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# ExerciseD2 - t = 0 be S = 100 Suppose that after one year...

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EC3070 FINANCIAL DERIVATIVES Exercise 2 1. A stock price is currently S 0 = 40. At the end of the month, it will be either S u 1 =42or S d 1 = 38. The risk-free rate of continuously compounded interest is 8% per annum. What is the value c 1 | 0 of a one-month European call option with a strike price of \$39? 2. A stock price is currently 50. At the end of six months, it will be either 45 or 55. The risk free-rate of interest continuously compounded is 10% per annum. What is the value of a six-month European put option with a strike price of 50? 3. Let the annual rate of interest be r and let the price of a share at the present time of
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Unformatted text preview: t = 0 be S = 100. Suppose that, after one year, when t = 1, the price will be either S u 1 = 200 or S d 1 = 50. A call option to buy the share at time t = 1 at a price of K 1 | = 150 can be purchased at time t = 0 for c 1 | . Show that, unless c 1 | = { 100 − 50(1 + r − 1 ) } / 3, there will always exist a combination of x shares and y options that will yield a proFt. (Here, x is negative, if you are selling shares at time t = 0, and postive, if your are purchasing them, and likewise for the number of options purchased or sold.) 1...
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