Construct an interest rate swap receiving the fixed-rate payments in exchange for the floating-rate payments.
Compute the at-the-money rate for this interest rate swap.
Construct three swaps.
Here are cash flows for the paying leg of your interest rate swap.
Here are cash flows for the receiving leg of your interest rate swap.
These are days when coupon payments are scheduled to occur.
Price these swaptions using the Hull-White trinomial tree.
Price your swaptions using the tree constructed above.
You can also price these swaptions using an explicitly constructed trinomial tree.
Price your swaptions using the second tree.