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A stock price is currently $50. Over each of the next two six-month periods, it is expected to go up by 20% or down by

A stock price is currently $50. Over each of the next two six-month periods, it is expected to go up by 20% or down by 10%. The risk-free interest rate is 5% per annum with continuous compounding.

a. What is the value of a one-year European call option with a strike price of $55?

b. What is the value of a one-year American put option with a strike price of $55?

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