Term Structure Models I

Questions 1-5should be answered by building ann=10-period binomial model for the short-rate,ri,j. The lattice parameters are:r0,0=5%,u=1.1,d=0.9andq=1q=1/2.

Que 1) Compute the price of a zero-coupon bond (ZCB) that matures at timet=10and that has face value 100.

Que 2) Compute the price of a forward contract on the same ZCB of the previous question where the forward contract matures at timet=4.

Que 3) Compute the initial price of a futures contract on the same ZCB of the previous two questions. The futures contract has an expiration oft=4.

Que 4) Compute the price of an American call option on the same ZCB of the previous three questions. The option has expirationt=6and strike=80.

Que 5) Compute the initial price of a swaption that matures at timet=5and has a strike of 0. The underlying swap is the same swap as described in the previous question with a notional of 1 million. To be clear, you should assume that if the swaption is exercised att=5then the owner of the swaption will receive all cash-flows from the underlying swap from timest=6tot=11inclusive. (The swaption strike of 0 should also not be confused with the fixed rate of 4.5% on the underlying swap.)

Term Structure Models I Questions 1-6 should be answered by building an n=10-period binomial model for the shortrate, ri,j. The lattice parameters are: r0,0=5%, u=1.1, d=0.9 and q=1q=1/2. Que 1) Compute the price of a zero-coupon bond (ZCB) that matures at time has face value 100. t=10 and that Que 2) Compute the price of a forward contract on the same ZCB of the previous question where the forward contract matures at time t=4. Que 3) Compute the initial price of a futures contract on the same ZCB of the previous two questions. The futures contract has an expiration of t=4. Que 4) Compute the price of an American call option on the same ZCB of the previous three questions. The option has expiration t=6 and strike =80. Que 5) Compute the initial price of a swaption that matures at time t=5 and has a strike of 0. The underlying swap is the same swap as described in the previous question with a notional of 1 million. To be clear, you should assume that if the swaption is exercised at of the swaption will receive all cash-flows from the underlying swap from t=5 then the owner times t=6 to t=11 inclusive. (The swaption strike of 0 should also not be confused with the fixed rate of 4.5% on the underlying swap.)