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

Submission Guideline: Give your answer rounded to the nearest integer. For example, if you compute the answer to be $-220,432.23$, submit -220432 .