A capped swap is an interest rate swap with an interest rate cap option where the floating rate of the swap is capped at a certain level while a floored swap is an interest rate swap with a floor option where the floating rate of the swap is floored at a certain level. Capped swaps or floored swaps limit the risk of the floating rate payer or receiver to adverse movements in interest rates. A capped swap can be decomposed into a swap and a cap whereas a floored swap can be decomposed into a swap and a floor.
This presentation gives an overview of capped/floored swap product and valuation.
3. Capped Swap
Capped Swap Definition
β A capped swap is an interest rate swap with a cap where the floating
rate of the swap is capped at a certain level.
β It limits the risk of the floating rate payer to adverse movements in
interest rates.
β Given the optionality, an up-front fee or premium has to be paid by the
floating rate payer.
β A capped swap can be decomposed as an interest rate swap plus an
interest rate cap.
4. Capped Swap
Floored Swap Definition
β A floored swap is an interest rate swap with a floor where the floating
rate of the swap is floored at a certain level.
β It limits the risk of the floating rate receiver to adverse movements in
interest rates.
β Given the optionality, an up-front fee or premium has to be paid by the
floating rate receiver.
β A floored swap can be decomposed as an interest rate swap plus an
interest rate floor.
5. Capped Swap
Valuation
β There are four types of capped or floored swaps.
β Capped payer swap
β Capped receiver swap
β Floored payer swap
β Floored receiver swap
β The present value of a capped payer swap is given by
πππΆππππππππ¦ππππ€ππ π‘ = πππππππ‘ π‘ β πππππ₯ππ π‘ β πππππ(π‘)
where
πππππππ‘ is the present value of the floating leg of the underlying swap;
πππππ₯ππ is the present value of the fixed leg of the underlying swap;
πππππ is the present value of the embedded cap.
6. Capped Swap
Valuation (Cont)
β The present value of a capped receiver swap can be expressed as
πππΆππππππ πππππ£ππππ€ππ π‘ = πππππ₯ππ π‘ β πππππππ‘ π‘ + πππππ(π‘)
β The present value of a floored payer swap can be represented as
πππΉπππππππππ¦ππππ€ππ π‘ = πππππππ‘ π‘ β πππππ₯ππ π‘ + πππππππ(π‘)
Where πππππππ is the present value of the embedded floor.
β The present value of a floored receiver swap can be computed as
πππΉπππππππ πππππ£ππππ€ππ π‘ = πππππ₯ππ π‘ β πππππππ‘ π‘ β πππππππ(π‘)
7. Capped Swap
Valuation (Cont)
β The present value of the fixed leg is given by
πππππ₯ππ π‘ = π π ππ π·π
π
π=1
where R β the fixed rate; N β the notional; ππ β the day count fraction for period
[ππβ1, ππ]; π·π = π·(π‘, ππ) β the discount factor.
β The present value of the floating leg is given by
πππππππ‘ π‘ = π (πΉπ + π )ππ π·π
π
π=1
where s β the floating spread; πΉπ = πΉ π‘; ππβ1, ππ =
1
ππ
π· πβ1
π· π
β 1 β the simply
compounded forward rate
8. Capped Swap
Valuation (Cont)
β The present value of the cap is given by
πππππ π‘ = π ππ π·π πΉπΞ¦ π1 β πΎΞ¦(π2)
π
π=1
where π1,2 = ln
πΉπ
πΎ
Β± 0.5ππ
2
ππ /(ππ ππ) and Ξ¦ β the cumulative normal
distribution function.
β The present value of the floor is given by
πππππ π‘ = π ππ π·π πΎΞ¦ βπ2 β πΉπΞ¦ βπ1
π
π=1
9. Capped Swap
A real world example
Cap/Floor specification Underlying swap specification
Buy Sell Buy Leg 1 Leg 2
Cap Floor Floor Currency USD Currency USD
Strike 0.001 Day Count dcAct360 Day Count dcAct360
Trade Date 11/3/2016 Leg Type Fixed Leg Type Float
Start Date 11/4/2016 Notional 200000000 Notional 200000000
Maturity Date 11/2/2020 Payment Freq 1M Payment Freq 1M
Currency USD Pay Receive Pay Pay Receive Receive
Day Count dcAct360 Star tDate 11/4/2016 Start Date 11/4/2016
Notional 200000000 End Date 11/1/2020 End Date 11/1/2020
Pay Receive Receive Fixed Rate 0.01043 Spread 0
Payment Freq 1M Index specification
Index specification Type LIBOR
Day count dcAct360 Tenor 1M
Tenor 1M Day Count dcAct360
Type LIBOR