The current stock price of ABC is So = 17. Your boss is convinced that the...
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The current stock price of ABC is So = 17. Your boss is convinced that the stock price in 3 months (T= 0.25) will be close to 15. The ABC stock is not expected to pay dividend the following 8 months. Your boss considers therefore to buy the following butterfly on this stock: A long call option with exercise price K₁ 14.50, 2 short call options with exercise price K2 15, and a long = 15.5. = call option with exercise price K3 = a) Draw a graph which shows the payoff in 3 months of the butterfly. Does the investment strategy make sense, given your boss' beliefs? Your boss has already calculated the time 0 market prices of the 3 options included in the butterfly by the use of a 3 period binomial model. Denote by C(K) the time 0 market price of a European call option with exercise price K. The calculated prices are: C(14.5)= 2.7593, C(15) = 2.3324 og C(15.5) = 1.9055. The calculations are based on the parameter values: r = 0, 02, o = 0,3, U = = exp((r−8)h +o√h), and d = exp((r-8)h-oh), where exp(z) = e², and using the otherwise standard notation. b) Verify one (choose yourself!) of the 3 price calculations of your boss. c) Calculate the time 0 price of the butterfly strategy. d) Do you find the price you calculated in question c) reasonable? e) Use another pricing model to calculate the time 0 value of the butterfly. Hint: You find the Black-Scholes-Merton formula for a call option, where the underlying stock has dividend rate 6, in Exercise 3 of this exam. f) Compare the time 0 market prices you calculated in questions e) and c). Which one is more meaningful? g) What is the explanation for the result in question c)? The current stock price of ABC is So = 17. Your boss is convinced that the stock price in 3 months (T= 0.25) will be close to 15. The ABC stock is not expected to pay dividend the following 8 months. Your boss considers therefore to buy the following butterfly on this stock: A long call option with exercise price K₁ 14.50, 2 short call options with exercise price K2 15, and a long = 15.5. = call option with exercise price K3 = a) Draw a graph which shows the payoff in 3 months of the butterfly. Does the investment strategy make sense, given your boss' beliefs? Your boss has already calculated the time 0 market prices of the 3 options included in the butterfly by the use of a 3 period binomial model. Denote by C(K) the time 0 market price of a European call option with exercise price K. The calculated prices are: C(14.5)= 2.7593, C(15) = 2.3324 og C(15.5) = 1.9055. The calculations are based on the parameter values: r = 0, 02, o = 0,3, U = = exp((r−8)h +o√h), and d = exp((r-8)h-oh), where exp(z) = e², and using the otherwise standard notation. b) Verify one (choose yourself!) of the 3 price calculations of your boss. c) Calculate the time 0 price of the butterfly strategy. d) Do you find the price you calculated in question c) reasonable? e) Use another pricing model to calculate the time 0 value of the butterfly. Hint: You find the Black-Scholes-Merton formula for a call option, where the underlying stock has dividend rate 6, in Exercise 3 of this exam. f) Compare the time 0 market prices you calculated in questions e) and c). Which one is more meaningful? g) What is the explanation for the result in question c)?
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Solution a The payoff graph of the butterfly spread would look like a butterfly shape It would be lo... View the full answer
Related Book For
Fundamentals of Corporate Finance
ISBN: 978-0133400694
1st canadian edition
Authors: Jonathan Berk, Peter DeMarzo, Jarrad Harford, David A. Stangeland, Andras Marosi
Posted Date:
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