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Establish the price of a $35-strike American put option maturing in 6 months when the stock is trading for $30. The stock will not pay

Establish the price of a $35-strike American put option maturing in 6 months when the stock is trading for $30. The stock will not pay dividends during this period. The risk-free rate is 5% per annum, with continuous compounding, and the stock's volatility is 40%. Use a three-period binomial lattice to value this option. 



Will the option ever be exercised prematurely given that the stock pays no dividends? If so, determine the value of its early exercise privilege?

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