Problem 1: Should be answered by building an n =n=10-period binomial model for the short-rate, r_{i,j}r.
The lattice parameters are: r_{0,0} = 5\%r 0,0 =5%, u = 1.1u=1.1, d = 0.9d=0.9 and q =1-q = 1/2q=1-q=1/2
Problem 2: Compute the price of a forward contract on the same ZCB of the previous question where the forward contract matures at time t = 4t=4.
Problem 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 = 4t=4.
Problem 4: Compute the price of an American call option on the same ZCB of the previous three questions. The option has expiration t = 6t=6 and strike = 80=80.
Problem 5: Compute the initial price of a swaption that matures at time t = 5t=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 t = 5t=5 then the owner of the swaption will receive all cash-flows from the underlying swap from times t = 6t=6 to t = 11t=11 inclusive. (The swaption strike of 0 should also not be confused with the fixed rate of 4.5% on the underlying swap.)
Give your answer rounded to the nearest integer.
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