Question $1$: Assume b$=0\mathrm{.}05$ is a constant for all i in the BDT model as we assumed in the video lectures. Calibrate the ai parameters so that the model term$-$structure matches the market term$-$structure. Be sure that the final error returned by Solver is at most $10-8.($This can be achieved by rerunning Solver multiple times if necessary, starting each time with the solution from the previous call to Solver.$)$

Once your model has been calibrated, compute the price of a payer swaption with notional $$1$M that expires at time t$=3$ with an option strike of $0.$ You may assume the underlying swap has a fixed rate of $3\mathrm{.}9\%$ and that if the option is exercised then cash$-$flows take place at times t$=4,...,10.($The cash$-$flow at time t$=$i is based on the short$-$rate that prevailed in the previous period, i$.$e$.$ the payments of the underlying swap are made in arrears.$)$

Submission Guideline: Give your answer rounded to the nearest integer. For example, if you compute the answer to be $10,456\mathrm{.}67,$ submit $10457.$