Cap/Floor

ORE defines the product as follows:

A single floating swap leg with interest payments benchmarked to IBOR or CMS indices, may have a cap, floor, or collar. This creates a series of European interest rate options (caplets or floorlets) where the cap or floor rate is the strike price, and each floating rate reset date is an option expiry date.

Source: ORE User Guide, Products catalogue, capfloor.tex.

ORE states the collar composition as follows:

A collar is the combination of a series of long caplets and short floorlets for a long position in the collar.

Source: ORE User Guide, Products catalogue, capfloor.tex.

ORE also supports the standalone form:

Standalone caps and floors with a single payoff on an IBOR or CMS index are also supported.

Source: ORE User Guide, Products catalogue, capfloor.tex.

A floating coupon pays whatever the index fixes. A cap sets a ceiling on that payment. A floor sets a floor beneath it. A collar does both. The option buyer pays a premium. If the fixing is above the cap rate, the caplet pays the difference. If the fixing is below the floor rate, the floorlet pays the difference.

The CapFloorData node is the trade data container for the CapFloor trade type. It carries a LongShort sub-node for the position. One LegData sub-node sets the leg type. The type can be Floating for IBOR and OIS indices, CMS, CMSSpread, DurationAdjustedCMS, CPI, or YY. The Caps or Floors elements, or both, sit outside the leg node. With both, the instrument is a collar and Caps must come above Floors. ORE notes that the Payer flag is ignored for this instrument. The optional PaymentDates node in the leg serves only OIS and IBOR indices.

ORE states the caplet payoff on an IBOR floating leg coupon period as follows:

Caplet payoff = N x max(0, L - K) x δ

N is the notional. L is the IBOR index fixing for the period. K is the cap rate, the strike. δ is the day-count fraction for the coupon period. The floorlet payoff is the mirror image:

Floorlet payoff = N x max(0, K - L) x δ

For a caplet or floorlet on a CMS index, L is replaced by the CMS rate of the relevant tenor. The standalone form pays:

Payoff = N x max(0, ω x (L - K))

ω is 1 for a cap and -1 for a floor.

• The level of the reference index against the strike.
• The cap or floor rate itself.
• The volatility of the index fixings.
• The reset frequency and the day-count convention.
• The discount curve.

The cap pays when the fixing exceeds the strike. The floor pays when the fixing falls below it. Near the strike, each caplet or floorlet shows its strongest gamma and vega.

Caplets and floorlets settle one per period. Each reset date is the expiry date of that period's option. Once a fixing settles, that option is decided and gone. The remaining value is the strip of options not yet decided. As each period passes, the number of live options falls by one.

A borrower with floating debt buys a cap to bound the funding cost. An investor holding floating notes buys a floor to protect income. A collar sells one side to pay for the other. In ORE Studio a customer books caps and floors to value them and run sensitivities on the ORE engine.

ORE's catalogue shows a long cap on a floating leg with a 5 percent cap rate and an upfront premium:

<CapFloorData>
  <LongShort>Long</LongShort>
  <LegData>
    <Payer>false</Payer>
    <LegType>Floating</LegType>
     ...
  </LegData>
  <Caps>
    <Cap>0.05</Cap>
  </Caps>
  <Premiums>
    <Premium>
      <Amount>1000</Amount>
      <Currency>EUR</Currency>
      <PayDate>2021-01-27</PayDate>
    </Premium>
  </Premiums>
</CapFloorData>

Source: ORE User Guide, Products catalogue, capfloor.tex, listing Cap/Floor data.