(Pricing swaps using term structure model)

Consider an n = n=10-period binomial model for the short-rate, r_{i,j}ri,j. The lattice parameters are: r_{0,0} = 5\%r0,0=5%, u = 1.1u=1.1, d = 0.9d=0.9 and q =1-q = 1/2q=1q=1/2.

Compute the initial value of a forward-starting swap that begins at t=1t=1, with maturity t = 10t=10 and a fixed rate of 4.5%. The first payment then takes place at t = 2t=2 and the final payment takes place at t = 11t=11 as we are assuming, as usual, that payments take place in arrears. You should assume a swap notional of 1 million and assume that you receive floating and pay fixed.