(Two-step tree) A stock price is currently $10. Over each of the next two 3-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. Consider a 6-month American put option with a strike price of $11. Determine the value of this American put option. (Note: You need to determine, at each node prior to the maturity, (i) whether an early exercising decision is optimal (ii) value of the option