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5.2.2 Cap/floorlets
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The capfloor parity relation (2.2.4#eq.3) shows that both
share many features with swaps. The contract is again decomposed into
elementary intervals and the valuation of every caplet or floorlets
is carried out backwards starting from zero, since a finite time has
to pass to accumulate interest rate earnings.
The incremental change reflects the difference between the spot and the
cap/floor rates; contrary to swaps, this difference can never become
negative, since caps and floors do not carry any obligation.
Using the Vasicek model, the contract can therefore be viewed as a bond
paying a continuously compounded annual coupon of
for
caplets and
for floorlets. By analogy with the swap
rate, define the
 the interest cap/floor rate (
or
StrikePrice ),
expressed as the relative annual return above /below which the
contract pays the rate difference, e.g. 0.04 for a cap rate of 4%.
The VMARKET applet below calculates the
value of a caplet with a cap rate of 8%, as a function of the spot
rate and an increasing time to the maturity.
VMARKET applet: press Start/Stop
to simulate the value of a caplet V(r) as a function of the
spot rate r for an increasing lifetime of the contract.
The parameters assume a cap rate of 8% and a market with a volatility
of 1%.

The same models used to forecast drifts in the interest rate can also
be used here, but the volatility should be modified to reflect the
uncertainty in the interest earnings (exercise 5.07).
SYLLABUS Previous: 5.2.1 Vanilla swaps
Up: 5.2 Credit derivatives
Next: 5.3 Methods for bonds
