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A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by

A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a one-year American put option with a strike price of $100?

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