Assume that a stock price is currently at $100. It is known that in one year, the stock price will either increase by 50% or decrease by 50%. The annual interest rate is 5% with continuous compounding. Consider a European put option with strike price equal to $75 and with maturity in one year. 1) Draw the trees for stock and the risk-free asset. 2) What is the portfolio of the stock and the risk-free asset that replicates the payoff of the put? What is the initial cost of this portfolio? 3) What is the fair value of the put? 4) What is the probability measure associated with the risk-free asset being the numeraire? Show that the ratio of the put price to the risk-free asset price is a martingale under this measure. 5) What is the probability measure associated with the stock being the numeraire? Show that the ratio of the put price to the stock price is a martingale under this measure