1. Define the exchange rate S(t) as the number of dollars per Euro at time t. Consider a one-period Put Option with a strike X=1 and maturity t+1. That is, this Put gives you the right to sell 100 Euros at t+1 at an exchange rate X=1. Suppose the interest rate is zero.
   1. What is the price of the Put at t+1 if S(t+1)=1.2?
   2. Suppose that S(t) = 1 and that S(t+1) may take only two values: If S(t+1) = 1.4 with probability 0.5 and = 0.8 with probability 0.5. Under risk-neutrality, what is the price of the Put at time t, i.e., P(t, X=1)?
   3. Suppose instead that S(t) = 1 and S(t+1) may take three values : S(t+1) = 1.4 with probability 0.4 and = 1.0 with probability 0.2 and = 0.6 with probability 0.4 . What is P(t, X=1)?
   4. Compute the variance of S(t+1) in case (b) and in case (c).