## Frequent Links

# Interest rate derivative

An **interest rate derivative** is a derivative where the underlying asset is the right to pay or receive a notional amount of money at a given interest rate. These structures are popular for investors with customized cashflow needs or specific views on the interest rate movements (such as volatility movements or simple directional movements) and are therefore usually traded OTC; see financial engineering.

The interest rate derivatives market is the largest derivatives market in the world. The Bank for International Settlements estimates that the notional amount outstanding in June 2012 ^{[1]} were US$494 trillion for OTC interest rate contracts, and US$342 trillion for OTC interest rate swaps. According to the International Swaps and Derivatives Association, 80% of the world's top 500 companies as of April 2003 used interest rate derivatives to control their cashflows. This compares with 75% for foreign exchange options, 25% for commodity options and 10% for stock options.

Modeling of interest rate derivatives is usually done on a time-dependent multi-dimensional Lattice ("tree") built for the underlying risk drivers, usually domestic or foreign short rates and foreign exchange market rates, and incorporating delivery- and day count conventions; see Short-rate model. Specialised simulation models are also often used.

## Contents

## Types

### Vanilla

The basic building blocks for most interest rate derivatives can be described as "vanilla" (simple, basic derivative structures, usually most liquid):

- Interest rate swap (fixed-for-floating)
- Interest rate cap or interest rate floor
- Interest rate swaption
- Bond option
- Forward rate agreement
- Interest rate future
- Money market instruments
- Cross currency swap (see Forex swap)

### Quasi-vanilla

The next intermediate level is a quasi-vanilla class of (fairly liquid) derivatives, examples of which are:

- Range accrual swaps/notes/bonds
- In-arrears swap
- Constant maturity swap (CMS) or constant treasury swap (CTS) derivatives (swaps, caps, floors)
- Interest rate swap based upon two floating interest rates

### Exotic derivatives

Building off these structures are the "exotic" interest rate derivatives (least liquid, traded over the counter), such as:

- Power reverse dual currency note (PRDC or Turbo)
- Target redemption note (TARN)
- CMS steepener [1]
- Snowball [2]
- Inverse floater
- Strips of Collateralized mortgage obligation
- Ratchet caps and floors
- Bermudan swaptions
- Cross currency swaptions

Most of the exotic interest rate derivatives are structured as swaps or notes, and can be classified as having two payment legs: a funding leg and an exotic coupon leg.^{[citation needed]}

- A funding leg usually consists of series of fixed coupons or floating coupons (LIBOR) plus fixed spread.
- An exotic coupon leg typically consists of a functional dependence on the past and current underlying indices (LIBOR, CMS rate, FX rate) and sometimes on its own past levels, as in Snowballs and TARNs. The payer of the exotic coupon leg usually has a right to cancel the deal on any of the coupon payment dates, resulting in the so-called Bermudan exercise feature. There may also be some range-accrual and knock-out features inherent in the exotic coupon definition.

## Example of interest rate derivatives

### Interest rate cap

An interest rate cap is designed to hedge a company’s maximum exposure to upward interest rate movements. It establishes a maximum total dollar interest amount the hedger will pay out over the life of the cap. The interest rate cap is actually a series of individual interest rate caplets, each being an individual option on the underlying interest rate index. The interest rate cap is paid for upfront, and then the purchaser realizes the benefit of the cap over the life of the contract.

### Range accrual note

Suppose a manager wished to take a view that volatility of interest rates will be low. He or she may gain extra yield over a regular bond by buying a range accrual note instead. This note pays interest only if the floating interest rate (i.e.London Interbank Offered Rate) stays within a pre-determined band. This note effectively contains an embedded option which, in this case, the buyer of the note has sold to the issuer. This option adds to the yield of the note. In this way, if volatility remains low, the bond yields more than a standard bond.

### Bermudan swaption

Suppose a fixed-coupon callable bond was brought to the market by a company. The issuer however, entered into an interest rate swap to convert the fixed coupon payments to floating payments (perhaps based on LIBOR). Since it is callable however, the issuer may redeem the bond back from investors at certain dates during the life of the bond. If called, this would still leave the issuer with the interest rate swap. Therefore, the issuer also enters into Bermudan swaption when the bond is brought to market with exercise dates equal to callable dates for the bond. If the bond is called, the swaption is exercised, effectively canceling the swap leaving no more interest rate exposure for the issuer.

## See also

## References

**^**Bank for International Settlements "Semiannual OTC derivatives statistics" at end-June 2012. Retrieved 5 July 2013.

## Further reading

- Leif B.G. Andersen, Vladimir V. Piterbarg (2010).
*Interest Rate Modeling in Three Volumes*(1st ed. 2010 ed.). Atlantic Financial Press. ISBN 978-0-9844221-0-4. - Damiano Brigo, Fabio Mercurio (2001).
*Interest Rate Models - Theory and Practice with Smile, Inflation and Credit*(2nd ed. 2006 ed.). Springer Verlag. ISBN 978-3-540-22149-4. - John C. Hull (2005)
*Options, Futures and Other Derivatives*, Sixth Edition. Prentice Hall. ISBN 0-13-149908-4 - John F. Marhsall (2000).
*Dictionary of Financial Engineering*. Wiley. ISBN 0-471-24291-8

## External links

- Basic Fixed Income Derivative Hedging - Article on Financial-edu.com.
- Interest Rate Modeling by L. Andersen and V. Piterbarg