At time 0, the 6-month rate is 5.54% so the floor is out-of-the-money, and pays 0 at time 0.5. The later payments of the floor depend on the path ofinterest rates. Suppose rates follow the path in the tree below.
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Debt Instruments and MarketsProfessor CarpenterCaps, Floors, and Collars13Example: Payments of a Floater with a FloorTime 0.5Time 1Time 05.54%6.004%4.721%$2.776.915%5.437%4.275%$2.3605Time 1.57.864%6.184%4.862%$2.253.823%Time 2$102.431Consider the payments of a $100 par of a 2-year semi-annual floater with a 4.5% floor. Suppose rates follow the path in the tree below.Put on Yield•A put on a yieldis an instrument that pays off the difference between a given strike rate and the level of some underlying yield, when positive, times a given notional amount.•We will consider payment in arrears. For example, a put on the 6-month rate observed at time t-0.5 will payoff at time t. The payoff, for $100 notional amount and strike rate k, is 100max(k-t-0.5rt,0) / 2