23caph.pdf

# At time 0 the 6 month rate is 554 so the floor is out

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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 of interest rates. Suppose rates follow the path in the tree below.

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Debt Instruments and Markets Professor Carpenter Caps, Floors, and Collars 13 Example: Payments of a Floater with a Floor Time 0.5 Time 1 Time 0 5.54% 6.004% 4.721% \$2.77 6.915% 5.437% 4.275% \$2.3605 Time 1.5 7.864% 6.184% 4.862% \$2.25 3.823% Time 2 \$102.431 Consider 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 yield is 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- 0.5 r t , 0) / 2