2. Consider a 3-year American call option on a stock which pays dividends in 1 year and 2 years. The first dividend is $5 and the second dividend is $6. The current stock price is $100, the exercise price is $90, the stock price volatility is 30% per annum, the continuously risk-free rate of interest is 6% per annum. (a) Is it rational to exercise the American call option in 1 year? Explain your answer. (b) Show that the call option can be (but not necessary) exercised in 2 years by considering the interest of strike price. Black's approximation takes the greatest value of the option when it can be (but not necessary) exercised in 2 years or 3 years. Calculate Black's approximation. (c) Suppose the stock price is 130 after paying dividend in 2 years. What is the decision of a rational investor? Explain your answer.
2. Consider a 3-year American call option on a stock which pays dividends in 1 year and 2 years. The first dividend is $5 and the second dividend is $6. The current stock price is $100, the exercise price is $90, the stock price volatility is 30% per annum, the continuously risk-free rate of interest is 6% per annum. (a) Is it rational to exercise the American call option in 1 year? Explain your answer. (b) Show that the call option can be (but not necessary) exercised in 2 years by considering the interest of strike price. Black's approximation takes the greatest value of the option when it can be (but not necessary) exercised in 2 years or 3 years. Calculate Black's approximation. (c) Suppose the stock price is 130 after paying dividend in 2 years. What is the decision of a rational investor? Explain your answer.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:2. Consider a 3-year American call option on a stock which pays dividends in 1 year and 2
years. The first dividend is $5 and the second dividend is $6. The current stock price is $100,
the exercise price is $90, the stock price volatility is 30% per annum, the continuously
risk-free rate of interest is 6% per annum.
(a)
Is it rational to exercise the American call option in 1 year? Explain your answer.
(b) Show that the call option can be (but not necessary) exercised in 2 years by
considering the interest of strike price. Black's approximation takes the greatest value of the
option when it can be (but not necessary) exercised in 2 years or 3 years. Calculate Black's
approximation.
(c)
Suppose the stock price is 130 after paying dividend in 2 years. What is the decision of
a rational investor? Explain your answer.
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