CHEET FINAL - Homework 9, FINA 471 Fall, 2011 PROBLEM 1 The...

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Homework 9, FINA 471 Fall, 2011 PROBLEM 1 The current exchange rate is $1.44/€, the euro interest rate is 3.5%, the dollar interest rate is 2%, and the price of a 3-month $1.45-strike European put option is $0.12. What is the price of a 3-month $1.45-strike European call? A. By put-call parity, C = P + xe-rfT – Ke-rT = 0.12 + 1.44e-0.035*0.25 – 1.45e- 0.02*0.25 = $0.1047. PROBLEM 2 A stock currently sells for $42. The 6-month European call option with a strike of $45 has a premium of $2.50, and the 6-month European put option with a strike of $45 has a premium of $5.15. The annual continuously compounded interest rate is 2%. What should be the present value of dividends over the next 6 months? A. By put-call parity, PV(Div) = S – C + P – Ke-rT = 42 – 2.5 + 5.15 – 45e-0.02*0.5 = $0.10. ( PROBLEM 3 A stock currently sells for $42. A 6-month European put option with a strike of $45 has a premium of $6.50. Assuming a 2% annual continuously compounded interest rate and a 4% dividend yield, what should be the price of the associated European call option? B. By the put-call parity, C = 6.5 + 42e-0.04*0.5 - 45e-0.02*0.5 = $3.12 PROBLEM 4 Consider the same situation as in the previous . Suppose that the market price of the call option is $3. How should an arbitrager profit if there is an arbitrage opportunity? B. From previous, the call is underpriced. To arbitrage, buy call, short stock, and sell put. PROBLEM 5 The price of a stock is $42 and the annual continuously compounded interest rate is 2%. The stock pays a dividend of $2 in 2 months. The European call option of strike price $45 and 3 months to expiration is sold at $0.25. What is the no-arbitrage price of the European put option with the same strike price and time to expiration? B. By put-call parity, P = 0.25 – (42 – 2e-0.02*2/12) + 45e-0.02*3/12 = $5.02. PROBLEM 6 Consider an American call option. Which of the following makes the option less valuable? C. decreasing maturity always leads to lower prices for American options. PROBLEM 7 The premium of a 1-year 35-strike call is $3.50 and the premium of a 1-year 37.50-strike call is $3.75. How should an arbitrager profit if there is an arbitrage opportunity? C. Creating a bull spread will lock in a profit of at least $0.25 in present value terms. PROBLEM 8 Suppose the premium of a 1-year 80-strike call is $15 and the premium of a 1-year 90- strike call is $4.75. How should an arbitrager profit if there is an arbitrage opportunity? D. Creating a bear spread w ill lock in a profit of at least $0.25 in present value terms. PROBLEM 9 Consider the same situation as in the previous. Assuming zero interest rate, what is the minimum profit that the arbitrage strategy can generate at expiration? B. If the stock price is greater than 90, both calls are exercised. Profit = (15-4.75)-(S-80)+(S-90) = 0.25. PROBLEM 10 The prices of three 1-year call options are Strike Call 14.45 10.85 7 . 50 55 60 How should an arbitrager profit if there is an arbitrage opportunity?
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This note was uploaded on 01/16/2012 for the course FINA 471 taught by Professor Mr.yan during the Fall '11 term at South Carolina.

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CHEET FINAL - Homework 9, FINA 471 Fall, 2011 PROBLEM 1 The...

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