(II) Answer by building and calibrating a 10-period Black-Derman-Toy model for the short-rate, r_{i,j}

You may assume that the term-structure of interest rates observed in the market place is:

Period 1 2 3 4 5 6 7 8 9 10

Spot Rate 3.0% 3.1% 3.2% 3.3% 3.4% 3.5% 3.55% 3.6% 3.65% 3.7%

(Interest rates assume per-period compounding)

Assuming b=0.1, compute the price of a payer swaption with notional $1M that expires at time t=3 with an option strike of 0.

You may assume the underlying swap has a fixed rate of 3.9% and that if the option is exercised then cash-flows take place at times t=4.