Online Finance – Interest Rate Swaps – Terminology, concepts, glossary

28 mins read

Complex swaps

Key concepts

Although the standard swap structures meet the needs of many hedgers and investors, there are occasions on which the circumstances of the parties require more highly-structured swap products. Many of these swaps take the standard interest rate swap structure and, by incorporating foreign exchange rate linkages, complex indexing of the payment streams and notional principal amounts, options and other contingencies, allow swap users to define their views on particular markets or the relationship between markets more precisely than with vanilla swaps and more economically than using a basket of standard derivatives. Indeed in some cases, the payoffs cannot be constructed with standard derivatives. In the same way that structured assets are created by combining vanilla fixed-income instruments with derivatives, so many of these swaps are constructed by taking standard swap structures and combining them with the vanilla and exotic options defined elsewhere in this book.


accrual swap

An interest rate swap under which a counterparty pays a vanilla floating reference rate, usually three- or six-month Libor, and receives Libor plus a significant spread. Interest payments to this counterparty will only accrue on days (or another pre-set period) when rates stay within a certain range dictated by pre-set upper and lower boundaries. A more aggressive variant, the binary [coupon] accrual swap (also known as a one-touch swap), is also available in which any breach of the range boundaries cancels all further potential for accrual. The simple accrual swap is constructed from a conventional interest rate swap plus a short digital strangle (short a digital put at the lower boundary of the range, short a call at the upper limit) with a maturity equal to the Libor fixings (usually daily, weekly or monthly). Versions are available where the upper and lower ranges step-up or down over the life of the swap and where the holder can reset or cancel the range at specified times.

Callable swap

An interest rate swap in which either the fixed-rate payer or the fixed-rate receiver has the right to terminate the swap at one or more predetermined points during its life. These points are either defined in terms of time or in terms of points on the swap curve. Most usually, a callable swap is one in which the fixed-rate payer has the right to terminate the swap, that is has bought the call. A callable swap is the combination of an interest rate swap and a receiver swaption. Also known as a cancellable swap, collapsible swap, retractable swap. A swap in which the fixed-rate receiver has the right to terminate, that is has bought a put, is known as a puttable swap. It is the combination of a standard swap and a payer swaption and allows the holder usually an investor to benefit from a rise in interest rates.

A treasurer paying 10% fixed and receiving Libor flat under a five-year swap might like to cancel the swap if rates decline. A cancellable swap gives him to option to stop paying fixed (and so effectively to start paying floating) and he pays for this option by paying a fixed rate on the cancellable swap that is higher than prevailing vanilla swap rates. The counterparty with the right to terminate has effectively bought a swaption from the other counterparty which protects them against adverse moves in interest rates. In this case the treasurer has bought a receiver swaption (say two year) that gives him the right to receive a fixed rate of 10% against paying Libor flat for a period of three years. In two year’s time if the prevailing three-year swap rate is below 10%, the treasurer can exercise the option to enter into a three-year swap. This new swap effectively cancels the existing swap since the cash flows of one are offset by the other. This allows the treasurer to lock in a lower swap rate at a future point in time.

The structure can be used by investors too. An investor is paying Libor and receiving 7% fixed in a five-year swap. He purchases a payer swaption giving him the right to enter a three-year swap in which he pays 7% fixed against receiving Libor at the end of two years. If in two years’ time three-year swap rates rise above 7% he can exercise the swaption and enter into a three-year swap paying 7% fixed and receiving Libor. This swap offsets the existing swap that has three years to run and the investor can now enter into a new three-year swap under which he receives the prevailing three-year swap rate against paying Libor.

Clean index principal swap

A path-dependent version of the index principal swap. In the standard IPS the notional principal can accrete or amortize, and once the process of accretion or amortization has started it either continues at the level set by the initial barrier or is accelerated as rates move to the next barrier. In the clean IPS the notional principal is reset according to the Libor rate prevailing at the beginning of each calculation period. It is clean in the sense that for each calculation period the swap notional is totally independent of previous settings. This means that the swap’s notional amount is far more directly linked to the direction of Libor than is the case for a generic index principal swap.

Example Clean index principal swaps can be used by hedgers thus: A corporate decides to pay fixed and receive six-month Libor and the amortization factors are set such that, if Libor is below 5.0%, the notional principal on the swap is zero. This means that if Libor is below 5.0% at the beginning of a calculation period, then for that period the hedger simply pays Libor the swap is deactivated. The higher Libor rises, the more of the hedger’s outstanding liability is swapped into fixed until, at a predetermined point, the full liability is capped at the fixed rate payable on the swap. The product allows clients to fix without being affected by the cost of carry associated with a steep yield curve. In exchange for this, before the swap is fully activated the corporate pays a blended rate made up of Libor on the unswapped portion of the liability plus an above-market fixed rate on the remainder.

Collared swap

An interest rate swap combined with an interest rate collar on the floating leg. Also known as a floor/ceiling swap.

Commodity-linked interest rate swap

A hybrid swap in which an interest rate index such as Libor is exchanged for a commodity-price linked fixed rate. A user of aluminium might wish to link the price of his major cost, aluminium, to the price of his debt. He could elect to receive Libor and pay an aluminium-linked rate such that as the price of aluminium rises, the fixed rate he pays declines. It is also possible to swap a commodity price itself for Libor see commodity swap.

Contingent swap

A swap activated by a specified event and usually paid for with a premium. Swaptions can be viewed as contingent swaps.

Currency protected swap

A quantized interest swap. That is, an interest rate basis swap in which the buyer pays an interest rate in one currency, usually his domestic Libor, and receives a second currency’s Libor plus or minus a spread with all payment streams denominated in the same usually the buyer’s domestic currency. They can be used to reduce funding costs: floating-rate liabilities in high interest-rate currencies with inverted yield curves can be swapped into low current reference Libors plus a spread where the yield curve is steep without the risk of currency exchange on coupons or principal amounts.

The benefit arises from the implied forward curve in each currency. High forward Libors implied in the low interest reference yield curve combined with lower forward Libors implicit in the high interest domestic curve result in a current interest saving. So the longer the maturity of the quanto swap the more attractive the upfront benefit in interest savings. This should be balanced against the increased uncertainty of actual future Libor settings. Liability hedgers who use the structure take the view that the yield curves overstate the future path of one or both of the Libors over the life of the swap.

A borrower of dollars wants to benefit from the fact that floating money market rates in yen are currently well below equivalent floating money market rates in dollars. He enters into a currency protected swap under which he pays yen Libor denominated in dollars plus a margin and receives dollar Libor. As long as the interest rate differential between yen and dollars exceeds the margin he is paying, then he is benefiting from low yen rates.

It was the boom in this product that spurred the search for correlation risk because of its importance in pricing these swaps. A swap writer paying yen Libor in dollars and receiving dollar Libor in dollars funds the yen Libor payout through the swap market. He is therefore hedging US$ denominated yen interest rate risk using yen denominated instruments. So, even if interest rates remain the same, he is exposed to the risk that the dollar will strengthen, leaving him too few yen to pay his dollar liability. Although the prevailing exchange rate will determine the initial size (‘quantum’) of the hedge, ongoing changes in exchange rates will vary the size of the hedge required. Hedging this risk means taking a view on the correlation covariance between interest rates (yen Libor) and yen/US$ exchange rates. That is, to what extent will a rise in yen interest rates, and so the amount of money the swap writer must pay out to the buyer, be offset by a strengthening of the yen against the dollar?

Because the view taken is that the yield curves overstate the future path of one or both Libors they can also be used by investors to take yield curve views when they believe that the convergence or divergence of FRA curves is too acute without taking FX risk. So:
An investor wants to implement his views on the spreads between two markets without taking direct foreign exchange exposure. He enters a quanto CMS swap receiving US dollar 10-year CMS rates minus a spread and pays yen 10-year CMS in return, both payment streams denominated in dollars. He can take a view on more than one spread. For example, a quanto swap could be purchased that paid two-year US dollar CMS rate in exchange for 50% of the two-year sterling CMS and 50% of the Deutschmark, paid in dollars.

One variant is the limited risk differential swap. This is a differential swap combined with a cross-currency cap {floor}. The combination allows the user to benefit from the interest rate differentials between two currencies while capping {flooring} the maximum loss incurred if the differentials move adversely. The basic instrument it is known by a large number of names including differential swap, guaranteed exchange rate swap, cross-indexed basis (CRIB) swap, cross-rate swap, index differential swap, interest rate index swap, Libor rate differential swap, quanto swap.

Crack spread swap

A commodity swap that enables refiners to lock in a margin by paying the floating price of the refined product or products, calculated as an average over a pre-set period, and receiving the floating price of its chosen crude oil feedstock plus a fixed margin the crack spread. By locking in this margin, refiners can hedge against a narrowing in the differential between crude oil prices and the prices of the refined products it produces. However, in so doing they give up the right to profit from any widening of the spread. Also known as the refinery margin swap.

Curve/roll lock swap

A curve lock is any instrument which locks in the spread between two different points on a yield or price curve. A curve lock swap is a swap that locks in this spread for one of the swap counterparties. They are used either as outright speculation on future curve movements or to benefit from a favourable curve shape when the absolute level of the underlying market makes entering into a swap outright unappealing. Also known as a trigger swap because the counterparty wishing to lock in the spread can trigger it at any time during a predetermined trigger or lock-in period.

Instead of entering a contango swap, an oil producer unwilling to fix the price of his production at current low swap rates can enter a curve lock swap. The swap rate is set at a differential to a nearby futures contract before the expiry of that futures contract. If his belief that the contango will diminish proves correct and spot prices rise, the futures price will rise and he will be able to trigger the swap at a significantly higher level than was available in the swap market originally. The differential provides a cushion if spot prices fall.

For example, say the price of the December 1997 future is US$14.90 and the price for a calendar 1998 Brent crude swap is US$15.40. An oil producer wants to hedge some of its 1998 production by receiving fixed in an oil swap but believes the price is too low. However, it likes the level of contango and thinks it will diminish. A trigger swap would lock in the differential (in this case US$0.50) between the futures price and the swap price while delaying the moment at which the swap rate is finally fixed. The producer therefore enters into a calendar 1998 trigger swap the price of which is set at a differential of US$0.50/bbl to the price of the December 1997 IPE Brent future. At some time between the deal date and the expiry of the futures contract the producer must lock in the absolute level of the futures contract resulting in an all-in swap price of US$0.50 more than this chosen level. If the price of the December 1997 future on October 12 is US$15.80 and the producer pulls the trigger, the resulting swap price will be US$16.30. If the trigger is not pulled then the price immediately before expiry of the futures contract is used as the basis for the swap price. Alternately the basis is rolled forward to a subsequent futures contract with the differential adjusted accordingly. This structure gives the producer an opportunity to lock in the shape of the curve when it is favourable and fix the price of the swap when the market is at a more satisfactory level.

Double-up swap

A fixed-for-floating (usually commodity) swap in which the fixed-rate payments are set lower than the market rate. In exchange, the fixed-rate payer grants the floating-rate payer a put option to double the notional amount of the swap if the spot price of the underlying falls below a pre-set strike price, usually the same as the discounted swap rate. The difference between the off-market and market rates represents the premium for this embedded option. If the strike is hit, then not only is the fixed-rate payer paying a higher price for the underlying than the current spot rate, he is paying it on twice as much as the original notional principal of the swap. If a commodity user/producer uses double-up swaps to hedge more than half their real requirements/production and the option is exercised, he ends up over-hedged. That is effectively speculating, since he has fixed prices on more of the commodity.

Down-and-out floored swap

The combination of receiving floating under an interest rate swap and the sale of a down-and-in knock-in floor with the trigger set well below the fixed rate on the swap and with a strike at the swap rate.

A down-and-out floored swap might fix a floating-rate borrower’s cost of funds at 5.90% if rates rise above 5.90% while allowing him to benefit from rate falls down to 4%. If rates do hit 4% though, the down-and-in floor is exercised against him at 5.90%. So if Libor is above 5.90% or below 4% the borrower is fixed at 5.90%.

Drop-lock swap

A deferred-start interest rate swap in which the fixed-rate payment is reset to a lower {higher} pre-agreed level if, between the time of the agreement and the commencement of the swap, the floating reference rate drops below {rises} above a predetermined level.

Dual coupon swap

A fixed-for-floating interest rate swap in which one counterparty has the right to alter the currency in which payments are made contingent upon a predetermined move in exchange rates usually if rates move against the swap’s base currency. The structure combines an interest rate swap subsidized by the sale of a strip of currency options whose holders can choose the currency of the coupon payments. Also known as a currency indexed/linked swap.

Example A borrower wishes to swap a floating rate borrowing into fixed. To reduce the fixed rate swap payments he agrees to pay coupons in either his base currency or another at the option of the swap counterparty depending on whether the currencies’ exchange rate is above or below a pre-set index level (the strike of the options). If the options are in-the-money, the holder will exercise them against the borrower forcing him to deliver the coupons at an off-market (expensive) exchange rate. If they are out-of-the-money then the coupon is delivered in the borrower’s base currency and he benefits from the lower swap rate.

Dual currency swap

A currency swap in which the holder receives one currency on initial exchange, pays coupons in another and makes the final exchange of principal in a third currency. This type of swap is used by borrowers willing to lower their nominal interest cost by taking currency risk. A dollar borrower will achieve lower borrowing costs by agreeing to pay the principal at maturity in, say, Euros at the prevailing spot rate when Euro swap rates are below dollar swap rates.

Example A borrower who normally achieves sterling Libor less 0.25% wants to reduce his funding costs. He issues a US$100 million bond and enters a dual currency swap. In the initial exchange of notional amounts he pays the swap counterparty the US$100 million in exchange for the equivalent amount in sterling. He receives fixed-rate dollars (to service the initial dollar bond borrowing) and pays sterling Libor less a spread. On maturity he receives the US$100 million but pays the swap counterparty the equivalent amount in, say, Euros.

Extendible swap

A swap in which one counterparty has the right to extend a swap beyond its original term. It is the combination of a vanilla swap with a swaption (payer or receiver) whose expiry date coincides with the maturity date of the existing interest rate swap. Most commonly it is the fixed-rate payer who has the option. However, in the commodity markets, it is often the floating-rate payer. Swaptions can also be used to create reversible swaps. These are swap that allows the user to switch from being a floating rate payer in a swap to becoming a fixed rate payer. It is the combination of an interest rate swap with a receiver swaption with a notional principal twice that of the underlying swap. Half the swaption if exercised allows the holder to cancel an existing swap (in the same way as swaptions are used in callable and puttable swap) and the other half results in a new swaps position the same size as the old one with opposite interest obligations. See callable swap.

In an extendible swap an oil consumer who wishes to fix the price of his oil purchases can enter into a fixed-for-floating commodity swap under which he pays a fixed rate that is lower than the going swap rate and that is approximated to his budgeted rate and in exchange grants the floating-rate payer the option to, say, double the life of the swap if the price falls below a certain point. If it does, the consumer is paying his budgeted rate and the option writer is benefiting from paying out a lower floating price than he is receiving fixed.

Flex[ible] swap

An interest rate swap in which the buyer receives a floating rate and pays the higher of a fixed rate lower than the current swap rate or Libor minus a pre-set spread, at the option of the swap counterparty.

A corporation has US$100 million of floating dollar debt paying Libor plus 0.5% with three-year’s remaining life. Three-year swap rates are 7.59%. The company expects US rates to fall gradually over the three years to 7.00%. The company enters into a flexible swap under which it receives US dollar Libor and pays, at the counterparty’s option, the higher of 7.05% fixed or dollar Libor less 54bp. The company benefits most if dollar Libor stays above 7.05% (below which it would have been better to stay floating) and below 8.13% (above which it would have been better to fix at the 7.59% swap rate available at the outset. Even then the flexible swap gives the borrower a margin under the straight floating rate.) The borrower has effectively sold a floor at the implicit fixed rate under the flexible swap to the bank. The premium received is incorporated into the margin under the floating rate index and adjustment to the flexible fixed rate to a level below the prevailing swap rate for the maturity.

Incremental fixed {floating} swap

A swap in which the fixed {floating) rate is only payable on a certain percentage of the notional of the swap the rest staying floating {fixed}. In an incremental fixed {floating} swap the fixed {floating} portion of the swap increases with Libor according to a pre-set ratchet table. So in an incremental fixed swap, the fixed-rate payer pays the IFS swap rate on a resettable notional principal amount. Because this rate is not always paid on the full notional amount, it is much higher than vanilla swap rates. The IFS therefore appeals to floating-rate borrowers who believe that rates will stay considerably below the level at which the fixed rate is payable on a large proportion of the notional principal (which would push the blended rate well above swap rates. The IFS therefore performs a similar function to an interest rate cap, in that it fixes a maximum cost of funds, but instead of paying an upfront premium, users pay for the insurance against catastrophic rate rises in the form of a higher swap rate. In most cases the attraction of the blended rate at the outset of the swap is that it offers hedgers a way to protect themselves cheaply against rate rises when absolute rates are low but the implied forward curve is steep.

The index floating swap achieves much the same in the opposite way. Instead of starting with an off-market high IFS fixed rate and a low percentage of the notional on which it is payable, the swap is initiated with an off-market low IFS fixed rate payable on a high percentage (often 100%) of the notional, usually protected for a defined start period. After the protection period, the fixed-rate payer pays the IFS rate on a certain portion of the notional and Libor plus or minus a spread on the remainder. If Libor rises, the percentage of notional on which the floating rate is paid increases and the percentage on which the low fixed-rate is payable decreases. Also known as an index fixed {floating} swap, blended interest rate swap, self-regulating swap. Not to be confused with index principal swaps which also result in changes in effective rates paid depending on rate movements but whose notional principal actually changes.

Example In a five-year incremental fixed swap with a notional principal of US$100 million, the fixed portion of the swap could be determined as follows.

If Libor is above:

but below or equal to:

then the fixed portion is:

8.50% N/A 100%
8.00% 8.50% 80%
7.50% 8.00% 60%
7.00% 7.50% 40%
6.50% 7.00% 20%
0% 6.50% 0%

The IFS swap rate is 11.16% when the normal five-year swap rate is 9.50%. The payer then pays X* 11.16% +(1-X)*Libor and receives six-month Libor, where X = the percentage of the notional principal fixed in the swap. If the Libor setting on a reset date were 7.76%, the payer would pay 60% fixed at 11.16% and 40% floating at 7.66%, resulting in a rate of 10.07%. When Libor is above 8.50%, the IFS becomes a normal fixed rate swap at 11.16%.

The price of the IFS results from its complex structure. It is constructed from a cap on 20% of the notional principal at each strike (or 10% or 5% depending on the number of reset bands). The swap provider then writes digital options at these strikes for 20% of the notional principal, so that the premiums of the options cover the cost of the cap. So, if Libor is 7.20% the swap provider would have capped 20% at 6.50% and 20% at 7.00% and the swap would be 60% in floating. The losses on each digital in each Libor range are then calculated and the present value of these losses is spread over the life of the swap to calculate the IFS rate. By incorporating different combinations and types of digital options, these swaps can be tailored to meet a wide variety of different needs. The swap can even be indexed to a different asset class – linking interest payments with commodity prices, for example.

Index amortizing (rate) swaps (IAS)

The commonest types of index principal swap, IASs have a notional principal that can only amortize and which amortizes more quickly as rates fall. (A swap which amortizes more quickly as rates rise is called a reverse index amortizing swap.)

Typically in an IAS the fixed-rate is higher than would be payable on a swap with a fixed notional principal because the notional principal amount will amortize as interest rates fall (or as prepayment rates rise). The fixed-rate receiver obtains this high coupon because he has sold the fixed-rate payer a series of put options on an interest rate index which effectively gives the fixed-rate payer an option to shorten the swap’s life if rates move against him. The notional principal is generally fixed for an initial two-year period of the swap, known as the lock-out period during which time the buyer is protected against amortization. After that period, the notional of the swap will decrease as a function of the level of the index chosen.

Sample terms might state that if Libor stays between 5.0% and 5.5% the swap amortizes by 75%. If it rises to between 5.5% and 6.0% the swap amortizes by 50%. Between 6.0% and 6.5% it amortizes by 25%. And above 6.5% the swap notional remains at 100%. There is a lock-out period set in which the notional principal cannot amortize. The swap’s maturity date is the point at which any remaining notional principal outstanding matures. And there is generally a clean-up feature: if the notional principal falls below 5% of the initial amount, the swap amortizes completely.

Originally these instruments grew from the mortgage-backed securities market and the amortization schedule was designed to correspond to the expected timetable of prepayments on a pool of mortgages (by linking the amortization schedule with indices of mortgage prepayment rates or of prepayments on a tranche of collateralized mortgage obligations) hence their name: mortgage [replication] swaps or CMO swaps. Counterparties exchange a fixed-rate payment stream for a stream of mortgage-related flows generated by a pool of mortgages or an index on such a pool. Although the interest payments into this payment stream are fixed, the notional principal can amortize as borrowers prepay mortgages if interest rates fall significantly. If this happens, the notional principal on which the mortgage swap cashflows are calculated amortizes accordingly. This kind of swap creates off-balance sheet investments that behave like a portfolio of mortgages or like collateralized mortgage obligations without the need to take mortgage assets onto their balance sheets.
The fixed-rate receive side of an IAR has negative convexity through the sale of the embedded options. The fixed-pay side has positive convexity and can be used as a way of offsetting the negative convexity of receiving mortgage-linked cashflows from mortgage-backed securities which are affected by prepayment when rates decline. Most have had maturities of less than three years to maximize the amount paid on the fixed leg. In addition to mortgage-related investment and hedging, IARs can also be used for straightforward yield enhancement:

Instead of investing in, say, vanilla one-year paper, a corporate treasurer can maintain three-month rolling assets at Libor flat and pay that floating stream into an index amortizing swap with a one-year lock-out and a final maturity that represents the maximum period for which he is comfortable locking in his funds. As Libor decreases, the amortization speeds up. For the lock-out period, the treasurer earns an above-market rate on his assets. In return for this, after the lock-out period he accepts that, if Libor declines, instead of benefiting from paying less into the swap and receiving fixed on the full notional amount, the swap will amortize, forcing him to reinvest the freed-up cash at lower rates.
These swaps are usually structured so that as long as the amortization falls in a range between zero (the swap matures on the full original notional amount) and 100% immediately after the lock-out period, the treasurer achieves an above-market yield as well as a flexible medium-term investment vehicle. Because amortization is expected, the swap performs rather like a money market instrument after the lock-out period and provides cash liquidity as it amortizes. The swap works best in a steep yield curve environment.
IARs can also be used for liability management in a steep yield curve environment:
If a treasurer believes that short rates will not rise by more than, say, 100bp in the next two years, an alternative to the vanilla swap is the index amortizing swap. For the two-year lock-out period, the floating rate that the treasurer must pay into the swap can be up to 50bp less than he would have to pay into a vanilla swap of the same maturity. Second, after the lock-out period, the notional principal on the swap will amortize 50% as long as Libor does not rise more than 100bp, so that the treasurer’s net position existing liability plus swap reverts gradually to a fixed-rate liability. The transaction makes sense in yield-curve environments where the blended rate created by the transaction is cheaper than the vanilla swap for the full term of the liability, a vanilla swap for part of the remaining life of the liability or a cancellable swap. The danger is that the treasurer’s prediction that Libor will rise no more than 100bp might be significantly mistaken. If the rise is severe enough, no amortization will be triggered and the treasurer will have to remain a floating payer for the remaining life of the liability. However, this floating rate will still be less than that payable under the vanilla swap.

And these structures have now developed to the extent that now in an index amortizing swap almost any amortization schedule is possible by agreement. So, for example, the currency-linked index amortizing swap is an index amortizing swap whose notional principal is indexed to currency value movements.

A currency-linked index-amortizing swap could be used by a US exporter with such strong growth in its Deutschmark earning exports that it needs more working capital. It wants to borrow fixed-rate dollars while rates are low but wants protection against a strengthening dollar hitting its export business and so reducing its working capital requirement. It could enter into a callable interest rate swap but prefers an index amortizing swap under which it initially pays 4.30% fixed and receives Libor on a notional amount equal to its borrowing. However, as the US dollar appreciates against the Deutschmark, the notional principal of the swap reduces according to a pre-set schedule, effectively shortening its life and facilitating early repayment of the underlying loan and providing the required hedge profile, offsetting the reduced need for working capital as the stronger dollar reduces Deutschmark revenue flows.
And reverse index-amortizing swaps can solve a number of problems faced by investors and hedgers.

A reverse index amortizing swap is an indexed principal swap in which the notional principal amortizes faster as rates rise or which achieve the same effect by linking their floating-rate payments to an index and increasing them if the index declines. Counterparties that wish to hedge against instruments that amortize as rates decline can receive fixed in a reverse IAS. The instrument is also used instead of a vanilla interest rate swap to transform a floating-rate asset to a fixed-rate asset because it gets around the problem that an asset so swapped will lose its value if rates rise and returns will be reduced if the investor is short-funded. An interest rate cap incurs an upfront premium and may expire out of the money. The reverse IAS amortizes as rates rise thus reducing the size of the fixed-rate asset. Higher cost funding can then be utilized to invest in higher-yielding assets. In the same way, fixed-rate liabilities swapped into floating will incur increasing interest expense when rates rise. The reverse IAS can be used to hedge against this.

Indexed principal swap (IPS)

Generic term for a (generally fixed-for-floating) swap whose notional principal can accrete or amortize according to a predefined index, such as Libor, CMTs or a mortgage prepayment index such as PSA rates. See clean index principal swaps, index amortizing (rate) swaps, reverse index amortizing (rate) swap. Not to be confused with instruments whose interest payment streams alter according to the level of an index (usually Libor but sometimes foreign exchange rates or commodity prices) but whose notional principal remains constant, such as the incremental fixed swap, Libor regulating swap, semi-fixed swap

Inverse floater swap

An interest-rate swap under which one counterparty pays fixed and receives a floating rate indexed negatively to a reference index such as Libor. As Libor rises, the fixed payer would receive less; as it falls, he would receive more.

Libor function swap

An interest rate swap to whose floating-rate leg a customized mathematical function or equation has been applied to produce a payout profile tailored to a very specific view of rate movements.

Linear forex-linked swap

An interest rate swap one of whose legs is linked to movements in a foreign exchange rate. Changes in the reference foreign exchange spot rate result in linear changes in the coupon rate paid/received under the swap. This swap allows borrowers, for example, to swap their debt into an interest rate that varies directly with a foreign exchange exposure they have. Adverse movements in foreign exchange rates are offset by smaller interest rate payments on their debt.

Libor regulating swap

An interest rate swap under which one party receives Libor and pays a blended rate calculated as the combination of a predetermined fixed rate and a predetermined floating rate. The blended rate is capped at a maximum. It sits halfway between the incremental fixed {floating} swap and the semi-fixed swap. The former links interest payments to a predefined ratchet table that dictates the percentage of the notional principal on which fixed- and floating-rate payments are made. The latter specifies just two rates payable a high and low rate determined by the level of Libor (or some other underlying) on reset dates.

A treasurer that could pay fixed at 6.71% in a three-year semi-annual swap could instead elect to enter a US$100 million Libor regulating swap in which they receive six-month Libor and pay the minimum of (6.90% + six-month Libor)/2 and 7.75%. So, if the average of the fixed and floating rates stayed below 7.75%, then the treasurer would pay the blended rate. If that average were above 7.75%, his fixed-rate payments would be capped at 7.75%. In this example, the blend of fixed- and floating-rate is set at 50:50. This proportion can be customized according to the hedger’s views.

The swap is constructed from a swap and cap, each for the requisite proportion of the original notional amount. In this example, the swap can be imagined as two swaps, each on US$50 million of notional principal. One is a 6.90% pay fixed receive six-month Libor swap, the other a pay six-month-Libor receive six-month Libor. The second swap clearly cancels itself and so the treasurer has simply fixed US$50 million at the off-market rate of 6.90%. However, assuming he actually has a liability of US$100 million on which he must pay Libor, that leaves US$50 million of the original exposure unhedged. For the actual blended rate not to exceed 7.75%, a cap on that US$50 million floating portion is needed at 8.6% – ((7.75 x 2) – 6.9). The cap premium is the difference between the swap rate (6.71%) and the fixed rate portion of the blended rate (6.90%) so that no upfront premium is required.

In a positive yield curve environment the treasurer’s cost of funds will be lower than a regular swap (but higher than Libor). Also, the maximum rate is known in advance, though it will be higher than the current market swap rate. Like many other second generation swaps, this instrument is for treasurers who wish to hedge against rate rises but who feel that the current yield curve and implied forward curve overstate future rate rises.

Lookback swap

A swap in which, for example, the holder pays the highest Libor setting in the reset period and receives Libor set at the beginning of the period plus a spread. In a three-year deal with six resets, for example, the holder could receive six-month Libor plus 120bp and pay the highest daily six-month Libor rate in each six-month period.

Nearly-perfect swap

An interest rate swap in which a fixed rate is swapped into a low, off-market floating rate linked to a reference index such as Libor but subject to the following type of formula: for every basis point that Libor exceeds a pre-set cushion level between two reset dates, the spread over Libor increases by a pre-set amount, say, one basis point. Libor is set at the end of each payment period. The floating-rate payer is taking the view that the velocity of the increase in short rates will not exceed the cushion level.

A bond issuer issues a 7.0% fixed-rate bond and wants to swap it into floating. Under a nearly perfect swap the swap counterparty pays 7.0% and the issuer pays Libor + 115bp subject to the nearly perfect formula. Where Libor is set at the end of each payment period and where for each basis point increase in excess of 25bp that Libor increases between two reset dates, the Libor funding spread increases by one basis point. So if current six-month Libor is 3.85% then under the swap the initial interest cost is 5.0%. But if rates rise rapidly, then funding costs will rise with them.

Partial fill plus option

Commonest in the commodity derivatives markets, a partial fill plus option strategy is a swap agreement in which one counterparty receives an off-market high fixed rate in exchange for the market floating rate. In exchange for the off-market rate, the fixed-rate receiver grants the floating-rate receiver the option to double the amount of the swap if the price of the underlying exceeds the swap rate.

A company with a total hedge requirement of 100,000 barrels of crude oil per day could enter into a swap under which it was paid US$1 more than the going swap rate for its oil on 50,000 barrels. If oil prices rose substantially, then the floating-rate receiver would exercise the option and would not only receive a floating rate higher than the fixed rate it was paying but would receive it on twice the original notional principal of the swap. The swap can also be structured to be of use to the floating receiver.

Participating swap

Any swap in which one of the counterparties participates in favourable movements in the underlying price or rate while fixing a maximum cost. One interest rate version is an interest rate swap in which the floating-rate payer caps his maximum payment but, by combining the swap with a participating interest rate agreement, retains some participation in any falls in interest rates. The commodity version works in much the same way.

An oil consumer might elect to enter a participating swap under which he agrees to an off-market fixed rate US$1 above the swap rate on a conventional fixed-for-floating commodity swap in exchange for 50% participation in any downward movement in price. If the average of the index price over the reference period is above the agreed fixed rate, then the consumer pays that rate and receives the difference between it and the index rate capping its cost at the off-market swap rate. If the index price of the commodity is less than the off-market swap rate, then, instead of paying 100% of the difference to the counterparty and receiving the index price as would be the case in a normal fixed-for-floating swap, the consumer pays only 50% of the difference between the two, benefiting from 50% of the price decline below the cap rate.

Performance swap

An interest rate swap in which the fixed-rate payer pays the at-market fixed rate and receives Libor plus a margin unless Libor sets at a rate well above current implied forward rates. If Libor does breach the trigger level, then the counterparty continues to pay the at-market fixed rate but also receives the at-market fixed rate. If Libor does not breach the trigger level the fixed-rate payer has fixed at below-market levels. If it does the swap effectively disappears for that period but a rebate is paid in the form of a sub-Libor funding cost. The fixed-rate payer is long a standard interest rate swap, short a call option on Libor (a cap) and short a binary option on Libor.

Periodic reset swap

An interest rate swap whose floating payments are reset according to a pre-agreed schedule or index. Usually, the floating-rate payment is based on the average rate of the reference index over the previous period rather than its level on the reset date. Variants include the window reset swap a type of periodic reset swap in which the floating-rate payer is permitted to reset Libor at any time within each reset period, as opposed to the beginning of each period as in a conventional swap, at no additional cost. This embedded option allows the floating-rate payer immediately to take advantage of windows of opportunity presented by declining rates or sudden dips in rates.

Polynomial swap

An interest rate swap in which polynomial equations (e.g., Ax2+bx+C) are applied to the Libor leg creating payment profiles that can be tailored to outperform vanilla swaps within precisely defined interest rate boundaries. The positions created give the precision of exotic options without the associated all-or-nothing profiles.

Power Libor swap

Strictly speaking a swap that pays Libor squared or cubed (and so on) less a fixed amount/rate in exchange for a floating rate. More generally, any leveraged swap that pays a multiple of Libor usually in exchange for a greatly increased fixed rate if interest rates move against the end user. Power Libor swaps often contain complex embedded options.

The most notorious example is the five-year/30-year swap entered into by Procter & Gamble whose formula dictated that for every 1% increase in CMT yields above 5.78%, P&G’s payment increases by more than 17% of notional principal per year and every 1% decline in long bond prices costs P&G 1% of notional principal.

Semi-fixed swap

An interest rate swap in which there are not one but two fixed rates. Which of the two is payable/receivable depends on whether Libor has reached a predetermined trigger point during each periodic Libor setting. For example, a floating-rate borrower who believes that rates will not rise as quickly as the implied forward curve predicts can receive Libor and pay a below market fixed rate while Libor remains below the trigger point. If Libor exceeds the trigger, then the higher fixed rate is payable. The trigger mechanism is created with an embedded binary option. There are also commodity-linked semi-fixed swaps, particularly in the oil market. For example, an oil consumer might pay a fixed rate of 4% if oil prices stay above US$12 but if prices go below that level, he is swapped into 3.5%. That is, he has bought a swap plus a binary option on oil.

Trigger swap

A swap that pays a fixed-rate below the market rate. However, if rates rise above a certain trigger level, the fixed-rate payer will pay a floating rate minus a spread determined by the then prevailing floating rate. The result is a below market fixed swap that reverts to a below market floating rate swap when the trigger is hit. The subsidized swap is the combination of a pay-fixed swap and the sale of a cap. The cap premium is used to reduce the fixed rate paid under the swap. Also known as a subsidized swap.

The sale of a five-year sterling cap at 10.60% will earn the seller 50bp semi-annually. This amount improves the five-year swap rate from 8.83% to 8.33%. If sterling Libor exceeds 10.60%, the client will be put back into floating at a subsidized rate of Libor less 2.27%. The instrument is ideal for borrowers who want to lock in their floating rate, but do not want to pay the market rate as they believe the implied forward curve significantly overstates future rate rise. It generates an attractive fixed rate as long as their rate ceiling is not breached. And even if it is, they still do better than competitors paying vanilla floating rates.

Superfloater swap

A swap that imitates the characteristics of a superfloater bond in exchange for paying a fixed rate, the counterparty receives a multiple of Libor minus a constant.

A floating rate borrower wishes not just to protect itself against expected rate rises but actively to benefit from them. It enters a superfloater swap in which it pays fixed and receives Libor as long as floating rates stay between an upper and lower strike rate struck on either side of the fixed rate payable. In a two-times multiplier superfloater for every basis point above the upper strike rate that floating rates rise, the borrower receives two basis points of floating rate payment. If the floating rate falls below the lower strike then the floating rate multiplier paid to the borrower falls at a predetermined rate. So the borrower’s effective fixed-rate under the swap increases as rates fall below the lower strike band but decreases as rates increase above the upper strike level. The borrower has bought a cap and sold a floor.

Swap differential/difference agreement (SDA)

An interest rate basis swap contract to exchange or lock in the differential between a bond or note yield and the swap rate of the same maturity. The contract moves with reference to the difference between the same point on the two different yield curves. It allows an investor to profit from the widening or narrowing between two yield curves. The SDA is customized with defined settlement dates, a defined value per basis point move, and one defined point on two yield curves. All payments are made in one currency so there is no currency exposure.


An investor might believe that the differential between the two-year Euro swap rate and the two-year Swiss franc swap rate will narrow over the next year. The investor enters a narrowing Euro-Swiss franc SDA for one-year settlement. The value per point can be set at any value in either currency, say Sfr10,000. The SDA price is given in terms of basis points. If at maturity the difference between the two-year swap rates in the two currencies has fallen below the SDA entry level, the investor will receive Sfr10,000 for every basis point lower. If the difference is higher than the entry level the curves have widened the investor will lose this amount. The entry price is calculated by taking the difference between the implied forward rates from the two yield curves. In the example, the one-year forward two-year Euro and Swiss franc rates are calculated and the difference is the SDA price. Investors who buy the SDA expect curves to widen; those who sell expect curves to narrow.

Thomas A. Fetherston at the University of Albama put this together at some point in time – a mix of teaching notes, core concepts, a glossary and a 109 page handy desk reference that you would end up referring to if you work with derivatives in any shape and form.

I stumbled across this resource about 5 years ago and it had been stewing invisibly in one of the many resource folders I have on my hard drive. I believe it would be a crime to sit or hide on a resource like this. The Glossary is here and I will try and post the teaching notes over the next few days after turning them into bite sized pieces as and when I get time.

I looked for Tom’s home page but a Google search on Tom’s name only pulls up his authored books, no home page that I could possibly link to.