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A stock price is currently 20. Over each of the next two 6-month periods the stock price will either go up by 10% or down

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A stock price is currently 20. Over each of the next two 6-month periods the stock price will either go up by 10% or down by 10%. The risk free interest rate is 5% with continuous compounding. Price an Asian call option with strike K = 19 and payoff (S - K)^+, where S = 1/3 (S_0 + S_1 + S_2) and S_0, S_1, S_2 are stock prices at times 0, 1/2, and 1, respectively

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