2. Black, Derman, and Toy binomial short-term interest rate model (40 points) In the Black, Derman, and Toy model, the binomial tree of the 6-month short-term interest rate is in the table below. Each period represents a six-month time interval. From each node, the 6- month short-term interest rate goes up in the next period with 50% probability and goes down with 50% probability. 3 2 r2e40 rze 40 ro r2e20 13e20 13 2. Black, Derman, and Toy binomial short-term interest rate model (40 points) In the Black, Derman, and Toy model, the binomial tree of the 6-month short-term interest rate is in the table below. Each period represents a six-month time interval. From each node, the 6- month short-term interest rate goes up in the next period with 50% probability and goes down with 50% probability. 3 2 r2e40 rze 40 ro r2e20 13e20 13