Q4. 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 ra = 0.0400. Finally, the current 2-year rate is r(0,2) = 0.0540. (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 = 95 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 = 0.0520, 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 = $10,000)? e) Compute the risk-neutral probability consistent with the given tree and zcb prices. f) Verify the answers to parts b) and d) using the risk-neutral probabilities. Q4. 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 ra = 0.0400. Finally, the current 2-year rate is r(0,2) = 0.0540. (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 = 95 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 = 0.0520, 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 = $10,000)? e) Compute the risk-neutral probability consistent with the given tree and zcb prices. f) Verify the answers to parts b) and d) using the risk-neutral probabilities