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Question 1 [20 marks] Current stock price is $22. Time to maturity is 8 months. Continuously compounded, risk-free interest rate is 6 percent per annum. European options prices are given in the following table: Strike Price Call Price m $500 $005 K2=$20.00 $3.00 K3=$22.50 $1.75 $1.75 K4=$25.00 $0.75 EE (a) What is the aim of a long (or bottom) straddle strategy? Create a long straddle by buying a call and put with strike price K3=$22.50 [10 marks] (b) What is the aim of a short (or top) strangle strategy? Create a short strangle by writing a call with strike price K3=$22.50 and a put with strike price K2=$20. [10 marks] 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 6 percent per annum. The options expire in 120 days. The stock will pay a dividend equal to 4 percent of its value in 50 days. (a) Draw the three-period stock tree and the corresponding trees for the call and the put. [7.5 marks] (1:) 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]