Question:

A 9-month American put option with an exercise price of $1250 iswritten on a stock whose current price is $1245. The stock willdistribute a 0.5% cash dividend six months from now. The riskfreeinterest rate is 1% and the stock's volatility is 16% per annum.

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

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

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