Interest rate swap

An interest rate swap is an interest rate derivative in which two contracting parties agree to exchange interest payments for fixed nominal amounts at certain future points in time . The interest payments are usually set in such a way that one party pays a fixed interest rate that is fixed when the contract is signed , while the other party pays a variable interest rate . The variable interest rate is usually based on a reference interest rate in interbank business. Interest rate swaps are used both to hedge against the risk of changes in interest rates and as a speculative investment.

Options on interest rate swaps are called swaptions .

structure

Interest rate swaps are over-the-counter transactions : they are not standardized like futures , for example , but are negotiated individually between the contracting parties. Nevertheless, the definitions of the International Swaps and Derivatives Association are used as a standard contract in the swap market . These are generally stipulated in a framework agreement between the contractual partners in such a way that reference only needs to be made to the framework agreement in the specific exchange agreement .

In the case of an interest rate swap, the two contracting parties undertake to pay either a fixed or variable interest rate on a certain nominal value to the other contracting party. It is possible that the face values ​​of the two parties do not match or are in different currencies.

In order to keep administrative costs low and to minimize the loss that could arise if the counterparty defaults, the entire interest payments are not exchanged, but only the difference between the two interest payments. This netting is also known as netting .

In the most common form of interest rate swap, a variable interest rate is exchanged for a fixed interest rate. While the variable interest rate is based on a reference interest rate such as the three-month Euribor and changes over the term of the swap, the fixed interest rate remains fixed over the term. The fixed interest rate is chosen so that the market value of the swap is zero when the contract is concluded.

If the variable interest rate changes, the variable interest amount to be paid is not adjusted daily, but only on certain dates. On these fixing dates, the variable interest rate is adjusted to the underlying reference interest rate. For the period up to the next fixing, the variable-paying contractual partner pays the interest calculated from this interest rate.

How a swap works: Exchange of fixed and variable payment flows

The roles of the two contracting parties in an interest rate swap are usually named based on their position with regard to the fixed-income side of the swap:

• Payer (English payer ), the contractor who will pay the fixed rate.
• Receiver (English receiver ) is the other party, which receives the fixed rate.

In addition, the exchange transaction itself (English from the perspective of the payer payer swap is payer swaps ), as seen by the receiver as a receiver swap (English receiver swap designated).

example

Company A has received a variable-interest loan of EUR 1 million from a bank: The interest to be paid on the loan is regularly adjusted to the interest of the capital market.

In order to hedge against the risk of rising interest rates, this company A enters into an interest rate swap, also for 1 million euros, with company B : A undertakes to pay a fixed interest rate to B during the term. Company A and in return receives a variable interest payment from B to service its own variable interest at the bank .

Ideally, the variable interest rate is linked to the same reference interest rate as the bank loan. Then A can use the variable interest payment received to service his variable loan interest to the bank exactly.

If the interest rate rises in the market, the interest rate on the loan rises and so does the amount of interest that company A receives from the swap. If interest rates go down, both the loan interest rate and the amount of interest A gets from the swap go down. Regardless of the development of the market interest rate, company A always pays the fixed interest amount to B , the counterparty of the swap.

Company A has thus protected itself against rising interest rates - but at the same time it has taken the opportunity to benefit from falling interest rates. Even with a purely sideways trend in interest rates, company A would generally have been in a worse position by entering into the interest rate swap - insofar as costs are incurred or priced in for the swap transaction.

species

Monetary swaps

Monetary swaps are swaps in which both sides refer to the same currency.

Plain vanilla

The standard form of a swap is often called plain vanilla (both plain as vanilla english for usual ), respectively. What is meant is the exchange of fixed and variable interest payment flows described above.

Variable-variable exchange

Both sides of the swap are assigned floating rates. This can be, for example, an exchange of the 3-month interest rate for the 6-month interest rate. When concluding such a swap, one speculates on the slope of the yield curve. In addition, there are constant maturity swaps in which a variable interest rate is exchanged for a regularly adjusted longer-term interest rate (e.g. 10-year interest rate).

EONIA swap

Another common design variant is the EONIA swap. The overnight rate is exchanged for a variable or fixed interest rate. A payment of the accrued interest does not take place daily on the overnight side, but mostly once a year in the form of an averaged interest rate. The calculation of the average interest rate simulates the daily investment at the current interest rate. The daily allowance rate can apply for one day or for 3 days on weekends, and even longer on public holidays. If (i = 1, ..., n) are the overnight rates observed and the number of days for which these rates apply, then the averaged interest rate r is calculated from the property that an investment at this interest rate yields the same interest income as the Annex to the daily allowance rates: ${\displaystyle r_{i}}$ ${\displaystyle d_{i}}$

${\displaystyle \prod _{i=1}^{n}\left(1+r_{i}\cdot {\frac {d_{i}}{360}}\right)=1+r{\frac {\sum _{i=1}^{n}d_{i}}{360}}}$

Non-currency swaps

In the case of non-currency swaps, the swap is influenced by more than one currency.

Currency swap

In a currency swap ( cross currency swap ), the two sides of the swap are quoted in different currencies. For example, interest payments in euros can be exchanged for interest payments in US dollars . In the case of a currency swap, it is common for the denominations to be exchanged at the beginning and end of the term.

Quanto swap

In a Quanto -Swap shall only be paid in one currency, while the interest rates are determined by indices of different currencies.

rating

To evaluate an interest rate swap, the present value is determined separately for each of the two sides of the contract and offset against the present value of the interest rate swap.

When determining the value of a standard interest rate swap (“plain vanilla”), the present value of the fixed and variable side can be calculated using the present value method. For the payer and the recipient of the swap, the present values ​​are the same, only with different signs (abbreviation BW in the formulas):

For the payer is

${\displaystyle BW_{\text{Swap}}\,=\,BW_{\text{variabel}}-BW_{\text{fix}}}$,

for the recipient is

${\displaystyle BW_{\text{Swap}}\,=\,BW_{\text{fix}}-BW_{\text{variabel}}}$.

Evaluation of the fixed and the variable side

The following values ​​are used to calculate the present values ​​for the fixed and variable sides:

• Parent:
  • ${\displaystyle P}$: The nominal of the interest rate swap
• For the fixed side:
  • ${\displaystyle m}$: The number of payments (corresponds to the number of interest periods)
  • ${\displaystyle C}$: The fixed interest rate (also known as the swap rate)
  • ${\displaystyle t_{i}}$: The number of days in the i -th interest period
  • ${\displaystyle T_{i}}$: The basis (number of days per year) related to the interest calculation method
  • ${\displaystyle df_{i}}$The discount factor for the i th payment
• For the variable side:
  • ${\displaystyle n}$: The number of payments (corresponds to the number of interest periods)
  • ${\displaystyle f_{i}}$: The forward interest rate as an estimate of the variable interest rate that will accrue in the i -th interest period
  • ${\displaystyle {\tilde {t}}_{i}}$: The number of days in the i -th interest period
  • ${\displaystyle {\tilde {T}}_{i}}$: The basis (number of days per year) related to the interest calculation method
  • ${\displaystyle {\widetilde {df}}_{i}}$The discount factor for the i th payment.

The value of the fixed side is the sum of the cash values ​​of the individual interest payments:

${\displaystyle {\begin{aligned}BW_{\text{fix}}&=\sum _{i=1}^{m}P\cdot C\cdot {\frac {t_{i}}{T_{i}}}\cdot df_{i}\\&=P\cdot C\cdot \sum _{i=1}^{m}{\frac {t_{i}}{T_{i}}}\cdot df_{i}\end{aligned}}}$

Similarly, the value of the variable side is the sum of the cash values ​​of the individual interest payments. It should be noted that generally only one interest rate is known on the variable side: the one that has already been fixed. The remaining interest rates will only be known in the future. Accordingly, the respective forward interest rates , which can be calculated from the interest rate curve observable on the market , are used to approximate future interest rates. With these interest rates , the variable interest payments result in a cash flow that is discounted using the present value method. The value of the variable side is therefore given by:

${\displaystyle {\begin{aligned}BW_{\text{variabel}}&=\sum _{i=1}^{n}P\cdot f_{i}\cdot {\frac {{\tilde {t}}_{i}}{{\tilde {T}}_{i}}}\cdot {\widetilde {df}}_{i}\\&=P\cdot \sum _{i=1}^{n}f_{i}\cdot {\frac {{\tilde {t}}_{i}}{{\tilde {T}}_{i}}}\cdot {\widetilde {df}}_{i}\end{aligned}}}$

This valuation technique can be used at any time during the term of a swap to determine its value. The market interest rates change over time and thus both the forward interest rates, which are used on the variable side to approximate the variable interest rates, and the discount factors. The present value of a swap changes accordingly.

The swap rate

It is customary that when a swap is entered into, there is no compensation payment from one of the two counterparties to the other. This means that the present value of the swap at the time of conclusion is zero and neither of the two contracting parties has the option of arbitrage .

If one considers the present value of the swap and thus the sum of the present values ​​of both sides, only the interest rate of the fixed side can be chosen by the two contractual partners; Both the discount factors, the variable interest rate fixed at the beginning and the forward interest rates are given by the market.

The fixed interest rate C must therefore be selected so that the present value of the fixed side is equal to the present value of the variable side:

${\displaystyle BW_{\text{fix}}=BW_{\text{variabel}}\,}$

With the above formulas it follows:

${\displaystyle C={\frac {\sum _{i=1}^{n}f_{i}\cdot {\frac {{\tilde {t}}_{i}}{{\tilde {T}}_{i}}}\cdot {\widetilde {df}}_{i}}{\sum _{i=1}^{m}{\frac {t_{i}}{T_{i}}}\cdot df_{i}}}}$

The interest rate curve, which is made up of the swap rates for the swaps with corresponding terms, is also called the swap curve. This is communicated by many banks and brokers online and via trading platforms.

Risks

Interest rate swaps contain both market price and credit risks:

• Credit risk : Since with interest rate swaps only the interest difference between the fixed and the variable interest rate has to be paid, the credit risk at the time of interest payment for the recipient of the difference is limited to this difference. The difference payer is not exposed to any interest rate risk. In addition, there is a replacement risk for the party whose swap has a positive present value: If the contractual partner defaults, this party cannot maintain the success of the swap. Or, in order to conclude a new swap with a solvent partner under the same conditions, it just has to pay the cash value as compensation to the new counterparty.

• Market price risk: A swap is exposed to market price risk: If the market interest rate changes, this changes the discount factor with which the cash value of the swap is calculated from the interest payment flows. The fixed side of the swap is essentially subject to the market risk. On the variable side of the swap, a change in interest rates affects both the discount factor and the associated forward rate. This neutralizes the interest rate change effect. On the other hand, only the discount factor changes due to the market interest rate on the fixed side: Rising interest rates lead to a lower present value on the fixed side, while falling interest rates increase the present value.

Applications

Interest rate swaps are used to hedge against changes in interest rates or to speculate with them. In addition, there may be a comparative interest rate advantage if the two swap partners can refinance at different variable and fixed rates on the market.

Parameters of a swap

The parameters to be determined between the counterparties include:

• Start and end of the swap: If the first period of a swap does not start immediately, it is called a forward swap
• Trading place (to determine the holidays)
• Nominal amount on which the interest is paid (possibly per side)
• Interest calculation method
• Interest period of the sides
• Interest rate or reference interest rate and spread per side

literature

• John C. Hull : Options, Futures, and Other Derivatives , 2005, Fifth Edition, Prentice Hall

Web links

• International Swaps and Derivatives Association ( Engl. )
• Definition, motives and evaluation based on examples