This question has two independent parts (a) and (b). (a) A stock is selling at $123. It pays a dividend of $3.075 in two, five, and eight months from today, respectively. The risk free interest rate is 5% per annum continuously compounded. The fair price of a nine month European $123-strike put option is $11.647732. Suppose the actual market price of the corresponding nine month European $123-strike call option is $6.60, is there any arbitrage opportunity? Please show all the details. (9 marks) (b) Consider a European put option when the stock price is $52, the strike price is $55, the risk free interest rate is 6% per annum continuously compounded, the stock price volatility is 20%, and the option expires in nine months from today. A dividend of $1 is to be paid at the end of two months, five months, and eight months from now. (13 marks) (i) Use the Black-Scholes-Merton model to price the option. (5 marks) (ii) If the option in question is a European call instead, use the Black-Scholes-Merton model to price the option and verify that the put-call parity relationship holds. (5 marks) AP/ADMS4503 M&N Assignment #2 Winter 2016 Page 2 (iii) Use DerivaGem to value an American put option that shares the same characteristics as the European put option in question. Assume 50 time steps for the binomial tree and please show all the parameters of the tree. Please note: You do not need to display the binomial tree. (3 marks) Question 2 (18 marks) Please use the following information to answer parts (a), (b), and (c). A non-dividend-paying stock is trading at $36 and has an annual volatility of 30%. The continuously compounded annual riskless interest rate is 3.6%. Consider the following strategy involving one year European put options: Short one $20-strike put, short one $40-strike put, and long two $35-strike puts. (a) Price this strategy using a six step binomial tree. Please show all the parameters of the tree and the formulas used. You do not need to display the tree. (5 marks) (b) Draw the profit/loss pattern of the strategy and show the break-even point(s) and the maximum profit and the maximum loss. Please ignore the time value of money. (9 marks) (c) Without using either the binomial trees or the Black-Scholes-Merton model, what is the price of a $20/$40 bull call spread on the same stock? (4 marks) Question 3 (20 marks) This question has the following two independent parts (a) and (b). (a) A stock is selling at $30. Over each of the next three two-month periods the stock price is expected to rise or drop by 8%. The riskless interest rate is 7% annually with continuous compounding. The stock pays no dividend. Use a three-step binomial tree to value the following options. Please display the binomial trees below. For part (a) please do not use DerivaGem. (12 marks) (i) A European put option with a strike price of $32. (4 marks) (ii) An American call option with a strike price of $31. (4 marks) (iii) An American put option with a strike price of $32. (4 marks) (b) Consider a nine-month American put option on the CAD/Euro exchange rate with a strike price of CAD 1.29 per Euro. The spot exchange rate is CAD 1.30 per Euro and has a volatility of 25%. The risk free interest rates in Canada and in AP/ADMS4503 M&N Assignment #2 Winter 2016