. (25 MARKS)