Notional amount of an interest rate swap. Swaps

Id=".D0.A1.D1.82.D1.80.D1.83.D0.BA.D1.82.D1.83.D1.80.D0.B0">Structure [ | ]

In an IRS transaction, each counterparty agrees to pay a fixed or floating rate, denominated in one currency or another, to the other counterparty. Fixed or floating rate multiplied by notional principal amount(say $1 million). Sharing this notional amount between counterparties, as a rule, is not carried out; it is used only to calculate the amount of interest cash flows to be exchanged.

Side A currently pays a variable rate but wants to pay a fixed rate. B currently pays a fixed rate, but wants to pay a variable rate.
Upon conclusion of the IRS transaction, the net result is that the parties may " exchange» your current interest obligations to your desired interest obligations.

The most generally accepted by the IRS is a transaction in which one counterparty (the counterparty A) pays a fixed rate (swap transaction rate) in favor of the counterparty B, receiving in return a floating rate (usually linked to a base rate, such as LIBOR or MOSPRIME).

  • A pays a fixed rate in favor B (A receives a floating rate)
  • B pays a floating rate to A (B receives a fixed rate).

Consider an IRS transaction in which a party A, having a loan (to a third party) at a floating rate of LIBOR+150 (=+1.50%), undertakes to pay in favor of the party B fixed periodic interest payments at a rate of 8.65% ( swap rate) in exchange for periodic interest payments at the rate of LIBOR+70 basis points (“ bp", =+0.70%). That is A has a “sum” from which it receives a fixed income for swap rate, but would like to have income at a floating rate, that is, the same as the loan obligations: LIBOR+. She turns to IN for the purpose of concluding an interest rate swap - a transaction in which A will receive income from the “amount” at the LIBOR+ rate instead of a fixed rate ( swap rate), A IN will receive income from its amount at a fixed rate instead of the floating LIBOR+. Benefit for A is that the swap eliminates the discrepancy between the income from the "amount" and the expense of the loan - they are now both tied to the LIBOR rate.

It is worth paying attention to the fact that:

  1. there is no exchange of principal between the parties and that
  2. interest rates apply to the “notional” (i.e., imaginary) principal amount.
  3. interest payments are not paid in full, but are offset between the parties, after which the balance of the offset is paid.
(L I B O R + 1, 50%) + 8, 65% − (L I B O R + 0, 70%) = 9, 45% (\displaystyle (LIBOR+1.50\%)+8.65\%-(LIBOR+0 .70\%)=9.45\%),net.

The fixed rate (8.65% in this example) is called swap rate.

Drawing: A receives a fixed income of 8.65% and pays LIBOR+1.50%. A wants to convert both flows to LIBOR+. A enters into a swap with IN- “redirects him an income of 8.65%” (in reality, not all of it, but only the “netting” balance - the difference between 8.65% and LIBOR + 0.70%) and “receives income LIBOR + 0.70%.” Since the return on the asset is not explicitly shown in the figure, it can be misleading.

At the time of the transaction, the pricing of the swap is such that the swap has a zero current net value ( N P V = 0 (\displaystyle NPV=0)). If one party is willing to pay 50 bps over the swap rate, the other party must pay about 50 bps over LIBOR to compensate.

Types [ | ]

As an over-the-counter instrument, IRS transactions can be entered into on a variety of terms to meet the specific needs of the parties to the transaction.

The most common exchange transactions are:

The parties to the transaction may be in the same currency or in two different currencies. (Transactions f i x e d − f o r − f i x e d (\displaystyle fixed-for-fixed) in one currency are generally not possible since the entire flow can be predicted from the outset of the transaction and there is no point for the parties to enter into an IRS contract since they can settle immediately for known future interest payments).

Fixed-For-Floating, one currency[ | ]

Side IN

  • A And
  • A, indexed by the curve X for a notional amount N for a period of T years.

(in reality, a transfer is made from A to B (or vice versa - depending on whose payment is greater) by the amount of the balance (netting) - the difference in “payments”)

For example, you pay a fixed rate of 5.32% monthly in exchange for Libor USD 1M also monthly for notional amount$1 million over 3 years.

The party that pays a fixed rate in exchange for a variable rate has a long IRS position. Interest rate swaps are essentially a simple exchange of one set of interest payments for another.

Single currency swaps are used for exchange

  • assets/liabilities with a fixed rate on
  • floating rate assets/liabilities and vice versa.

For example, if a company has

  1. investment in the amount of 10 million USD with a yield of 1M USD Libor + 25 bp with monthly fixing and payments

she can contract with the IRS

According to it it will be:

  1. pay a floating rate USD 1M Libor+25 bp
  2. receive a fixed rate of 5.5%,
    thereby recording an income of 20 bp.

Fixed-For-Floating, 2 currencies[ | ]

Side P

  • pays (receives) a fixed rate in foreign currency A And
  • receives (pays) a floating rate in foreign currency B, indexed by the curve X for a notional amount N for a period of T years.

For example, you pay a flat rate of 5.32% quarterly on a notional amount 10 MM USD (\displaystyle (\text(10 MM USD))) in exchange for TIBOR USD 3M (\displaystyle (\text(TIBOR USD 3M))) also quarterly on notional amount 1.2 billion yen over 3 years.

Under a non-deliverable swap, the dollar equivalent of interest payments on the yen will be paid/received in accordance with the USD/JPY rate in effect on the fixing date for the value date of the interest payment. There is no exchange of principal amounts. Payments arise only when:

  • the arrival of the fixing date and
  • the beginning date of the swap (if the start date of the swap begins in the distant future relative to the date of the transaction).

Swaps F i x e d − f o r − f l o a t i n g (\displaystyle Fixed-for-floating) 2 currencies are used for exchange

  • assets/liabilities with a fixed rate in one currency for
  • floating rate assets/liabilities in another currency and vice versa.

For example, if a company

  1. It has
    • loan with a fixed rate of 5.3% for 10 million USD with monthly interest payments and
    • investment in the amount of 1.2 billion JPY with a yield of 1M JPY Libor + 50 bp with monthly fixing and payments and
  2. wants to fix income in US dollars, expecting that
    • JPY 1M Libor rate will fall or
    • USDJPY will rise (the value of the yen will fall against the dollar)

she can sign a contract f i x e d − f o r − f l o a t i n g (\displaystyle fixed-for-floating) IRS in two currencies, according to which it will be:

  1. pay floating rate JPY 1M Libor+50 bp
  2. receive a fixed rate of USD 5.6%,
    thereby recording an income of 30 bp on the interest rate and currency position.

Floating-For-Floating, one currency[ | ]

Side P

  • A, indexed by the curve X
  • receives (pays) a floating rate in foreign currency A, indexed by the curve Y for a notional amount N for a period of T years.

JPY LIBOR 1M (\displaystyle (\text(JPY LIBOR 1M))) monthly in exchange for JPY TIBOR 1M (\displaystyle (\text(JPY TIBOR 1M))) also monthly on notional amount 1 billion yen over 3 years.

swaps are used to hedge or speculate against a widening or narrowing spread between two indices.

For example, if a company

If the company

she can enter into an IRS contract in one currency in which she will, for example:

  1. pay floating rate JPY TIBOR + 30 bps
  2. receive a floating rate JPY LIBOR + 35 bps,
    thereby locking in a 35bp return on the interest rate instead of the current 40bp spread and index risk. The nature of the 5 bp difference lies in the cost of the swap, which consists of
    1. market expectations of changes in the spread between indices and
    2. bid/offer spread, which is the swap dealer's commission

F l o a t i n g − f o r − f l o a t i n g (\displaystyle Floating-for-floating) swaps are also used when using the same index, but

  • with different interest payment dates or
  • using different conventions for defining business days.

These swaps are practically not used by speculators, but are important for managing assets and liabilities. An example is the 3M LIBOR swap,

  • paid prior non-business day convention, quarterly according to the JAJO rule (i.e. January, April, July, October) on the 30th, against
  • FMAN (i.e. February, May, August, November) 28 modified following.

Floating-For-Floating, 2 currencies[ | ]

Side P

  • pays (receives) a floating rate in foreign currency A, indexed by the curve X
  • receives (pays) a floating rate in foreign currency B, indexed by the curve Y for a notional amount N at the original FX rate for the term T years.

For example, you pay a variable rate USD LIBOR 1M (\displaystyle (\text(USD LIBOR 1M))) quarterly in the amount of USD 10 million in exchange for JPY TIBOR 3M (\displaystyle (\text(JPY TIBOR 3M))) also monthly on notional amount 1.2 billion yen (at initial FX rate USD/JPY 120) over 4 years.

To understand this type of swap, consider an American company with operations in Japan. To finance its development in Japan, the company requires 10 billion yen. The simplest solution for a company would be to issue bonds in Japan. Since the company may be new to the Japanese market and may not have the required reputation among Japanese investors, issuing bonds may be an expensive option. In addition to all that has been said, the company may not have

  • an adequate insurance program for bond issues in Japan and
  • carry out developed treasury functions in Japan

To solve these problems, a company can issue bonds in the United States and convert dollars into yen. Although these actions solve the first problems, they create new risks for the company:

  • FX risk. If the USDJPY rate rises by the maturity date of the bonds, then when the company converts yen into dollars to pay off the debt on the bonds, it will receive fewer dollars and, accordingly, will incur exchange rate losses
  • Interest risk on USD and JPY. If yen rates fall, the profitability of a company's investments in Japan may fall - this gives rise to interest rate risk.

Currency risk can be eliminated by hedging using forward FX contracts, but this creates a new risk - the interest rate applied to determine the forward FX rate is fixed, while the return on investment in Japan has a floating structure.

Although there are several other options for hedging currency and interest rate risks, the simplest and most effective way is to enter into f l o a t i n g − f o r − f l o a t i n g (\displaystyle floating-for-floating) swap in two currencies. In this case, the company receives funds by issuing dollar bonds and swaps them in US dollars.

As a result, she

  • receives a floating rate in USD corresponding to its expenses for servicing the bonds issued to it and
  • pays a floating rate on JPY corresponding to its income on investments in yen.

Fixed-For-Fixed, 2 currencies[ | ]

Side P

  • pays (receives) a fixed rate in foreign currency A,
  • receives (pays) a fixed rate in foreign currency B for a period of T years.

For example, you pay JPY 1.6% on notional amount 1.2 billion yen in exchange for USD 5.36% per equivalent notional amount 10 million dollars at the initial FX rate of 120 USDJPY.

Other variations [ | ]

Other options are possible, although they are less common. They are mainly intended for perfect hedging the bond, ensuring full compliance of interest payments - on the bond and the swap. These options can give rise to swaps in which the principal is paid in one or more payments, as opposed to conventional swaps in which interest flows are simply exchanged - for example, to hedge coupon strip transactions.

Application [ | ]

Interest rate swaps are used in a wide variety of investment strategies. They are a popular tool for hedging and financial speculation.

Hedging [ | ]

Fixing the interest rate under a swap agreement allows you to hedge against falling interest rates.

On the other hand, the counterparty receiving the floating leg will benefit when interest rates fall.

Speculation [ | ]

Due to the low threshold for entering into an interest rate swap position, they are popular with traders speculating on interest rate movements.

So, instead of opening a full-fledged short position on an underlying asset for which the price is expected to fall, a trader only needs to enter into a swap agreement that fixes the interest rate for the same period.

Pricing[ | ]

more information en:wiki Rational pricing

The value of a fixed leg is defined as the present value of the fixed interest payments known at the time the transaction is entered into or at any point in its existence.

P V fixed = C × ∑ i = 1 M (P × t i T i × d f i) (\displaystyle PV_(\text(fixed))=C\times \sum _(i=1)^(M)(P\times (\frac (t_(i))(T_(i)))\times df_(i))) Where C (\displaystyle C)- swap rate M (\displaystyle M)- number of periods of fixed interest payments, P (\displaystyle P) t i (\displaystyle t_(i)) i (\displaystyle i), T i (\displaystyle T_(i)) d f i (\displaystyle df_(i))- discount factor.

At the beginning of the swap, only the future interest payments on the fixed leg are known. Future LIBOR rates are unknown, so the floating leg is calculated in one of two ways:

  • based on the current value of floating interest payments determined at the time of the transaction (like a zero-coupon bond);

In the first method, each flow is discounted using a zero-coupon rate. The rate curve data available in the market is also used. Zero-coupon bets are used because they generate only one cash flow - just like in our calculation case. Thus, an interest rate swap is treated as a series of zero-coupon bonds.

In the second method, each floating interest payment is calculated based on forward interest rates for the corresponding payment dates. Using these rates results in a series of interest payments.

As a result, the cost of the floating leg of the swap for the FRA method is calculated as follows:

P V float = ∑ j = 1 N (P × f j × t j T j × d f j) (\displaystyle PV_(\text(float))=\sum _(j=1)^(N)(P\times f_(j )\times (\frac (t_(j))(T_(j)))\times df_(j))) Where N (\displaystyle N)- number of interest floating payments, f j (\displaystyle f_(j))- forward interest rate, P (\displaystyle P)- nominal amount of the transaction, t j (\displaystyle t_(j))- number of days in the interest period j (\displaystyle j), T j (\displaystyle T_(j))- financial base of the currency in accordance with the convention and d f j (\displaystyle df_(j))- discount factor. The discount factor always starts at 1.

The factor is calculated as follows.

Structure

In an IRS transaction, each counterparty agrees to pay a fixed or floating rate, denominated in one currency or another, to the other counterparty. Fixed or floating rate multiplied by notional principal amount(say $1 million). Sharing this notional amount between counterparties, as a rule, is not carried out; it is used only to calculate the amount of interest cash flows to be exchanged.

  • A pays a fixed rate in favor B (A receives a floating rate)
  • B pays a floating rate to A (B receives a fixed rate).

Consider an IRS transaction in which a party A, having a loan (to a third party) at a floating rate of LIBOR+150 (=+1.50%), undertakes to pay in favor of the party B fixed periodic interest payments at a rate of 8.65% ( swap rate) in exchange for periodic interest payments at the rate of LIBOR+70 basis points (“ bp", =+0.70%). That is A has a “sum” from which it receives a fixed income for swap rate, but would like to have income at a floating rate, that is, the same as the loan obligations: LIBOR+. She turns to IN for the purpose of concluding an interest rate swap - a transaction in which A will receive income from the “amount” at the LIBOR+ rate instead of a fixed rate ( swap rate), A IN will receive income from its amount at a fixed rate instead of the floating LIBOR+. Benefit for A is that the swap eliminates the discrepancy between the income from the "amount" and the expense of the loan - they are now both tied to the LIBOR rate.

It is worth paying attention to the fact that:

  1. there is no exchange of principal between the parties and that
  2. interest rates apply to the “notional” (i.e., imaginary) principal amount.
  3. interest payments are not paid in full, but are offset between the parties, after which the balance of the offset is paid.
(L I B O R + 1, 50%) + 8, 65% − (L I B O R + 0, 70%) = 9, 45% (\displaystyle (LIBOR+1.50\%)+8.65\%-(LIBOR+0 .70\%)=9.45\%),net.

The fixed rate (8.65% in this example) is called swap rate.

Drawing: A receives a fixed income of 8.65% and pays LIBOR+1.50%. A wants to convert both flows to LIBOR+. A enters into a swap with IN- “redirects him an income of 8.65%” (in reality, not all of it, but only the “netting” balance - the difference between 8.65% and LIBOR + 0.70%) and “receives income LIBOR + 0.70%.” Since the return on the asset is not explicitly shown in the figure, it can be misleading.

At the time of the transaction, the pricing of the swap is such that the swap has a zero current net value ( N P V = 0 (\displaystyle NPV=0)). If one party is willing to pay 50 bps over the swap rate, the other party must pay about 50 bps over LIBOR to compensate.

Types

As an over-the-counter instrument, IRS transactions can be entered into on a variety of terms to meet the specific needs of the parties to the transaction.

The most common exchange transactions are:

The parties to the transaction may be in the same currency or in two different currencies. (Transactions f i x e d − f o r − f i x e d (\displaystyle fixed-for-fixed) in one currency are generally not possible since the entire flow can be predicted from the outset of the transaction and there is no point for the parties to enter into an IRS contract since they can settle immediately for known future interest payments).

Fixed-For-Floating, one currency

Side IN

  • A And
  • A, indexed by the curve X for a notional amount N for a period of T years.

(in reality, a transfer is made from A to B (or vice versa - depending on whose payment is greater) by the amount of the balance (netting) - the difference in “payments”)

For example, you pay a fixed rate of 5.32% monthly in exchange for Libor USD 1M also monthly for notional amount$1 million over 3 years.

The party that pays a fixed rate in exchange for a variable rate has a long IRS position. Interest rate swaps are essentially a simple exchange of one set of interest payments for another.

Single currency swaps are used for exchange

  • assets/liabilities with a fixed rate on
  • floating rate assets/liabilities and vice versa.

For example, if a company has

  1. investment in the amount of 10 million USD with a yield of 1M USD Libor + 25 bp with monthly fixing and payments

she can contract with the IRS

According to it it will be:

  1. pay a floating rate USD 1M Libor+25 bp
  2. receive a fixed rate of 5.5%,
    thereby recording an income of 20 bp.

Fixed-For-Floating, 2 currencies

Side P

  • pays (receives) a fixed rate in foreign currency A And
  • receives (pays) a floating rate in foreign currency B, indexed by the curve X for a notional amount N for a period of T years.

For example, you pay a flat rate of 5.32% quarterly on a notional amount 10 MM USD (\displaystyle (\text(10 MM USD))) in exchange for TIBOR USD 3M (\displaystyle (\text(TIBOR USD 3M))) also quarterly on notional amount 1.2 billion yen over 3 years.

Under a non-deliverable swap, the dollar equivalent of interest payments on the yen will be paid/received in accordance with the USD/JPY rate in effect on the fixing date for the value date of the interest payment. There is no exchange of principal amounts. Payments arise only when:

  • the arrival of the fixing date and
  • the beginning date of the swap (if the start date of the swap begins in the distant future relative to the date of the transaction).

Swaps F i x e d − f o r − f l o a t i n g (\displaystyle Fixed-for-floating) 2 currencies are used for exchange

  • assets/liabilities with a fixed rate in one currency for
  • floating rate assets/liabilities in another currency and vice versa.

For example, if a company

  1. It has
    • loan with a fixed rate of 5.3% for 10 million USD with monthly interest payments and
    • investment in the amount of 1.2 billion JPY with a yield of 1M JPY Libor + 50 bp with monthly fixing and payments and
  2. wants to fix income in US dollars, expecting that
    • JPY 1M Libor rate will fall or
    • USDJPY will rise (the value of the yen will fall against the dollar)

she can sign a contract f i x e d − f o r − f l o a t i n g (\displaystyle fixed-for-floating) IRS in two currencies, according to which it will be:

  1. pay floating rate JPY 1M Libor+50 bp
  2. receive a fixed rate of USD 5.6%,
    thereby recording an income of 30 bp on the interest rate and currency position.

Floating-For-Floating, one currency

Side P

  • A, indexed by the curve X
  • receives (pays) a floating rate in foreign currency A, indexed by the curve Y for a notional amount N for a period of T years.

JPY LIBOR 1M (\displaystyle (\text(JPY LIBOR 1M))) monthly in exchange for JPY TIBOR 1M (\displaystyle (\text(JPY TIBOR 1M))) also monthly on notional amount 1 billion yen over 3 years.

swaps are used to hedge or speculate against a widening or narrowing spread between two indices.

For example, if a company

If the company

she can enter into an IRS contract in one currency in which she will, for example:

  1. pay floating rate JPY TIBOR + 30 bps
  2. receive a floating rate JPY LIBOR + 35 bps,
    thereby locking in a 35bp return on the interest rate instead of the current 40bp spread and index risk. The nature of the 5 bp difference lies in the cost of the swap, which consists of
    1. market expectations of changes in the spread between indices and
    2. bid/offer spread, which is the swap dealer's commission

F l o a t i n g − f o r − f l o a t i n g (\displaystyle Floating-for-floating) swaps are also used when using the same index, but

  • with different interest payment dates or
  • using different conventions for defining business days.

These swaps are practically not used by speculators, but are important for managing assets and liabilities. An example is the 3M LIBOR swap,

  • paid prior non-business day convention, quarterly according to the JAJO rule (i.e. January, April, July, October) on the 30th, against
  • FMAN (i.e. February, May, August, November) 28 modified following.

Floating-For-Floating, 2 currencies

Side P

  • pays (receives) a floating rate in foreign currency A, indexed by the curve X
  • receives (pays) a floating rate in foreign currency B, indexed by the curve Y for a notional amount N at the original FX rate for the term T years.

For example, you pay a variable rate USD LIBOR 1M (\displaystyle (\text(USD LIBOR 1M))) quarterly in the amount of USD 10 million in exchange for JPY TIBOR 3M (\displaystyle (\text(JPY TIBOR 3M))) also monthly on notional amount 1.2 billion yen (at initial FX rate USD/JPY 120) over 4 years.

To understand this type of swap, consider an American company with operations in Japan. To finance its development in Japan, the company requires 10 billion yen. The simplest solution for a company would be to issue bonds in Japan. Since the company may be new to the Japanese market and may not have the required reputation among Japanese investors, issuing bonds may be an expensive option. In addition to all that has been said, the company may not have

  • an adequate insurance program for bond issues in Japan and
  • carry out developed treasury functions in Japan

To solve these problems, a company can issue bonds in the United States and convert dollars into yen. Although these actions solve the first problems, they create new risks for the company:

  • FX risk. If the USDJPY rate rises by the maturity date of the bonds, then when the company converts yen into dollars to pay off the debt on the bonds, it will receive fewer dollars and, accordingly, will incur exchange rate losses
  • Interest risk on USD and JPY. If yen rates fall, the profitability of a company's investments in Japan may fall - this gives rise to interest rate risk.

Currency risk can be eliminated by hedging using forward FX contracts, but this creates a new risk - the interest rate applied to determine the forward FX rate is fixed, while the return on investment in Japan has a floating structure.

Although there are several other options for hedging currency and interest rate risks, the simplest and most effective way is to enter into f l o a t i n g − f o r − f l o a t i n g (\displaystyle floating-for-floating) swap in two currencies. In this case, the company receives funds by issuing dollar bonds and swaps them in US dollars.

As a result, she

  • receives a floating rate in USD corresponding to its expenses for servicing the bonds issued to it and
  • pays a floating rate on JPY corresponding to its income on investments in yen.

Fixed-For-Fixed, 2 currencies

Side P

  • pays (receives) a fixed rate in foreign currency A,
  • receives (pays) a fixed rate in foreign currency B for a period of T years.

For example, you pay JPY 1.6% on notional amount 1.2 billion yen in exchange for USD 5.36% per equivalent notional amount 10 million dollars at the initial FX rate of 120 USDJPY.

Other variations

Other options are possible, although they are less common. They are mainly intended for perfect hedging the bond, ensuring full compliance of interest payments - on the bond and the swap. These options can give rise to swaps in which the principal is paid in one or more payments, as opposed to conventional swaps in which interest flows are simply exchanged - for example, to hedge coupon strip transactions.

Application

Interest rate swaps are used in a wide variety of investment strategies. They are a popular tool for hedging and financial speculation.

Hedging

Fixing the interest rate under a swap agreement allows you to hedge against falling interest rates.

On the other hand, the counterparty receiving the floating leg will benefit when interest rates fall.

Speculation

Due to the low threshold for entering into an interest rate swap position, they are popular with traders speculating on interest rate movements.

So, instead of opening a full-fledged short position on an underlying asset for which the price is expected to fall, a trader only needs to enter into a swap agreement that fixes the interest rate for the same period.

Pricing

More information en:wiki Rational pricing

The value of a fixed leg is defined as the present value of the fixed interest payments known at the time the transaction is entered into or at any point in its existence.

P V fixed = C × ∑ i = 1 M (P × t i T i × d f i) (\displaystyle PV_(\text(fixed))=C\times \sum _(i=1)^(M)(P\times (\frac (t_(i))(T_(i)))\times df_(i))) Where C (\displaystyle C)- swap rate M (\displaystyle M)- number of periods of fixed interest payments, P (\displaystyle P) t i (\displaystyle t_(i)) i (\displaystyle i), T i (\displaystyle T_(i)) d f i (\displaystyle df_(i))- discount factor.

At the beginning of the swap, only the future interest payments on the fixed leg are known. Future LIBOR rates are unknown, so the floating leg is calculated in one of two ways:

  • based on the current value of floating interest payments determined at the time of the transaction (like a zero-coupon bond);

In the first method, each flow is discounted using a zero-coupon rate. The rate curve data available in the market is also used. Zero-coupon bets are used because they generate only one cash flow - just like in our calculation case. Thus, an interest rate swap is treated as a series of zero-coupon bonds.

In the second method, each floating interest payment is calculated based on forward interest rates for the corresponding payment dates. Using these rates results in a series of interest payments.

As a result, the cost of the floating leg of the swap for the FRA method is calculated as follows:

P V float = ∑ j = 1 N (P × f j × t j T j × d f j) (\displaystyle PV_(\text(float))=\sum _(j=1)^(N)(P\times f_(j )\times (\frac (t_(j))(T_(j)))\times df_(j))) Where N (\displaystyle N)- number of interest floating payments, f j (\displaystyle f_(j))- forward interest rate, P (\displaystyle P)- nominal amount of the transaction, t j (\displaystyle t_(j))- number of days in the interest period j (\displaystyle j), T j (\displaystyle T_(j))- financial base of the currency in accordance with the convention and d f j (\displaystyle df_(j))- discount factor. The discount factor always starts at 1.

The factor is calculated as follows:

d f C u r r e n t P e r i o d = d f P r e v i o u s P e r i o d 1 + F o r w a r d R a t e P r e v i o u s P e r i o d × Y e a r F r a c t i o n (\displaystyle (df_(CurrentPeriod))=(\frac (df_(PreviousPeriod))(1+ForwardRate_( PreviousPeriod)\times YearFraction))).

Fixed rate quoted on a swap transaction - a rate that gives the present value of fixed cash flows equal to the present value of floating interest flows, calculated at forward interest rates in effect on the calculation date:

C = P V float ∑ i = 1 M (P × t i T i × d f i) (\displaystyle C=(\frac (PV_(\text(float)))(\sum _(i=1)^(M)( P\times (\frac (t_(i))(T_(i)))\times df_(i)))))

At the time of conclusion of the transaction, none of the parties to the contract has an advantage in the cost of the legs of the swap, that is:

P V fixed = P V float (\displaystyle PV_(\text(fixed))=PV_(\text(float)))

Thus, at the time of conclusion of the transaction, no payments occur between the parties.

Over the life of the trade, the same pricing technique is used to estimate the value of the swap, but as forward rates change over time, the present value ( P V) the floating leg of the swap will be different from the unchanged fixed leg.

Consequently, the swap will become an obligation of one party and a requirement of the other - depending on the direction of changes in interest rates.

  • John C. Hull. Options, Futures and Other Derivatives. - 6th ed. - M.: "Williams", 2007. - P. 1056. - ISBN 0-13-149908-4.
  • Interest rate swap - English Interest Rate Swap, a contract between two parties to exchange interest payments that are for a pre-agreed and specified amount in the contract, called the contract amount. That is, on a predetermined date (or dates if the swap involves the exchange of payments at specified intervals during the contract period), one party will pay the other a payment calculated on the basis of a fixed interest rate, and in return will receive a payment calculated on the basis of a floating interest rate (for example , at the LIBOR rate). In practice, such payments are netted and one of the parties pays only the difference of the above payments.

    The advantages of interest rate swaps include the fact that they make it possible to reduce the cost of attracting and servicing a loan. For example, a borrower who has the opportunity to obtain a loan at a fixed interest rate wants to take out a loan with interest accrued at a floating rate, but is not able to obtain such a loan on favorable terms. At the same time, there is another borrower who has the advantage of obtaining a loan on which interest is calculated on the basis of a floating rate, but he wants to receive a loan at a fixed interest rate. In this case, the parties can enter into an interest rate swap, which involves the exchange of payments that are calculated based on fixed and floating interest rates on the loan amount. As a rule, the parties do not exchange the principal amounts of the contract, but transfer only payments calculated on the basis of the difference in contract interest rates.

    Let's look at an interest rate swap as an example.

    The first counterparty to the swap (company) can take out a loan in the amount of 10 million USD with a repayment period of 3 years with a fixed rate of 12% or with a variable rate equal to LIBOR + 1%.

    The bank can obtain credit resources on the interbank market in the same amount and for the same period with a variable interest rate equal to LIBOR or a fixed rate of 10%.

    In this case, the difference between fixed interest rates is 1% greater than the difference between variable rates.

    To conclude a swap, the company takes out a loan with an interest rate equal to LIBOR + 1%, and the bank - with an interest rate of 10%.

    After concluding a swap, the bank periodically pays the company a floating interest - LIBOR, and the company periodically pays the bank a fixed interest - 10.5% (0.5% is a bonus to the bank, 10% is a fixed percentage of the bank for loans taken for the company). Thanks to the swap, the company reduces the financing costs of a loan with a fixed interest rate by 0.5%, and the bank also saves on the costs of financing debt with a variable interest rate of 0.5%.

    An interest rate swap is an agreement between parties to make a series of payments to each other on agreed dates before the expiration of the agreement. The amount of interest payments of each party is calculated based on different formulas, based on principal amount specified in the swap agreement.

    In interest rate swaps the principal amount rarely passes from counterparty to counterparty - it is used only as reference point to calculate the amount of payments. This means that the parties change the interest payment bases on the debt or investment without changing the principal amount of the loan or investment. Interest payment is made in the same currency.

    Example of a simple interest rate swap

    This example considers the exchange of interest payment for fixed rate for interest payment on floating rate.

    An enterprise with a BBB credit rating needs a loan (credit) of $50 million for 5 years with fixed interest rate. This rate allows you to plan the future cost of financing - allows the company to hedge interest rate risk.

    An international bank with a credit rating of AAA needs a loan (credit) of $50 million for 5 years with a floating interest rate. This rate allows the Bank to manage the profit margin in the event of a discrepancy between the levels of interest rates on assets and liabilities - it allows the Bank to hedge the interest rate risk.

    Table 1. Classification of foreign exchange market instruments.

    The enterprise and the Bank enter into a swap agreement, which allows them to reduce interest payments. In this case, there will be no exchange of the main amounts; $50 million will appear as conditional The principal amount on which interest will accrue.

    The enterprise and the Bank receive a loan on terms available to them, and then exchange interest payments. The company receives a loan with a floating rate of LIBOR +1%, and the Bank receives a loan with a fixed rate of 8.25%. Thus, the two entities enter into a 5-year fixed/floating rate swap.

    Rice. 1. Payment exchange scheme.

    In practice, only one payment is made when the due date arrives. Only the net difference between payments in the relevant currency is paid. For this reason, interest rate swaps are often called transactions for difference.

    As a result of the exchange of interest payments, the net payments of both parties are lower than in any other case. Interest rate swaps work as follows.

    • The company receives a loan at a floating rate of LIBOR + 1%
    • The bank receives a loan at a fixed rate of 8.25%
    • The Enterprise and the Bank enter into an interest rate swap with a notional principal amount of $50 million for a period of 5 years, under which:
      • The company will make payments at a fixed rate of 9.75% in favor of the Bank
      • The Bank will make payments at a floating rate of LIBOR + 1% in favor of the Enterprise

    The entity pays the Bank a higher fixed rate as compensation for its participation in the swap.

    Rice. 2. Scheme of exchange of payments and interest payments to Creditors.

    Table 2. Benefits received by the Enterprise and the Bank from a five-year swap.

    Conclusion from Table 2:

    • - without swap, the Enterprise and the Bank pay 10.00% + LIBOR
    • - with a swap, parties pay 9.25% + LIBOR

    By using the swap, there is a net saving of 0.75%, which is distributed as 0.25% to 0.50% to the bank because it is the institution with a higher credit rating.

    Features of interest rate swaps

    An interest rate swap is an exchange of interest payments, the amount of which is determined using different formulas based on notional principal amount agreements.

    The swap does not involve the exchange of principal amounts - the participants in the swap do not lend to each other.

    Counter interest payments are offset, and only the difference between them is paid.

    The swap has no effect on the underlying loan or deposit. A swap is an independent transaction.

    Success in financial terms implies education and knowledge in this area. In order not to lose your opportunity to earn money, you need to know exactly how to do this. In this article we will look at what swap transactions with foreign currency are and in what situations they can be used.

    What is a swap transaction?

    A swap transaction is a financial transaction based on the exchange of one currency for another. In this case, the exchange agreement is concluded in both directions. On a certain date, currency is purchased, and on another date it is reversed - sold. Moreover, this transaction usually implies pre-known conditions for the purchase and sale of currency; they can be either the same or different.

    However, it is not always very easy to understand what a swap transaction means. To understand this and better understand how it works, examples are needed. Several of them will be presented below.

    Let's look at a few examples where this concept can come in handy. This way you can better understand how it works and in what cases it can help you.

    Currency swap: example transaction

    There is an investor who has the opportunity to make a profitable transaction by purchasing bonds in the amount of $1 million. According to the terms of this deal, he will be able to make a profit of 5% in just one year, that is, 50 thousand dollars. However, the problem is that the bonds are sold for dollars, but the investor keeps his money in euros.

    In this case, he has several options for developing the situation.

    Let's consider the simplest and, perhaps, the first one that comes to mind - currency exchange. The bank offers the investor to buy currency from it at a rate of, for example, 1.350. Moreover, after a year, he will be able to sell this currency back to the bank at a different rate. At the time of sale, he could have sold the same currency at 1.345.

    Let's calculate the amount of investment in euros, dividing by the current exchange rate. We get 741 thousand euros for 1 million dollars. In this case, a year after receiving a profit from the transaction, namely 50 thousand dollars, it is necessary to convert the money back into euros.

    Through simple calculations, we find that if the rate rises above 1.417, then in the reverse transaction you will already receive small losses. This is bad, because initially everything was planned only to make a profit. In this case, it is very inappropriate to depend on the exchange rate.

    This means that it is necessary to look for other ways to solve this problem. To do this, you can use a swap deal.

    For such a transaction, the bank offers the following conditions:

    • The purchase of 1 million dollars is now at an exchange rate of 1.350, that is, for 741 thousand euros.
    • Selling 1 million dollars in a year at an exchange rate of 1.355, that is, for 738 thousand euros.

    At the same time, your 50 thousand dollars of profit from the transaction with the purchase of bonds remains in your hands. Converting them into euros will depend on the market rate, but you, as an investor, still remain in the black.

    If during this time the exchange rate has increased in favor of the investor, then the net profit will be more than 37 thousand euros. And at the same time, there are no risks and dependence on the course.

    Yes, of course, if the exchange rate changes to a more favorable one for you, it will mean that you could earn more. However, the risks you would have to take are not worth it.

    As we can see, a foreign currency swap transaction gives the investor confidence that his investment will be justified and will not cause losses when exchanging currencies. In this situation, both parties benefit, both the investor, who insures himself against the risks of losing money, and the bank, which receives a specific profit from the transaction.

    The bank knows that it will now give away 1 million dollars at one rate, and then buy them back at a rate already known in advance and make a profit of 3 thousand euros. And at the same time, he will remain with his money, will not lose anything and does not risk anything.

    There is also such a thing as an interest rate swap.

    This is an agreement between two parties, which is concluded with the condition of making payments from both one side and the other with a certain percentage.

    Interest is calculated depending on the terms of the transaction and is different for both parties. To make it more clear what this is, consider the example of an interest rate swap.

    For example, the World Bank needs a long-term loan in francs. At the same time, the interest rate for such lending from a Swiss bank is too high. But at the same time, the bank has the opportunity to attract, for example, a long-term loan in rubles from a Russian bank, which, for example, can borrow francs at a more favorable interest rate and needs to replenish ruble capital.

    To solve this problem, banks can begin to cooperate through an interest rate swap.

    In this case, banks take out the loans described above and exchange currencies, paying a certain percentage. After the expiration of the concluded agreement, banks make a reverse transaction.

    As a result, both parties are in the black, since they received the desired amounts at a lower interest rate and did not lose a lot of money.

    As you can see, swap transactions are very useful in many cases. Their application can be found in many fields and for different purposes. It is very important to understand all the subtleties and nuances of transactions so as not to miss anything important.

    Let's sum it up

    A swap transaction is a process of exchange between two parties of different, or rather opposite, currency conversion operations.

    In this case, one party receives confidence in receiving a fixed profit, and the other receives a guarantee of a constant exchange rate in case of reverse currency exchange. Moreover, this rate (both purchase and sale) is determined in advance, at the conclusion of the transaction, and may even contain the same purchase and sale costs.

    Swap transactions are a good solution for saving money. A currency swap allows you to know the specific rate before the exchange takes place. You know in advance how much you will pay for a certain amount, and how much you will receive for it later. The bank, in turn, knows in advance what profit it will receive. Both sides do not take risks and are not affected by exchange rate fluctuations.