This question concerns the following binomial model for the 1-year LIBOR rate. The current rate is r(0,1) = r = 0.0500; in one year, the rate can be ru = 0.0600 or rd = 0.0400. Finally, the current 2-year rate is r(0,2) = 0.0510. (All rates are with annual compounding.) a) Consider a European put with maturity T on a zero-coupon bond that matures at T = 2 with a strike of KP = 96 per 100 face. What portfolio of the 1-year and 2-year zero-coupon bonds has the same payoff as this put at time T = 1? b) What is the price of the put? c) Consider a caplet maturing at T = 2 that pays to the owner, on date T, interest at rate r(T 1,T) net of the fixed rate KC = 0.0420, if the owner elects to receive the payment. What portfolio of the 1-year and 2-year zero-coupon bonds has the same payoff as the value of this caplet at time T = 1 on a notional amount N = $10,000? d) What is the value of this contract (on the notional amount N = $1M)? e) Compute the risk-neutral probabilities consistent with the given