Interest Rate Caps, Floors and Collars

							           FINC 4320

Interest Rate Caps, Floors and Collars
Interest Rate Caps and Floors
  • Cap - a series of European interest rate call options used
    to protect against rate moves above a set strike level

  • Floor - a series of European interest rate put options used
    to protect against rate moves below a set strike level

  • Recall some basic option valuation points, and apply them
    to caps and floors:
The buyer of a cap receives a cash payment from the seller. The payoff is the
maximum of 0 or 3-month LIBOR minus 4% times the notional principal
amount.
                                                  A. Cap = Long Call Option on 3-Month LIBOR
                               Dollar Payout
                               (3-month LIBOR                                                  +C
                              -4%) x Notional
                               Principal Amount


• If 3-month LIBOR exceeds
  4%, the buyer receives cash
  from the seller and nothing
  otherwise.
• At maturity, the cap expires.
                                                                                                    3-Month
                                                                                                    LIBOR
                                                                      4 Percent

      Rate
                B. Cap Payoff: Strike Rate = 4 Percent*
                                                                              Floating
                                                                              Rate
  4 Percent




                 Value        Value          Value           Value       Value
                 Date         Date           Date            Date        Date
                                          Time
Interest Rate Caps and Floors
  Example: a three-year cap, n.p. of $100,000 with a strike rate of 9.6%

                                                                 13.824%
                                                                 $4224
                                               11.52%
                                               $1920
                             9.6%                                9.6%

           8.0%                                8.0%

                             6.667%                              6.667%

                                               5.556%

                                                                 4.629%
Interest Rate Caps and Floors
  Example: a three-year floor, n.p. of $1000,000 with a strike rate of 6%
                                                                 13.824%

                                               11.52%

                             9.6%                                9.6%

           8.0%                                8.0%

                             6.667%                              6.667%

                                               5.556%
                                               $444
                                                                 4.629%
                                                                 $1370
What about Collars?
• Interest rate collar
  …the simultaneous purchase of an interest rate cap
  and sale of an interest rate floor on the same index
  for the same maturity and notional principal amount.
   – The cap rate is set above the floor rate.
• The objective of the buyer of a collar is to protect
  against rising interest rates.
   – The purchase of the cap protects against rising rates while
     the sale of the floor generates premium income.
• A collar creates a band within which the buyer’s
  effective interest rate fluctuates.
And Reverse Collars?

• Reverse collar
  …buying an interest rate floor and simultaneously selling an
  interest rate cap.
• The objective is to protect the bank from falling
  interest rates.
   – The buyer selects the index rate and matches the maturity
     and notional principal amounts for the floor and cap.
• Buyers can construct zero cost reverse collars when it
  is possible to find floor and cap rates with the same
  premiums that provide an acceptable band.
The size of cap and floor premiums are
determined by a wide range of factors
• The relationship between the strike rate and the prevailing 3-
  month LIBOR
   – premiums are highest for in the money options and lower for at the
     money and out of the money options
• Premiums increase with maturity.
   – The option seller must be compensated more for committing to a fixed-
     rate for a longer period of time.
• Prevailing economic conditions, the shape of the yield curve,
  and the volatility of interest rates.
   – upsloping yield curve -- caps will be more expensive than floors.
   – the steeper is the slope of the yield curve, ceteris paribus, the greater
     are the cap premiums.
   – floor premiums reveal the opposite relationship.
Putting It All Together
  • What are the the relationships among
    swaps, caps and floors? Think about this:
              • Floor = Cap - Swap
              • Cap = Floor + Swap

  • HOW?