24. This question concerns the following binomial model for the 1-year LIBOR rate. The urrent 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(T1,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 tree and zcb prices. f) What are the possible values of the return between 0 and 1 on the zcb maturing at 2 , and what is the expectation of this return under the risk-neutral probability (i.e., the weighted average of the returns using the RNP as weights)? Answer the same questions for the return between 0 and 1 of the put, and compare with the bond. How would you describe the comparison? g) Verify the answers to parts b) and d) using the risk-neutral probabilities