At time 0, the 6
month rate is
5.54% so the floor is outofthemoney, 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 2year 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 6month 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