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 t=5 then the owner of the swaption will receive all cash-flows from the underlying swap from 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.)

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