cross-currency interest-rate swap

Interest rate swap — Definition, valuation

cross-currency interest-rate swap

An interest rate swap is a financial derivative instrument in which two parties agree to exchange interest rate cash flows. It is used in order to hedge against or speculate on changes in interest rates.

Example of use of interest rate swaps:

In order to fix the future interest expenses relative to a debt (hedging of the interest rate risk), a corporate can enter into a swap: the debt is finally at fixed rate. However, if the interest rates decline, the corporate will not benefit from low rates.

Therefore, the net debt of corporate should be sufficiently fixed to secure interest expenses. However, the corporate can benefit from falling rates with a residual floating net debt.

As already mentioned, interest rate swaps can be used for speculation ends: if a bank anticipates a drop of rates, it can enter into a swap to pay floating rates and to receive fixed rates. As a consequence, if the interest rates really drop, the bank will pay less interest expenses (meanwhile, the bank will continue to receive the same fixed cash flows).


In an interest rate swap traded by two parties, each counterparty agreed to pay either a fixed or floating rate to the other counterparty. The swap has two legs: one is related to the cash flows paid by the counterparty A to the counterparty B ; the other is related to the cash flows paid by the counterparty B to the counterparty A.

Characteristics of an interest rate swap are the following:
Notional: this notional amount is only used for calculating the size of cash flows to be exchanged. The notional amount is not exchanged if the 2 legs have the same currency
Currency: typically, currencies are the same for both legs (for instance: euro, dollar, etc.).

By trading another financial derivative instrument, the Cross Currency Swap, 2 counterparties agreed to exchange cash flows in 2 different currencies.
Trade date: this is the date at which the swap is traded.
Value date: this is the date at which the swap is really effective, that is to say the date from which cash flows are calculated.

End date: this is the maturity date of the swap.

For each leg of a swap, the following characteristics are determined:
Rate type: fixed rate or floating rate. For example, the counterparty A pays a fixed rate to B (fixed leg) and B pays a floating rate to A (floating leg).

Frequency: this is the frequency at which cash flows are paid or received (often 3 months, 6 months or 1 year). The frequency of each leg can be different.
Time basis: this is the basis on which the cash flows calculation is based.

For example, it can be 30/360: in this case, we consider that a year is equivalent to 360 days and a month is equivalent to 30 days.

Interest rate swap valuation:

The valuation of an interest rate swap is based not only on its characteristics (mentioned above), but also on market data (interest rates, foreign exchange rates, etc.). This is what we usually call «Mark-to-Market».

At inception date, the rate of the fixed leg is generally determined in order to calculate a valuation equal to 0 at this date.

If the valuation is not equal to 0, a cash payment will occur (the counterparty for which the valuation is positive will pay the other party).

To valuation an interest rate swap, several yield curves are used:

The zero-coupon yield curve, used to calculate the discount rates of future cash flows, paid or received, fixed or floating. Cash flows of each leg have to be discounted.

The forward rate curve, used to calculate the size of the floating cash flows paid (or received).

If the rate of the floating leg is 6 month Libor, this curve will inform on the level of the 6 month Libor at each fixing date (we calculate therefore the size of the cash flows).

This curve can be deducted from the zero-coupon yield curve, or collect directly on a data market provider (Bloomberg, Reuters, etc.).

Once cash flows calculated, we have to sum each discounted cash flow on each leg.

Finally, the swap valuation is the difference between the sum of the discounted received cash flows and the sum of the discounted paid cash flows.

Example of the valuation of an interest rate swap which the following characteristics:

  • Trade date: December 31, 2014
  • End date: December 31, 2019
  • Valuation date: June 30, 2015
  • Notional: 100 000 000 EUR
  • Payment frequency: 6 months for the fixed leg and for the floating leg
  • Fixed rate paid: 2%
  • Floating rate received: Euribor 6 mois
  • Basis: 30/360 (a month is equivalent to 30 days)

Please find below the market data on valuation date (June 30, 2015). Figures are the following:

  • Discount rate: used to discount the future cash flows
  • Distance from the valuation date: used to calculate the discount factor
  • Discount factor: future cash flows has to be multiplied by this factor to be discounted. It is equal to: 1/(1+Discount rate)(Distance from the valuation date)
  • Rates of floating cash flows (calculated from the forward rate curve): used to calculated the size of the floating cash flows
DateDiscount rate(zero-coupon curve)Distance from June 30, 2015 (basis 30/360)DiscountfactorRate of floating cash flows(forward rate curve)


Interest rate swaps — definitions, examples and applications

cross-currency interest-rate swap

An interest rate swap in its most basic form, often called a plain vanilla swap, is a financial contract in which two parties agree to simultaneously lend from, and borrow to, each other a certain amount of money in the same currency for the same duration but using different interest rates, generally a fixed rate and a floating rate. The nominal amount for each of these two parts to the swap, called legs, are not exchanged in that basic form as this would result in both parties paying and receiving an identical amount of money at the start and the end of the swap. The only cash flows which actually take place during the normal life of a vanilla swap are interest payments which are due periodically. If the interest payments on both legs occur at the same dates, they are often netted. That means that both due payments are compared and only the difference is paid by the party which owes the higher amount.

At swap initiation, the fixed rate is typically chosen in such a way as to make the present value of cash flows equal between the two counterparties. This fixed rate is referred to as the swap rate.

Characteristics of interest rate swaps

Interest rate swaps being financial over-the-counter instruments, the characteristics for each contract are subject to negotiation between the two counterparties.

Nominal or principal amount

This is the amount on which the interest is calculated. This amount generally remains the same over the entire lifetime of the swap, with the exceptions of amortizing or accreting swaps, which are described below.

The majority of types of interest rate swaps are single currency, which means that there is only one nominal amount and thus there is no exchange of nominal between the two counterparties as the payments would cancel each other out.

In the case of currency swaps, however, where there are two nominals, one for each leg, in different currencies, exchange of nominals usually takes place at the beginning and the end of the swap.

Fixed rate

The fixed rate is negotiated at the conclusion of the swap trade, and depends on market conditions at the time of the transaction and potentially the characteristics of an underlying to be hedged. The counterparties agree on the rate itself, as well as the day-count convention to be applied.

Floating rate

A floating rate is an interest rate which is calculated using a reference interest rate, for example a LIBOR or EURIBOR.


The lifetime of the swap. It can go from as short as one week to as long as 30 years or more.


The scheduling of all of the events that occur during the life of the swap are determined at the moment the swap transaction is concluded: start date, maturity date, periodicity of payments for each leg, fixing dates for the variable interest rate.

Sometimes, a swap can have a long or short first and/or last payment period, called a stub. This can happen when one of the counterparties needs to align the payment dates with those of another transaction. A frequent example is that of an asset swap, where one of the swap legs needs to match the payments generated by the asset.


The currency in which the swap is denominated and in which payments are made. As mentionned before, most interest rate swap types are single currency, but there are also types of interest rate swaps which are using more than one currency, currency swaps or quanto swaps.

Master agreement

Master agreements are contracts that are signed between two counterparties who frequently do over-the-counter derivatives trades with each other and sets out standard terms that apply to each transaction entered into between those two entities.

The most commonly used master agreement is the ISDA master agreement, published by the International Swaps and Derivatives Association (ISDA).

The advantage of signing a master agreement is that the terms agreed upon in that document do not need to be renegotiated for each individual transaction and apply automatically.

Cost of a swap transaction

Entering into a swap itself does not generate any particular cost, with the exception of fees due to brokers or electronic trading platforms, or the administrative cost of handling the confirmations, payments etc.

Cancellation of a swap

In case one of the counterparties would to get the swap transaction before its maturity, both parties can reach a mutual consent to terminate the swap early.

The party seeking termination has to pay the other party a lump-sum amount equal to the net present value of the swap at the time of termination.

The amount to be paid depends on how interest rates and spreads have evolved since the conclusion of the swap.

Typology of interest swaps

The basic plain vanilla swap described in the introduction is still the most common form of swaps, but with time many more forms of interest rate swaps have developed. Those most frequently encountered are briefly described below.

Basis swap

A basis swap is a variation of the standard interest rate swap with the particularity that the two interest rate flows which are exchanged are both variable rates, indexed on two different interest rate indexes. An example would be a 3-month LIBOR against a 6-month LIBOR.

Indexes in a basis swap may have different payment frequencies, as in a 3-month LIBOR for 6-month LIBOR swap. One solution is to have respective sides of the swap make payments according to their own schedules.

The 3-month LIBOR side would make quarterly payments and the 6-month LIBOR side would make half-yearly payments. Another alternative is to accumulate the more frequent payments with compound interest.

In this case, 3-month LIBOR payments would be accumulated and paid half-yearly to match the half-yearly payments of the 6-month LIBOR side.

Basis swaps are quoted with a spread over one of the two indexes with the other index being paid «flat».

A basis swap is used for example when a bank pays interest indexed on one rate but refinances itself on a different rate and wants to protect itself against the risk of the spread between the two indexes moving in an unfavorable direction.

Currency swap

Also called cross currency swap, this type of swap is an interest rate swap where both legs are denominated in different currencies. In most cases, currency swaps are traded with an exchange of nominal at both the start and the end of the swaps lifetime.

Also, cash flows occurring during the lifetime of the swap cannot be netted, as they are denominated in different currencies.

Currency swaps can be used for example to convert a loan in one currency into a loan in a different currency where better conditions can be obtained.

Forward swap

A forward swap agreement, also referred to as a “forward start swap”, “delayed start swap”, and a “deferred start swap”. It can be created through the combination of two swaps with different durations and opposite interest rate references.

Forward swaps can provide the solution for a bank or corporation that needs protection against interest rate risk for a three-year duration beginning one year from now. By entering into both a one-year and four-year swap, it would create the forward swap that meets its needs.

Amortizing swap

An amortizing swap is a swap in which the principal amount decreases with time. Typically, amortizing swaps are entered into when hedging an underlying financial instrument or transaction which itself has a declining principal, such as a mortgage.

The decrease in the principal amount can be either regular or irregular.

A bank or investor will, for example, enter into an amortizing swap with irregular amortization when the swap is concluded as a hedge for a portfolio of mortgage loans where the mortgage borrowers have the possibility of early redemption. The principal of the swap is then adjusted as soon as the actual remaining amount to be hedged is known.

Accreting principal swap

An accreting principal swap is a swap in which the principal amount increases over the life of the swap. It is thus the opposite of an amortizing swap.

Other names of an accreting principal swap are accreting swap, accumulation swap, drawdown swap, and step-up swap.

Zero-coupon swap

In its most common form, a zero-coupon swap is a swap in which floating interest-rate payments are made periodically, but fixed-rate payments are made as one lump-sum payment when the swap reaches maturity. The amount of the fixed-rate payment is the swap's zero coupon rate. It is also possible for the floating-rate payments to be paid as a lump sum.

Alternative forms of zero coupon swaps also exist. Thus, a reverse zero-coupon swap will pay the lump-sum payment at the start of the swap rather than at the end, which reduces credit risk for the party paying the floating rate.

An exchangeable zero-coupon swap contains an embedded option to turn the lump-sum payment into a series of payments.

Asset swap

An asset swap is an interest rate swap which is used to transform cash flows generated by an asset. Therefore, the real particularity of an asset swap is that the interest rate payments of one of its legs match exactly the cash flows the asset generates, but in the opposite direction.

Apart from that, any type of transformation described in the previous types of swaps may be made, i.e. fixed to floating, floating to fixed, floating to floating, one currency to another, etc. The most frequent case, however, is the transformation from fixed rate to floating rate or vice versa.

Quanto swap

Sometimes also called differential swap, a quanto swap is a swap in which interest on both legs is paid in the same currency, called the reference currency, but calculated on interest rate indexes in two different currencies. Examples would be for example a swap where one counterparty would pay 3-month USD LIBOR and receive 3-month EURIBOR with both legs settled in US Dollars. This variant is called a floating-for-floating quanto swap.

A different form of quanto swap is the fixed-for-floating quanto swaps. An example of this would be a swap where one counterparty would pay a fixed rate and receive 3-month EURIBOR with both legs settled in US Dollars.

Constant Maturity Swap (CMS)

A constant maturity swap is an interest rate swap where the interest rate on one leg is reset periodically, but with reference to a long-term market swap rate that goes beyond the swap's reset period, for example the 5-year swap rate. The second leg of the swap can be either a fixed rate or another floating rate, either a money market index, or another market swap rate.

A CMS can be used to speculate on, or hedge against, a change in the shape of the yield curve. When a bank or company believes for example that the three-month LIBOR rate will fall relative to the five-year swap rate for a given currency, it enters into a constant maturity swap paying the three-month LIBOR rate and receiving the five-year swap rate.


Currency Swap Contract — Definition, How It Works, Types

cross-currency interest-rate swap

A currency swap contract (also known as a cross-currency swap contract) is a derivative contract between two parties that involves the exchange of interest payments, as well as the exchange of principal amountsPrincipal PaymentA principal payment is a payment toward the original amount of a loan that is owed.

In other words, a principal payment is a payment made on a loan that reduces the remaining loan amount due, rather than applying to the payment of interest charged on the loan. in certain cases, that are denominated in different currencies.

Although currency swap contracts generally imply the exchange of principal amounts, some swaps may require only the transfer of the interest payments.

Breaking Down Currency Swap Contracts

A currency swap consists of two streams (legs) of fixed or floating interest payments denominated in two currencies. The transfer of interest payments occurs on predetermined dates.

In addition, if the swap counterparties previously agreed to exchange principal amounts, those amounts must also be exchanged on the maturity date at the same exchange rateFixed vs. Pegged Exchange RatesForeign currency exchange rates measure one currency's strength relative to another.

The strength of a currency depends on a number of factors such as its inflation rate, prevailing interest rates in its home country, or the stability of the government, to name a few..

Currency swaps are primarily used to hedge potential risks associated with fluctuations in currency exchange rates or to obtain lower interest rates on loans in a foreign currency.

The swaps are commonly used by companies that operate in different countries.

For example, if a company is conducting business abroad, it would often use currency swaps to retrieve more favorable loan rates in their local currency, as opposed to borrowing money from a foreign bank.

For example, a company may take a loan in the domestic currency and enter a swap contract with a foreign company to obtain a more favorable interest rateInterest RateAn interest rate refers to the amount charged by a lender to a borrower for any form of debt given, generally expressed as a percentage of the principal. on the foreign currency that is otherwise is unavailable.

How Do Currency Swap Contracts Work?

In order to understand the mechanism behind currency swap contracts, let’s consider the following example. Company A is a US-based company that is planning to expand its operations in Europe. Company A requires €850,000 to finance its European expansion.

On the other hand, Company B is a German company that operates in the United States. Company B wants to acquire a company in the United States to diversify its business. The acquisition deal requires US$1 million in financing.

Neither Company A nor Company B holds enough cash to finance their respective projects. Thus, both companies will seek to obtain the necessary funds through debt financingDebt vs Equity FinancingDebt vs Equity Financing — which is best for your business and why? The simple answer is that it depends.

The equity versus debt decision relies on a large number of factors such as the current economic climate, the business' existing capital structure, and the business' life cycle stage, to name a few..

Company A and Company B will prefer to borrow in their domestic currencies (that can be borrowed at a lower interest rate) and then enter into the currency swap agreement with each other.

The currency swap between Company A and Company B can be designed in the following manner. Company A obtains a credit line of $1 million from Bank A with a fixed interest rate of 3.5%.

At the same time, Company B borrows €850,000 from Bank B with the floating interest rate of 6-month LIBORLIBORLIBOR, which is an acronym of London Interbank Offer Rate, refers to the interest rate that UK banks charge other financial institutions for.

The companies decide to create a swap agreement with each other.

According to the agreement, Company A and Company B must exchange the principal amounts ($1 million and €850,000) at the beginning of the transaction. In addition, the parties must exchange the interest payments semi-annually.

Company A must pay Company B the floating rate interest payments denominated in euros, while Company B will pay Company A the fixed interest rate payments in US dollars. On the maturity date, the companies will exchange back the principal amounts at the same rate ($1 = €0.85).

Types of Currency Swap Contracts

Similar to interest rate swaps, currency swaps can be classified the types of legs involved in the contract. The most commonly encountered types of currency swaps include the following:

  • Fixed vs. Float: One leg of the currency swap represents a stream of fixed interest rate payments while another leg is a stream of floating interest rate payments.
  • Float vs.Float (Basis Swap): The float vs. float swap is commonly referred to as basis swap. In a basis swap, both swaps’ legs both represent floating interest rate payments.
  • Fixed vs.Fixed: Both streams of currency swap contracts involve fixed interest rate payments.

For example, when conducting a currency swap between USD to CAD, a party that decides to pay a fixed interest rate on a CAD loan can exchange that for a fixed or floating interest rate in USD. Another example would be concerning the floating rate. If a party wishes to exchange a floating rate on a CAD loan, they would be able to trade it for a floating or fixed rate in USD as well.

The interest rate payments are calculated on a quarterly or semi-annually basis.

How a Currency Swap is Priced

Pricing is expressed as a value LIBOR +/- spread, which is the credit risk between the exchanging parties.

LIBOR is considered a benchmark interest rate that major global banks lend to each other in the interbank market for short-term borrowings.

The spread stems from the credit risk, which is a premium that is the lihood that the party is capable of paying back the debt that they had borrowed with interest.

More Resources

CFI offers the Financial Modeling & Valuation Analyst (FMVA)™FMVA® CertificationJoin 350,600+ students who work for companies Amazon, J.P. Morgan, and Ferrari certification program for those looking to take their careers to the next level. To keep learning and advancing your career, the following CFI resources will be helpful:

  • Interest Rate SwapInterest Rate SwapAn interest rate swap is a derivative contract through which two counterparties agree to exchange one stream of future interest payments for another
  • Credit RiskCredit RiskCredit risk is the risk of loss that may occur from the failure of any party to abide by the terms and conditions of any financial contract, principally,
  • Floating Interest RateFloating Interest RateA floating interest rate refers to a variable interest rate that changes over the duration of the debt obligation. It is the opposite of a fixed rate.
  • International Fisher Effect (IFE)International Fisher Effect (IFE)The International Fisher Effect (IFE) states that the difference between the nominal interest rates in two countries is directly proportional to the changes in the exchange rate of their currencies at any given time. Irving Fisher, a U.S. economist,  developed the theory.


Swap Rate (Definition,Types) | Interest Rate & Currency Swap Examples

cross-currency interest-rate swap

A swap rate is a rate, the receiver demands in exchange for the variable LIBOR or MIBOR rate after a specified period and hence it is the fixed leg of an interest rate swap and such rate gives the receiver base for considering profit or loss from a swap.

The swap rate in a forward contract is the fixed-rate (fixed interest rate or fixed exchange rate) that one party agrees to pay to the other party in exchange for uncertainty related to the market.

In an interest rate swap, a fixed amount is exchanged at a specific rate with respect to a benchmark rate such as LIBOR. It can be either plus or minus of spread.

Sometimes, it may be an exchange rate associated with the fixed portion of a currency swap.

#1 – Interest Rate Swap

Interest rate swap is where cash flows are exchanged at the fixed rate in reference to the floating rate. It is an agreement between two parties in which they have decided to exchange a series of payment between them. In such a payment strategy, a fixed amount will be paid by the one party and the floating amount will be paid by another party at a certain period of time.

The notional amount is usually referred to decide the size of the swap, in the whole process of the contract, the notional amount remains intact. Examples of Interest Rate Swap Include

  • Overnight Index Swaps – Fixed v/s NSE overnight MIBOR Index and
  • INBMK Swap – Fixed v/s 1-year INBMK rate

Types of Interest Rate Swaps

  • A Plain Vanilla Swap – In this type, a fixed rate is exchanged for a floating rate or vice versa on a pre-specified interval during the course of the trade.
  • A Basis Swap – In the case of floating to floating swap, it is possible to exchange the floating legs on the basis of benchmark rates.
  • An Amortizing Swap – In the amortization swap, the notional amount decreases with the decrease in the amortization loan amount, respectively, swap amount also decreases.
  • Step-up Swap – In this swap, the notional amount upsizes on the prescheduled day.
  • Extendable Swap – When one of the counterparties has the right to extend the maturity of the trade. That swap is known as an extendable swap.
  • Delayed Start Swaps/Deferred Swaps.

    Inward Swaps – It all depends upon the parties, what they have agreed upon when the swap will come into effect, whether on delayed start Swaps or Deferred Swap or Forward Swap.

#2 – Currency Swap

It is a swap in which the cash flows of one currency are exchanged for the cash flow of another currency, which is almost similar to the interest swap.

#3 – Basis Swap

In this swap, the cash flow of both the legs refers to different floating rates. Some of the swaps majorly refer to fixed against floating legs LIBOR. While in the basis swap, both the legs are floating rates. A basis swap can be either an interest swap or a currency swap in both the cases, both legs are floating legs.

Formula to Calculate Swap Rate

It is the rate that is applicable to the fixed payment leg of the swap. And we can use the following formula to calculate the swap rate.

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C =

It represents that the fixed-rate interest swap, which is symbolized as a C, equals one minus the present value factor that is applicable to the last cash flow date of the swap divided by the summation of all the present value factors corresponding to all previous dates.

With respect to change in time, fixed leg rate, and floating leg rate changes with respect to time that was initially locked. The new fixed rates corresponding to the new floating rates is termed as the equilibrium swap rate.

The mathematical representation as follows:


  • N = Notional Amount
  • f =  fixed rate
  • c =  fixed rate negotiated and locked at the initiation
  • PVF = Present value factors

Example 1

  1. Six month USD LIBOR against three months USD LIBOR
  2. 6-month MIFOR against six month USD LIBOR.

Example 2

If we consider an example in which you negotiate a 2% pay fixed, in reverse receive a floating swap at a variable rate to convert 5-years $200 million loans to a fixed loan. Evaluate the value of swap after one year, given in the following floating rates present value factor schedule.

The calculation of the swap rate formula will be as follows,

F = 1 -0.93/(0.98+0.96+0.95+0.93)

The equilibrium fixed swap rate after one year is 1.83%

The calculation of the equilibrium swap rate formula will be as follows,

=$200 million x(1.83% -2%) * 3.82

Initially, we locked up in 2% fixed rate on loan, the overall value of the swap would be  -129.88 million.


There are basically two reasons why companies want to engage in swaps:

  • Commercial Motivations: There are few companies that engage in to meet the businesses with specific financing requirements, and interest swaps, which help managers to attain pre-specified goals of the organization. The two most common types of businesses that get benefited from the interest swaps are Banks & Hedge Funds
  • Comparative Advantages: Most of the time, companies want to take advantage of either receiving a fixed or floating rate loan at an optimal rate than the other borrowers are offering. However, it is not financing they are seeking a favorable opportunity of hedging in the market so they can make a better return it


Interest swaps are associated with huge risk, which we have specified below:

  • Floating rates are variable rates due to this reason. It adds more risk to both parties.
  • Counterparty risk is another risk that adds an additional level of complicacy to the equation.


They could be a great means for a business to manage outstanding loans.  And the value behind them is the debt that can be either fixed or floating rate. They are usually performed between large companies to meet the specific financing requirements that could be a beneficial arrangement to meet everyone’s requirements.

This has been a guide to what Swap Rate is and its definition. Here we discuss the types of swaps along with examples, advantages, and disadvantages. You may learn more about risk management from the following articles –

  • What are Equity Swaps?
  • Derivatives in Finance
  • Commodity Derivatives


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