A 12-month American put option with an exercise price of $1250 is written on a stock whose current price is $1300. The stock will distribute a 2% dividend six months from now. The riskfree interest rate is 4% and the stock's volatility is 20% per annum.

1. Please use a three-step binomial tree to estimate the option value and the hedge ratio. (Hint: build the tree in spreadsheet to calculate the option value).

2.However, if everything else is the same, what percentage dividend would imply a price of $75 for the option? (Hint:use the tree in part a to find the correct percentage dividend by trial and error.)

3. Also, if everything else is the same, what volatility would imply a price of $75 for the option? (Hint: as in part b)