Question 2 [10 marks]

(a) Why is the binomial model a useful technique for approximating options prices from the Black-Scholes model? [5 marks]

(b) Describe some applications and uses of this model. [5 marks]

Question 3 [20 marks]

Consider the binomial model for an American call and put on a stock whose price is $90. The exercise price for both the put and the call is $65. The standard deviation of the stock returns is 25 percent per annum, and the risk-free rate is 3 percent per annum. The options expire in 120 days. The stock will pay a dividend equal to 2 percent of its value in 60 days.

(a) Draw the three-period stock tree and the corresponding trees for the call and the put. [7.5 marks]

(b) Compute the price of these options using the three-period trees. [7.5 marks]

(c) Explain when, if ever, each option should be exercised. [5 marks]

Question 4 [30 marks]

Consider a stock with a price of $120 and a standard deviation of 30 percent. The stock will pay a dividend of $5 in 40 days and a second dividend of $5 and 140 days. The current risk-free rate is 3 percent per annum. An American call on this stock has an exercise price of $150 and expires in 100 days. Price the American call option using the Black-Scholes Model. Show all calculations.