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Understanding Interest Rate Capped Swap Valuation and Risk

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.<br><br>This presentation gives an overview of capped/floored swap product and valuation. You find more information at http://www.finpricing.com/lib/IrCappedSwap.html<br>

dmitrypopov
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Understanding Interest Rate Capped Swap Valuation and Risk

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  1. Interest Rate Capped Swap Valuation and Risk Dmitry Popov FinPricing http://www.finpricing.com

  2. Capped Swap Summary ◆ Capped Swap Definition ◆ Floored Swap Definition ◆ Valuation ◆ A real world example

  3. Capped Swap Capped Swap Definition ◆ A capped swap is an interest rate swap with a cap where the floating rate of the swap is capped at a certain level. ◆ It limits the risk of the floating rate payer to adverse movements in interest rates. ◆ Given the optionality, an up-front fee or premium has to be paid by the floating rate payer. ◆ A capped swap can be decomposed as an interest rate swap plus an interest rate cap.

  4. Capped Swap Floored Swap Definition ◆ A floored swap is an interest rate swap with a floor where the floating rate of the swap is floored at a certain level. ◆ It limits the risk of the floating rate receiver to adverse movements in interest rates. ◆ Given the optionality, an up-front fee or premium has to be paid by the floating rate receiver. ◆ A floored swap can be decomposed as an interest rate swap plus an interest rate floor.

  5. Capped Swap Valuation ◆ There are four types of capped or floored swaps. ◆ Capped payer swap ◆ Capped receiver swap ◆ Floored payer swap ◆ Floored receiver swap ◆ The present value of a capped payer swap is given by ?????????????????? = ???????? − ???????? − ?????(?) where ??????? is the present value of the floating leg of the underlying swap; ??????? is the present value of the fixed leg of the underlying swap; ????? is the present value of the embedded cap.

  6. Capped Swap Valuation (Cont) ◆ The present value of a capped receiver swap can be expressed as ????????????????????? = ???????? − ???????? + ?????(?) ◆ The present value of a floored payer swap can be represented as ??????????????????? = ???????? − ???????? + ???????(?) Where ??????? is the present value of the embedded floor. ◆ The present value of a floored receiver swap can be computed as ?????????????????????? = ???????? − ???????? − ???????(?)

  7. Capped Swap Valuation (Cont) ◆ The present value of the fixed leg is given by ? ???????? = ?? ???? ?=1 where R – the fixed rate; N – the notional; ??– the day count fraction for period [??−1,??]; ??= ?(?,??)– the discount factor. ◆ The present value of the floating leg is given by ? ???????? = ? (??+ ?)???? ?=1 1 ?? ??−1 ?? where s – the floating spread; ??= ? ?;??−1,?? = compounded forward rate − 1– the simply

  8. Capped Swap Valuation (Cont) ◆ The present value of the cap is given by ? ?????? = ? ??????Φ ?1 − ?Φ(?2) ?=1 ?? ? distribution function. ◆ The present value of the floor is given by 2?? /(?? ??) and Φ– the cumulative normal where ?1,2= ln ± 0.5?? ? ?????? = ? ?????Φ −?2 − ??Φ −?1 ?=1

  9. Capped Swap A real world example Cap/Floor specification Buy Sell Cap Floor Strike Trade Date Start Date Maturity Date Currency Day Count Notional Pay Receive Payment Freq Index specification Day count Tenor Type Underlying swap specification Leg 1 USD dcAct360 Fixed 200000000 Payment Freq 1M Pay Receive Pay Star tDate 11/4/2016 End Date 11/1/2020 Fixed Rate 0.01043 Buy Floor 0.001 11/3/2016 11/4/2016 11/2/2020 USD dcAct360 200000000 Receive Leg 2 Currency Day Count Leg Type Notional Currency Day Count Leg Type Notional Payment Freq Pay Receive Start Date End Date Spread Index specification Type Tenor Day Count USD dcAct360 Float 200000000 1M Receive 11/4/2016 11/1/2020 0 1M LIBOR 1M dcAct360 dcAct360 1M LIBOR

  10. Thanks! You can find more details at http://www.finpricing.com/lib/IrCappedSwap.html

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