A Europeanputoption has a strike price of $75 and expires in six months. It is written over a stock that is currently $80, but could either increase by 5% or decrease by 5% overeachof the next two three-month periods.The risk-free interest rate is 5% per annum with continuous compounding.

i)Draw a binomial tree and identify the stock prices in the positions

ii)Calculate the price of this option today.

iii)Explain why the corresponding American put has the same value.