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# Interest rate derivative

In finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of different interest rate indices that can be used in this definition.

IRDs are popular with all financial market participants given the need for almost any area of finance to either hedge or speculate on the movement of interest rates.

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• ✪ Interest rate swap 1 | Finance & Capital Markets | Khan Academy
• ✪ Interest Rate Derivatives (IRD) - Forward Rate Agreements (FRA)
• ✪ Interest Rate Swap Explained

#### Transcription

Let's say that we've got company A over here, and it takes out a \$1 million loan, and it pays a variable interest rate on that loan. It pays LIBOR plus 2%. And LIBOR stands for London Interbank Offer Rate. It's one of the major benchmarks for variable interest rates. And so it pays that to some lender. This is the person who lent company A the money. It pays them a variable interest rate every period. So for example, in period one if LIBOR is at 5%, then in that period, company A will pay 7%, or \$70,000 to the lender in that period. In period two, if LIBOR goes, let's say LIBOR goes down a little bit to 4%, then company A is going to pay 4 plus 2, which is 6%, which is \$60,000 in interest. Let's say that we have another company, company B, right over here. It also borrows \$1 million, but it borrows it at a fixed rate. Let's say it borrows it at a fixed rate of 8%. So in each period, regardless of what happens to LIBOR or any other benchmark-- so this is to probably another lender, or different lender, than the person that A borrowed it from. And it could be a bank, or it might be another company, or an investor of some kind. We will call this Lender 1 and Lender 2. So regardless of the period, right now company B will pay 8% of \$1 million in each period, which is about \$80,000, or exactly \$80,000, each period. Now let's say that neither of these parties are really happy with that situation. Company A doesn't like the variability, the unpredictability in what happens to LIBOR, so they can't plan for how much they have to pay. Company B feels like they're overpaying for interest. They feel like, wow, the people who are doing variable interest rates, they're paying a less amount of interest every period. And maybe they also, company B also, thinks that interest rates are going to go down, or that short term, or that variable rate is going to go down, LIBOR is going to go down. So that's an even bigger reason why they want to become a variable rate borrower. So what they can do, and neither of them can get out of these lending agreements, but what they can do is agree to essentially swap some or all of their interest rate payments. So for example, they can enter into an agreement, and this would be called an interest rate swap, where company A agrees to pay B-- maybe, let's make up a number here-- 7% on a notional \$1 million loan. So, the \$1 million will never change hands, but company A agrees to pay B 7% of that notional \$1 million, or \$70,000 per period. And in return, company B agrees to pay A a variable rate. Let's say it's LIBOR plus 1%, right over here. And this little agreement-- and they agreed they would agree to do this for some amount. And once again, this is LIBOR plus 1% on a notional \$1 million. And that word notional just means that \$1 million will never change hands, and they're just going to exchange the interest payments on \$1 million. And this agreement right over here is called an interest rate swap. And I'll leave you there. In the next video, we'll actually go through the mechanics to see that A is truly now paying a fixed rate when you put in all of their different payments into both the swap and the lender, and Company B, after entering into this swap agreement, is now really paying a variable interest rate.

## Types

The most basic subclassification of interest rate derivatives (IRDs) is to define linear and non-linear.

Linear IRDs are those whose net present values (PVs) are overwhelmingly (although not necessarily entirely) dictated by and undergo changes approximately proportional to the one-to-one movement of the underlying interest rate index. Examples of linear IRDs are; interest rate swaps (IRSs), forward rate agreements (FRAs), zero coupon swaps (ZCSs), cross-currency basis swaps (XCSs) and single currency basis swaps (SBSs).

Non-linear IRDs form the set of remaining products. Those whose PVs are commonly dictated by more than the one-to-one movement of the underlying interest rate index. Examples of non-linear IRDs are; swaptions, interest rate caps and floors and constant maturity swaps (CMSs). These products' PVs are reliant upon volatility so their pricing is often more complex as is the nature of their risk management.

Further classification of the above is then made to define vanilla (or standard) IRDs and exotic IRDs. The categorisation of linear and non-linear and vanilla and exotic is not universally acknowledged and a number of products might exist that can be arguably assigned to different categories. These terms may also overlap.

Vanilla, in vanilla IRSs and vanilla swaptions, is often taken to mean the basic, most liquid and commonly traded variants of those products.

Exotic is usually used to define a feature that is an extension to a IRD type. For example an in-arrears IRS is a genuine example of an exotic IRS, whereas an IRS whose structure was the same as vanilla but whose start and end dates might be unconventional, would not generally be classed as exotic. Typically this would be referred to as a bespoke IRS (or customised IRS). Bermudan swaptions are examples of swaption extensions that qualify as exotic variants. Other products that are generally classed as exotics are;power reverse dual currency note (PRDC or Turbo), target redemption note (TARN), CMS steepener [1], Snowball (finance),[1][2] Inverse floater, Strips of Collateralized mortgage obligation, Ratchet caps and floors, and Cross currency swaptions.

## Trivia

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[3] 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.