A European put option has a strike price of $56 and expires in six months. It is written over a stock that is currently $59, but could either increase by 5% or decrease by 5% over each of the next two three-month periods. The risk-free interest rate is 4% per annum with continuous compounding.

i) On the binomial tree diagram below identify the stock prices in the positions indicated by the letters A to F, and the value of the put option at positions D, E and F.

ii) Calculate the price of this option today.

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