forward rate agreement

Содержание
  1. Соглашение о будущей процентной ставке, FRA
  2. Формула
  3. Условные обозначения соглашения о будущей процентной ставке
  4. Пример 1
  5. Пример 2
  6. Forward Rate Agreement (FRA): Meaning and Its Pricing
  7. Meaning of Forward Rate Agreement (FRA):
  8. Salient Features of Forward Rate Agreements (FRAs):
  9. Market Conventions of Forward Rate Agreements (FRAs):
  10. Pricing a Forward Rate Agreement:
  11. Understanding The Important Financial Products — Interest Rate Swaps & Forward Rate Agreements
  12. What Are Forward Rate Agreements (FRA)?
  13. What Are FRA Benefits?
  14. Understanding FRA Terminology
  15. Calculating Value of A FRA for Payer
  16. This brings us to the second part of the article: Interest Rate Swaps
  17. What Is A Swap?
  18. What Is An Interest Rate Swap?
  19. What Are IRS Types?
  20. What Is A Vanilla IRS?
  21. What Are Swap Legs?
  22. Other Types Of IRS
  23. Interest Rate Swap Properties
  24. Let’s Go Over Swap Initiation To Pricing Steps
  25. Fixing Data And Resets
  26. Why is the rate reset?
  27. 1. Price IRS as Two Bonds:
  28. 2. Price IRS as Series Of FRAs:
  29. Q. Let’s Price An IRS
  30. Methodology 1: Value IRS as bonds:
  31. Methodology 2: Value IRS as FRAs
  32. Summary
  33. Forward Rate Agreement (Meaning, Formula | Step by Step FRA Example
  34. Forward Rate Agreement Formula
  35. Forward Rate Agreements (FRA) Examples
  36. Example #1
  37. Example #2
  38. Example #3
  39. Advantages of Forwarding Rate Agreement (FRA)
  40. Disadvantages of Forwarding Rate Agreement (FRA)
  41. Important Points
  42. Conclusion
  43. Recommended Articles
  44. Forward rate agreements (FRAs) — definitions, examples and applications
  45. FRA terminology
  46. Calculation of the settlement amount of an FRA
  47. Step 1 — calculation of the interest differential
  48. Step 2 — calculation of the settlement amount
  49. The FRA market
  50. Notation and quoting of FRAs
  51. Quotation of forward rate agreements
  52. Usages of an FRA
  53. Example of an FRA
  54. Characteristics of the FRA known on trade date:
  55. Расчёты по соглашениям о будущей процентной ставке | Энциклопедия финансовых рынков
  56. Риски, связанные с соглашениями о будущей процентной ставке
  57. Форвард-форвардные ставки

Соглашение о будущей процентной ставке, FRA

forward rate agreement

Соглашение о будущей процентной ставке (англ. Forward Rate Agreement, FRA) является разновидностью форвардных контрактов, а, следовательно, производным финансовым инструментом, обращение которого происходит на внебиржевом рынке.

Суть этого соглашения заключается в том, что две стороны принимают на себя обязательство обменяться будущими процентными платежами, которые будут начислены на расчетную сумму (англ. Notional Amount).

При этом одна сторона принимает на себя обязательство выплачивать платежи по фиксированной процентной ставке (англ. Fixed Interest Rate), а другая сторона по плавающей процентной ставке, называемой ставкой ориентиром (англ. Reference Rate).

При этом покупатель контракта хеджирует риск роста процентных ставок, а продавец риск снижения процентных ставок.

Формула

Чтобы рассчитать размер компенсационного платежа (P), который должна выплатить одна из сторон в пользу другой стороны по истечении срока действия соглашения FRA, необходимо воспользоваться следующей формулой:

NA – расчетная сумма;

rR – ставка ориентир;

rF – фиксированная процентная ставка;

α – коэффициент, учитывающий продолжительность срока действия соглашения о будущей процентной ставке.

Коэффициент α необходим для того, чтобы привести ставку ориентир и фиксированную процентную ставку к продолжительности срока действия соглашения FRA.

Например, если процентные ставки даны в годовом выражении, а соглашение действует 3 месяца, то коэффициент α будет равен 0,25 или 90/360.

Следует отметить, что в некоторых странах, например, в Великобритании, учитывается точное число дней, поэтому в качестве временной базы берется не 360, а 365 дней.

Условные обозначения соглашения о будущей процентной ставке

Соглашения FRA имеют общепринятые условные обозначения, что удобно рассмотреть на примере:

USD 1×7 1.50/1.75%

где USD – валюта, в которой указана расчетная сумма, в этом примере доллары США;

1×7 – срок действия договора, в этом примере соглашение начинает действовать через 1 месяц и заканчивает действовать через 7 месяцев;

1.50% — фиксированная процентная ставка по которой сторона контракта будет получать платежи, а выплачивать по ставке ориентиру;

1.75% — фиксированная процентная ставка по которой сторона контракта будет выплачивать платежи, а получать по ставке ориентиру.

Разница между процентными ставками является спредом и составляет в данном примере 0,25%.

Другие стандартные сроки действия соглашения о будущей процентной ставке представлены в таблице.

Пример 1

Компания BFG намеревается взять кредит в Банке HJK в размере 2000000 USD через 1 месяц сроком на 6 месяцев. Чтобы избежать риска роста процентных ставок, компания покупает соглашение FRA [USD 1×7 3,75%] у Банка CVB, в котором ставкой ориентиром выступает 6-ти месячный LIBOR. Предположим, что по истечении 1 месяца (на дату фиксации) 6-ти месячный LIBOR составил 4,25%.

Ставка ориентир и фиксированная процентная ставка соответствуют сроку действия соглашения о будущей процентной ставке, поэтому коэффициент α в формуле использовать не нужно.

Поскольку опасения покупателя соглашения FRA относительно роста процентных ставок оправдались, Банк CVB выплатит в его пользу компенсационный платеж в размере 9592,33 USD1. В свою очередь, на реальном рынке Компания BFG возьмет кредит в Банке HJK под 4,25%, однако рост процентных ставок будет компенсирован платежом по соглашению FRA с Банком CVB.

Пример 2

Страховая компания собирается разместить депозит на сумму 10000000 USD через 3 месяца сроком на 6 месяцев.

Чтобы хеджировать риск снижения процентных ставок по депозитам она продает банку соглашение FRA [USD 3×9 4,50%], в котором ставкой ориентиром выступает 6-ти месячный LIBOR.

Предположим, что опасения страховой компании не подтвердились и 6-ти месячный LIBOR на дату фиксации (через 3 месяца) составил 5,15%. В этом случае размер компенсационного платежа составит 61816,45 USD, который она должна будет выплатить банку2.

На реальном рынке страховая компания сможет разместить депозит под 5,15%, что компенсирует потери по соглашению FRA. Другими словами, при любом развитии событий она фиксирует будущую ставку 6-ти месячного размещения депозита на уровне 4,50%.

1 Следует обратить внимание, что компенсационный платеж выплачивается на дату фиксации, т.е. в момент начала периода условного кредита. Поскольку эта сумма выплачивается раньше, чем необходимо, она может быть вложена для получения дополнительного дохода. В связи с этим компенсационный платеж дисконтируется по рыночной процентной ставке на дату фиксации.

2 Представленная выше формула расчета компенсационного платежа записана с точки зрения покупателя соглашения о будущей процентной ставке. Если расчетное значение положительное, то эту сумму продавец должен будет компенсировать покупателю, если отрицательное, то наоборот.

  • ← Паритет процентных ставок
  • Пут-колл паритет →

Источник: https://allfi.biz/investingbasics/DerivativeSecurities/soglashenie-o-budushhej-procentnoj-stavke.php

Forward Rate Agreement (FRA): Meaning and Its Pricing

forward rate agreement

After reading this article you will learn about:- 1. Meaning of Forward Rate Agreement (FRA) 2. Salient Features 3. Market Conventions of Forward Rate Agreements 4. Pricing.

Meaning of Forward Rate Agreement (FRA):

A FRA is a forward contract on the interest rate. It is a financial contract to exchange interest payments a fixed interest rate with payments floating interest rate 6 m LIBOR/ 3 m MIBOR. The exchange of payments is a notional principal of the FRA. Thus, there are 2 legs in a FRA – the fixed leg and the floating leg.

Consider a company which has an expected requirement for funds after 3 months. It is concerned that the interest rates will head higher from the current levels and hence it may have to pay higher interest rate on the loan.

The company can enter into a FRA, where it pays fixed interest rate to hedge or fix its borrowing cost today for an requirement after 3 months. The fixed rate agreed via the FRA will be compared to the benchmark rate at the settlement date to determine the settlement amount.

If a corporate borrowed for a period of 3 months, 3 months from now, it is referred to as a 3 X 6 FRA.

If the corporate buys a FRA, then it pays a particular fixed rate and receives a floating rate, hence, it hedges against any rise in the interest rates.

If a corporate sells a FRA, then it receives a particular fixed rate and pays a floating rate; hence, it hedges against any fall in the interest rates

Consider the following example of a FRA.

A corporate sells a FRA on the following terms:

1. Notional principal: INR 250 Million (INR 25 cr.)

2. Corporate to receive: 5.60% fixed

3. Corporate to pay: 3 month NSE MIBOR

4. Term of FRA: 3 x 6

5. Tenor of FRA: 90 days

6. On the settlement date, the 3 month NSE MIBOR is 6.00%

In this case the corporate will have to pay

(6.00% – 5.60%) X 25,00,00,000/- X 90/365 = Rs. 2,46,575.34

Example:

A Forward Rate Agreement is a contract between two parties by which they agree to settle between them the interest differential on a notional principal on a future settlement date for a specified future period.

Let us assume that a corporate wants to borrow a sum of Rs. 1 crore for a period of six months starting three months from today. Its main concern is that the six months interest rate may rise in three months-time and hence it wants to lock in a rate right today for a future borrowing commitment.

It enters into a 3 Vs 9 FRA with a counterparty for a notional amount of Rs.1 crore. If the counterparty quotes, say, 6.25/6.50 for a 3 Vs 9 FRA, the corporate buys the FRA at 6.50 which effectively means that it is locking itself for 6.5% for the above borrowing commitment.

If on the date of settlement, which is the date three months from today when the borrowing commitment has to be met, the bench mark rate agreed to by the counterparties settles, say, at 7.00%, the corporate’s view on the interest rate has come true and it is paid by the seller of FRA the difference of 0.50% (7 – 6.5) on the notional principal for a period of six months discounted at 7%.

The amount receivable by the corporate is calculated as under:

On the other hand, if the benchmark interest rate settles at, say, 6.25% on the settlement date, the corporate pays the seller of FRA the difference of 0.25% (6.5-6.25) on the notional principal of Rs. 1 crore discounted at 6.25%. Thus in both the cases (whether interest rate rises or falls) the corporate’s effective borrowing rate remains unchanged at 6.5%.

Salient Features of Forward Rate Agreements (FRAs):

1. Forward Rate Agreements, Financial Futures and Interest Rate Swaps are linear derivatives whereas Options are non­linear.

2. Forward Rate Agreements are over the counter type deriva­tives which are used to hedge short term interest rate risk.

3. A Forward Rate Agreement is a contract between two parties by which they agree to settle between them the interest differential on a notional principal on a future settlement date for a specified future period.

4. A person who has a commitment to borrow money at a future point of time buys a Forward Rate Agreement to protect himself against interest rate risk and a person who has a commitment to lend money at a future point of time sells a Forward Rate Agreement to hedge his interest rate exposure.

Market Conventions of Forward Rate Agreements (FRAs):

The principal amount is only notional. There is no commitment on either of the counterparties to either lend or borrow this amount. The convention in FRA markets is to denote the FRA as 3 Vs 6,6 Vs 9 etc.

A 6 Vs 9 FRA means seeking protection for a 3 months borrowing or lending commitment starting 6 months from today. A 9 Vs 12 FRA means seeking protection for a 3 months borrowing or lending commitment starting 9 months from today and so on.

Prices are quoted two ways in the market for FRAs. Obviously, the customer buys at the higher of the two rates and sells at the lower rate.

The benchmark interest rate is a reference rate, basically a floating rate T Bill rate, Libor etc., to compare the FRA rate on the settlement day and to enable the settlement of difference in rates on the notional principal.

The discounting of the amount to be settled is due to the fact that the difference of interest is settled at the beginning of a borrowing or lending commitment whereas normally interest is payable on maturity of a loan.

Borrowers at a future point of time buy the FRA to lock them­selves at a fixed rate whereas lenders sell FRA to lock in a fixed return on their future lending.

Pricing a Forward Rate Agreement:

Let us price a 3 Vs 12 FRA when the market rates for various months are as follows:

1 m = 6.00/6.25%

Источник: https://www.yourarticlelibrary.com/investment-management/forward-rate-agreement-fra-meaning-and-its-pricing/89440

Understanding The Important Financial Products — Interest Rate Swaps & Forward Rate Agreements

forward rate agreement
Aug 13, 2019 · 10 min read

In this article, I will provide an overview of the two most important financial products which are known as interest rate swaps and forward rate agreements.

I will also outline and explain the mathematical formulae which are used to value the two products.

Please read FinTech Disclaimer.

Photo by Austin Distel on Unsplash

What Are Forward Rate Agreements (FRA)?

  • FRAs are forwards hence they are private contracts between counterparties.
  • The forward rate is locked in a FRA contract.

Let’s assume you want to borrow £100'000 for three months from a bank. Also, assume you want to borrow this amount in a month’s time.

You can enter into a FRA contract with a bank where both parties can agree on locking the borrowing rate.

As a result, this rate will remain constant until the maturity of the contract.

What Are FRA Benefits?

FRA contracts can benefit buyers and sellers.

  • Buyer benefits when borrowing rate increases.
  • Seller benefits when borrowing rate decreases.

A trader can invest in buying a FRA if he fears that the rates will fall or he can enter into selling a FRA contract if he has borrowed money from a bank and he fears that the rates will rise.

So far, we have understood that FRAs help us with interest rate movements.

Photo by Etienne Martin on Unsplash

Understanding FRA Terminology

1 x 4 FRA means you will enter into a FRA contract to lock the rate in 1 month’s time for 3 months.

Calculating Value of A FRA for Payer

I wanted to explain FRAs because they make the foundation of interest rate swaps.

This brings us to the second part of the article: Interest Rate Swaps

Before I explain what interest rate swaps are, let’s understand what swaps are and why they are traded?

What Is A Swap?

  • Swaps are derivatives.
  • In terms of notional, swaps have the largest financial OTC derivative market. Hence it’s beneficial to learn about swaps. Most (if not all) large financial institutions invest in swaps.
  • The swap market is the most liquid market
  • Swaps allow parties to exchange a stream of payments for a period of time.
  • Swap rates become benchmark interest rates.
  • Swaps have different forms: Commodity Swaps, Interest Rate Swaps, Cross Currency Interest Rate Swaps and so on.

Traders trade swaps to:

  • Transform a floating rate loan into a fixed-rate loan.
  • Transform an asset earning a fixed rate of interest to an asset earning a floating rate of interest.
  • Companies can enter a market in which they have a comparative advantage e.g. company with a comparative advantage in floating rate markets can enter into a swap and receive a floating rate.
  • Benefit and hedge risk from interest rate movements.

Photo by Sharon McCutcheon on Unsplash

What Is An Interest Rate Swap?

Interest rate swap (IRS) is a type of swap and hence belongs to the class of derivatives. Its price is derived by market interest rates.

An interest rate swap is a financial agreement between parties to exchange fixed or floating payments over a period of time.

Vanilla IRS is an agreement whereby 2 parties exchange cash flows in the future and the payments are linked to market interest rates. Additionally, payments are exchanged periodically.

What Are IRS Types?

There are various types of IRS ranging from plain vanilla IRS to step-up compounding to Libor in arrears IRS. In this article, we will cover the most common IRS: Plain Vanilla IRS.

Plain Vanilla IRS is also known as Fixed For Float IRS or a par swap.

What Is A Vanilla IRS?

In a vanilla IRS:

  • 1 party commits to pay a percentage of notional a fixed rate and the other party commits to pay a percentage of notional indexed to a floating rate.
  • The fixed-rate is determined at the start and it is the price that the party pays to initiate a contract at a floating rate.
  • The floating rate, on the other hand, varies on a timely basis. Fixed and floating rate payments are the two legs of an IRS.

What Are Swap Legs?

A swap is a contract between two parties where one party pays to the other party periodically. As there are two sides of a swap, it is essentially a contract with two legs:

  • Pay Leg — This leg specifies 1. who pays, 2. what needs to be paid and 3. how frequent it needs to be paid
  • Receive Leg— This leg specifies 1. who receives, 2. what needs to be received and 3. how frequent it needs to be received

Each leg could be indexed on a fixed or floating rate. The frequency of a plain vanilla IRS is usually the same for both legs.

Photo by Markus Spiske on Unsplash

Other Types Of IRS

There are different types of interest rate swaps (IRS) including:

  • Plain vanilla swap: Fixed-rate payments are exchanged with payments LIBOR rates.
  • Basis IRS: Floating rate payments are exchanged with floating-rate payments. Both floating rates reference different indexes (rates/curves).
  • Cross-currency swap: Payments are in two different currencies
  • Non-deliverable swap: Payments are in two currencies (major and minor) and on the settlement date, value is settled by taking exchange rate and spot rate into account.
  • Fx reset notional swap: Payments are in two currencies. Notional reset and varies during the lifetime of a swap.

Interest Rate Swap Properties

Before we analyze how an IRS is priced, let’s quickly review the properties that are required to price an IRS:

  • Trade Date — when they entered into the contract
  • Effective Date — when they want to start payments or compound the interest rate
  • Business Day Convention — what needs to be done if payment falls on a holiday
  • Day Count Convention — number of days in a month of a year
  • Holiday Calendar — list of holidays
  • Maturity Date — when to terminate the contract
  • Type of rate — fixed/float
  • Position — Pay/Receive
  • Floating Rate — Reference of an interest rate curve
  • Fixed-Rate — Static percentage of notional which will be exchanged
  • Frequency of payments — Helps determine pay dates
  • Principal notional — Initial notional on which interest is applied

Photo by Didier Weemaels on Unsplash

Let’s Go Over Swap Initiation To Pricing Steps

  1. The first step is to agree on a fixed rate such that swap has a fair value for both parties.
  2. To prevent arbitrage, the fixed coupon cash flows should be equal to the floating rate cash flows.

    At the point of initiating a swap contract, the floating rate, frequency of cash flows and dates are known.

  3. A cashflow is Notional Principal x Rate x Date fraction.
  4. Spot floating rates are used to calculate implied forward rates. These rates are used to calculate floating-rate cash flows.

    These cash flows are discounted by the observed interest rates.

  5. Finally, a fixed rate is then derived to ensure that the sum of fixed and float cashflows is as close as possible (or equal) to floating cash flows. Usually, a spread is added to account for the differences or to charge a party due to its risks.

The image illustrates that on each fixing date, the floating rate for the next period is determined.

Fixing Data And Resets

In a plain vanilla swap, the floating rate for the next cashflow is chosen to be the current interest rate. The dates when the floating rate is decided are known as fixing dates. A fixing date is usually two days before the payment day, hence payment on the date is

exp(-forward implied rate x no of days in next payment) is used to discount the payment to present value.

  • On each reset/fixing date, the floating rate for the next coupon period is fixed. The next coupon rate is usually the current LIBOR rate + spread. Cashflows at floating leg are forward rates of the floating index.
  • First, the cashflows on the floating leg are calculated. Then a fixed rate (also known as coupon rate) is calculated for fixed leg such that it will ensure that the swap is at par to prevent arbitrage.
  • Finally, on every reset date, the floating rate of the floating leg is fixed for the next coupon period to ensure that the swap is at par.

Remember fixed leg’s rate was fixed at the initiation of the contract and is fixed till the end date.

  • This means that the last payment is the rate fixed on the penultimate coupon date.
  • Swap leg payments in a swap contract are netted against each other.

For example, if party A agreed to pay 5% fixed rate and party B agreed to pay LIBOR + spread of 0.05% on notional of $1 million then on the first payment date, assuming LIBOR rate is 10%:

Instead of Party A paying: 1 million x 0.05, and Party B paying: 1 million x (0.1+0.05), only the net amount will be paid from party B to party A.

Why is the rate reset?

  • The resetting of the rate ensures that the swap is at par. This is to prevent arbitrage opportunities and to ensure a swap is a fair deal for both sides of the contract.

Resetting ensures that the swap is always at par

  • What is a floating rate? Rates that change daily in the market, for example, LIBOR.
  • Is there any risk? Yes, if the floating rate changes in the opposite direction.
  • What are the day count conventions? Libor day count convention is actual/360 (it means we will take the actual number of days in a month and divide it by360) and for a fixed rate, usually, the day count convention is actual/365 or 30/360. This is the reason why a fixed rate is multiplied to 360/365 to make fixed and float rate compatible.

Photo by Adeolu Eletu on Unsplash

In this section, I will explain how we can price a plain vanilla IRS swap. There are two common strategies to price a swap:

An IRS could be treated as:

  1. Series of Forward Rate Agreements (FRAs)
  2. Two Bonds

Therefore understanding how to price a bond and a forward rate agreement can help us understand how to value a swap. It’s worth noting that swap cashflows are exchanged on several future dates, un a forward rate contract.

Furthermore, there are two legs/parts of a swap, un a bond which has one coupon rate.

1. Price IRS as Two Bonds:

Fixed-float leg swap is a portfolio of two bonds as it has equivalent cashflows as a bond with a fixed coupon and a bond with a floating coupon. The present value of cash flows of fixed and float bonds is then subtracted to calculate the price of a swap.

2. Price IRS as Series Of FRAs:

Value a swap as a sequence of forward contracts, the formula is:

Sum of all forward contract with continuous (or discrete) compounding, where each contract is valued as:

  • [Notional at maturity x (Forward rate for the payment — Fixed Rate)]/(1 + spot rate for the payment)payment number.

If we want to use continuous discounting then the formula is:

  • [Notional at maturity x (Forward rate for the payment — Fixed Rate)] * exponential (- spot rate for the payment * payment number)

Q. Let’s Price An IRS

Let’s consider an interest rate swap with the following properties:

  • Notional = £100,
  • Frequency In Years = 0.5. Semi-Annual payments
  • Start Date = Today,
  • Maturity Date = In 1 year,
  • Pay Dates = 6 Months (6/12=0.5) and 12 Months (1)
  • Current Reset Rate = 0.05
  • Fixed-Rate = 0.06
  • Floating payments are on Libor curve. Assume Libor interest rates are: Maturity 6M = 0.054, Maturity 12M = 0.058

This is a swap of £100, exchanging fixed on a float for 12 months, semi-annual payments on a 6% fixed rate and float leg on LIBOR.

Methodology 1: Value IRS as bonds:

The formula is: Present Value Of Fixed Bond Cashflows — Present Value Of Float Bond Cashflows

Step 1: Sum all fixed bond cashflows

1. For each pay date (period), calculate Discounted cash flow by:

The present value of (Notional x Fixed Rate * Frequency in a year)

2. For the last payment, cashflow includes notional amount too.

Step 2: Sum all float bond cashflows. 1 cashflow on current reset rate

1.Calculate float payment: Notional + (Notional x Current Reset Rate x Frequency)

2.Calculate the present value of float payment using LIBOR curve

Step 3: Find the net value of fixed — float cashflows

Note: Present value is calculated as Exp (-rate for current period x current period)

Methodology 2: Value IRS as FRAs

Each payment in IRS can be treated as a FRA.

Pricing formula:

  • [Notional at maturity x (Forward rate for the payment — Fixed Rate)] x (exponential (- spot rate for the payment*payment number).

As there are 3 payments, the swap price is a Sum of Present Value Of 3 FRAs

Note: The first payment is the current reset rate. Subsequent payments are forward rates.

  • For each payment, payment is calculated by multiplying Notional x Frequency x Forward Rate
  • Cashflow is discounted using the current period’s LIBOR rate

Summary

  • The article explained the foundations of FRA and swaps.
  • Swaps have the largest derivatives financial market by notional and nearly all financial institutions trade swaps. Therefore it is beneficial to learn about the IRS.
  • We have learned how to price an IRS using bond and FRA strategies.

I hope it helps.

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Источник: https://medium.com/fintechexplained/understanding-the-important-financial-products-interest-rate-swaps-forward-rate-agreements-4ab3c2dfda7

Forward Rate Agreement (Meaning, Formula | Step by Step FRA Example

forward rate agreement

Forward Rate Agreement, popularly known as FRA, refers to customized financial contracts that are traded Over the Counter (OTC) and allow the counterparties, which are primarily large banks, corporate to predefine interest rates for contracts which are going to start at a future date.

There are two parties involved in a Forward Rate Agreement, namely the Buyer and Seller. The Buyer of such contract fixes in the borrowing rate at the inception of the contract, and the seller fixes in the lending rate. At the inception of an FRA, both parties have no profit/loss.

However, as time passes, the Buyer of the FRA benefits if Interest Rates increases than the rate fixed at the inception, and the Seller Benefits if the interest rates fall than the rate fixed at the inception. In short, the Forward Rate Agreement is Zero-sum games where the gain of one is a loss for the other.

Forward Rate Agreement Formula

The formula for calculating Forward Rate is as follows:

Forward Rate Agreement Formula = R2 + (R2 – R1) x [T1 / (T2 – T1)]

Forward Rate Agreements (FRA) Examples

However, there are multiple ways to calculate the same, which are discussed through the examples below.

Example #1

Let’s understand the Concept of FRA with the help of a few examples:

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  • Forward Rate Agreements are usually denoted, such as 2×3 FRA, which simply means, 30-day loan, sixty days from now. The first number corresponds to the first settlement date, the second to the time to final maturity of the contract.
  • One should understand this terminology to understand the nuances of a Forward Rate Agreement. Now lets Raven Bank want to value a 1X4 FRA (which basically means a 90-day loan, 30 days from now)

Let’s calculate the 30-day loan rate and 120-day loan rate to derive the equivalent forward rate, which will make the value of FRA equivalent to zero at inception:

Example #2

  • Axon International entered into a Forward Rate Agreement to receive a rate of 3.75% with continuous compounding on the principal of USD 1 Mio between the end of the first year and end of the Second year.
  • The current Zero rates for one year are 3.25%, and for two years, it is 3.50%.

This is basically a 1X2 FRA Contract

Let’s calculate the value of the Forward Rate Agreement in two scenarios:

  • At the beginning of the contract

Thus we can see at the beginning of the Forward Rate Agreement, and there is no profit loss to any of the two parties.

Now let’s assume the rate falls to 3.5%, let’s compute the value of FRA again:

(Excel file attached)

Thus we can see as interest rates move the value of FRA changes resulting in again for one counterparty and equivalent loss to the other counterparty.

Example #3

  • Rand Bank entered into a Forward Rate Agreement on 20th Oct 2018 with Flexi Industries, whereby the Bank will pay a fixed interest of 10% and, in return, will receive a floating rate of interest- the Commercial Paper rate existing at the time of payment.
  • Payment is settled on a quarterly basis with the first payment due on 20th Jan 2019.

Below are the details:

(excel file attached)

Thus Rand Bank will receive USD 2.32 Mio from Flexi Industries.

Advantages of Forwarding Rate Agreement (FRA)

  • It enables the parties to such Agreement to reduce their risk of future borrowing and lending against any adverse movement by entering into such contracts. For instance, a market participant who is scheduled to receive payment in Foreign currency at the end of one year can avoid the currency fluctuation risk by entering into a Forward Rate Agreement. Similarly, a Bank which has borrowed funds at a fixed rate and expects the rates to decline in the future can benefit by such declined by entering into a Forward rate Agreement as a Floating ratepayer.
  • It is frequently used for Trading interest rate expectations of Market participants.
  • Forward Rate Agreements are derivative contracts that form part of the Off-Balance Sheet and, as such, doesn’t impact the Balance Sheet Ratios.

Disadvantages of Forwarding Rate Agreement (FRA)

  • FRA is customized and traded Over-the-counter and, as such carries, a higher amount of Counterparty Risk compared to a standardized Futures contract, which is settled through a Qualified Centralized Counterparty (QCCP)
  • It is difficult to find a third counterparty to close the contract before maturity if the original contract is to be closed, and the initial counterparty is not ready to reverse the position.

Important Points

  • The long position is effectively long the rates and benefits when rates increase. Similarly, the short position in a Forward Rate Agreement is effectively short the rates and benefits when rates decrease.
  • FRA is a Notional Contracts, and as such, there is no exchange of principal at the expiry date.
  • FRA is similar to Futures contracts, except they are known centrally cleared over-the-counter instruments, which can be customized by the parties between themselves for any maturity.
  • FRA is a Linear Derivative Instruments and derives its value directly from the underlying instrument.

Conclusion

Forward Rate Agreement has customized Interest Rate contracts which are Bilateral in nature and don’t involve any Centralized Counterparty and frequently used by Banks and Corporate.

This has been a guide to What is Forward Rate Agreement, and it’s meaning. Here we discuss the examples of forwarding rate agreement along with its formula, advantages, and disadvantages. You can learn more about excel modeling from the following articles –

Источник: https://www.wallstreetmojo.com/forward-rate-agreement/

Forward rate agreements (FRAs) — definitions, examples and applications

forward rate agreement

A forward rate agreement (FRA) is a cash-settled OTC contract between two counterparties, where the buyer is borrowing (and the seller is lending) a notional sum at a fixed interest rate (the FRA rate) and for a specified period of time starting at an agreed date in the future.

An FRA is basically a forward-starting loan, but without the exchange of the principal. The notional amount is simply used to calculate interest payments. By enabling market participants to trade today at an interest rate that will be effective at some point in the future, FRAs allow them to hedge their interest rate exposure on future engagements.

Concretely, the buyer of the FRA, who locks in a borrowing rate, will be protected against a rise in interest rates and the seller, who obtains a fixed lending rate, will be protected against a fall in interest rates. If the interest rates neither fall nor rise, nobody will benefit.

The life of an FRA is composed of two periods of time – the waiting period, or forward, and the contract period. The waiting period is the period up until the start of the notional loan and may last up to 12 months although durations of up to 6 months are most common. The contract period spans the duration of the notional loan and can also last up to 12 months.

Key dates of a forward rate agreement (FRA)

The FRA however effectively ends with the settlement date, as there is no longer any contractual engagement between the two counterparties once the settlement amount has been paid. The contract period is merely one of the calculation parameters used to determine the settlement amount (FRAs are off-balance sheet instruments).

FRA terminology

Below a short listing of the terms used for the different elements and events of an FRA:

contract rate (or FRA rate)The interest rate the two contracting parties negotiate on trade date. This rate will be compared to the settlement rate when calculating the settlement amount. It starts on the settlement (d3) date and ends on maturity date (d4)
contract periodThe time between the settlement date and maturity date of the notional loan. This period can go up to 12 months.
currencyThe currency in which the FRA's notional amount is denominated.
fixing dateThis is the date on which the reference rate is determined, that is, the rate to which the FRA rate is compared.
FRA buyerBy convention, the buyer of an FRA is the contracting party that borrows at the FRA rate (contract rate).
FRA sellerBy convention, the seller of an FRA is the contracting party that lends at the FRA rate (contract rate).
master agreementUsually, counterparties sign a master agreement between each other before entering into an OTC contract because doing so without a master agreement in place would mean huge amounts of paperwork having to be generated and processed for each single deal.
maturity dateThe date on which the notional loan is deemed to expire.
notional amountThis is the notional sum for which the interest rate will be guaranteed and on which all interest calculations will be based.
reference rateThe interest rate index the FRA rate will be compared against in order to determine the settlement amount. This will generally be an IBOR-type rate index with the same duration as the FRA's contract period. (for example 6-month EURIBOR for an FRA in euros with a 6-month contract period).
settlement amountThe amount calculated as the difference between the FRA rate and the reference rate as a percentage of the notional sum, paid by one party to the other on the settlement date. The settlement amount is calculated after the fixing date, for payment on the settlement date.
settlement dateThe date on which the notional loan period (the contract period) begins and on which the settlement amount is being paid.
spot dateThe date on which the FRA. Usually two business days after the trade date.
trade dateThe date on which the FRA is negotiated between the two counterparties.
waiting periodThe period comprised between the value date (d1) and the settlement date (d3).

Calculation of the settlement amount of an FRA

The amount to be exchanged on settlement date — the settlement amount — is calculated as described below. For the sake of clarity, the calculation has been split into two parts, but normally it is one single calculation.

Step 1 — calculation of the interest differential

The interest differential is the result of the comparison between the FRA rate and the settlement rate. It is calculated as follows:

Interest differential = | (Settlement rate − Contract rate) | × (Days in contract period/360) × Notional amount

Step 2 — calculation of the settlement amount

As stated above, the settlement amount is paid upfront (at the start of the contract period), whereas interbank rates LIBOR or EURIBOR are for operations with interest payment in arrears (at the end of the loan period). To account for this, the interest differential needs to be discounted, using the settlement rate as a discount rate. The settlement amount is thus calculated as the present value of the interest differential:

Settlement amount = Interest differential / [1 + Settlement rate × (Days in contract period ⁄ 360)]

If the settlement rate is higher than the contract rate, then it is the FRA seller who has to pay the settlement amount to the buyer. If the contract rate is higher than the settlement rate, then it is the FRA buyer who has to pay the settlement amount to the seller. If the contract rate and the settlement rate are equal, then no payment is made.

The complete formula used to calculate the settlement amount is the following:

\[ S=C \cdot \frac{\left ( r_{set} — r_{fra} \right ) \cdot \frac{\left (d_{mty}-d_{set} \right )}{dbase}}{1+\left (\frac{\left (d_{mty}-d_{set} \right )}{dbase} \cdot r_{set} \right )} \]

Point on the formula to see its legend

To summarize:

  • If settlement rate > contract rate, the FRA buyer receives the settlement amount
  • If contract rate > settlement rate, the FRA seller receives the settlement amount
  • If settlement rate = contract rate, no settlement amount is being paid

The FRA market

FRAs are money market instruments, and are traded by both banks and corporations. The FRA market is liquid in all major currencies, also by the presence of market makers, and rates are also quoted by a number of banks and brokers.

Notation and quoting of FRAs

The format in which FRAs are noted is the term to settlement date and term to maturity date, both expressed in months and usually separated by the letter «x».

Examples:

2×6 — An FRA having a 2-month waiting period (forward) and a 4 month contract period.

6×12 — An FRA having a 6-month waiting period (forward) and a 6 month contract period.

Quotation of forward rate agreements

FRA are quoted with the FRA rate. Thus, if an FRA 2×8 in US dollars quotes at 1.50%, and a future borrower anticipates the 6-month USD Libor rate in two months being higher than 1.50%, he should buy an FRA.

Usages of an FRA

An FRA can be used for different purposes:

  • As already mentioned above, it can be used by market participants to hedge future borrowing or lending engagements against adverse movements in interest rates by fixing an interest rate today.
  • It can further be used for trading purposes in which a market participant wants to make profits his expectations on the future development of interest rates.
  • Lastly, it can be employed in arbitrage strategies where a market participant tries to take advantage of price differences between an FRAs and other interest rate instruments.

Example of an FRA

A corporation learns that it will need to borrow 1 000 000 $ in six months' time for a 6-month period. The interest rate at which it can borrow today is 6-month LIBOR plus 50 basis points. Let us further assume that the 6-month LIBOR currently is at 0.89465%, but the company’s treasurer thinks it might rise as high as 1.30% over the forthcoming months.

The treasurer choses to buy a 6×12 FRA in order to cover the period of 6 months starting 6 months from now. He receives a quote of 0.95450% from his bank and buys the FRA for a notional of 1 000 000 $ on April 8th.

Characteristics of the FRA known on trade date:

Trade date08/04/2016
Spot date (t+2)

Источник: https://www.iotafinance.com/en/Article-Forward-rate-agreements-FRAs.html

Расчёты по соглашениям о будущей процентной ставке | Энциклопедия финансовых рынков

forward rate agreement

Расчётную ставку обычно устанавливают за два рабочих дня до начала контрактного периода на основе какой-либо ставки-ориентира, например, LIBOR.

Расчётный платеж происходит в начале контрактного периода, а не при его истечении, как в случае депозитов денежного рынка. В этой связи расчётные платежи следует дисконтировать по действующей на рынке процентной ставке для определения текущей стоимости.

Размер расчётного платежа определяется с помощью двух формул, одна из которых используется, когда расчётная ставка выше ставки контракта, и, следовательно, покупатель FRA выплачивает разницу продавцу, а другая – когда расчётная ставка ниже ставки контракта, а компенсацию выплачивает продавец FRA.

Расчётная ставка выше ставки контракта:

Расчётная ставка ниже ставки контракта:

где:

  • L – расчётная ставка в виде числа, а не процента
  • R – ставка контракта в виде числа, а не процента
  • В – годовая база (360 или 365 дней)
  • D – контрактный период в днях
  • А – сумма контракта

Пример 1:

Дано: 10 апреля 2016 года руководство Компании приходит к выводу, что ей потребуются финансовые ресурсы на 3 месяца (92 дня) – с 16 июня по 15 сентября 2016 года. Задача: определить расчётный платеж, если на 10 июня 3-х месячная ставка LIBOR равна 7,25%, и Кто получит платёж?

Руководство полагает, что процентные ставки будут расти, и поэтому прибегают к хеджированию – покупают FRA у Банка на следующих условиях:

Сумма FRA$ 10 000 000
Дата фиксации12 июня 2016 года
Расчётная дата16 июня 2017 года
Дата погашения15 сентября 2017 года
Ставка контракта6,75% годовых
Годовая база360 дней

Решение:

Хотя Компания и приобрела FRA, для привлечения денег на срок с 16 июня по 15 сентября ей все равно придется выходить на денежный рынок, когда процентная ставка выросла до 7,25%. Но, поскольку процентные ставки повысились, Банк должен компенсировать Компании разницу.

Расчетный платёж определяется по формуле 13а:

После этого FRA прекратит свое действие, а руководство Компании может реинвестировать расчётный платеж в инструменты денежного рынка или занять денег в меньшем объеме: $10 000 000 – $12 545,34.

В любом случае руководство Компании привлекает деньги по текущей ставке LIBOR. Платёж по FRA – лишь субсидия, снижающая чистую стоимость заимствования.

Пример 2:

Дано: 10 апреля 2016 года руководство Компании приходит к выводу, что ей потребуются финансовые ресурсы на 3 месяца (92 дня) – с 16 июня по 15 сентября 2016 года. Задача: определить каким будет расчётный платеж, если на 10 июня 3-х месячная ставка LIBOR равна 6,5%? Кто получит платёж?

Решение:

Так как текущая стоимость кредита ниже ставки контракта, то платёж получит Банк, и рассчитывается такой платёж по формуле 13б:

Риски, связанные с соглашениями о будущей процентной ставке

Наряду с процентным риском, связанным с размером окончательного расчётного платежа по FRA, и кредитным риском, связанным со способностью сторон рассчитаться по FRA, существует ещё один риск, который также необходимо принимать во внимание.

Базисный риск – это риск того, что ставка предложения на лондонском межбанковском рынке депозитов (LIBOR), которая используется для определения расчётного платежа по FRA, будет отличаться от фактической процентной ставки хеджируемого базового займа, то есть хедж окажется неидеальным.

Процентные ставки по инструментам денежного рынка тесно увязаны со ставкой LIBOR. Однако некоторые события на рынке способны вызвать отклонение ставок отдельных инструментов от LIBOR.

В этой ситуации заёмщик, который использует для хеджирования контракт FRA, связанный со ставкой LIBOR, по истечении срока FRA вынужден выплачивать форвардный процент по базовому займу. Если процентная ставка по базовому займу поднимается выше ставки LIBOR, используемой для расчётов по FRA, доход заёмщика по FRA не покрывает его убытка.

Другими словами, если ставка по базовому займу отличается от процентной ставки, к которой привязан контракт FRA, то соглашение о будущей процентной ставке не обеспечивает идеального хеджирования.

Таким образом, риск получения убытка в результате неидеального хеджирования называется базисным риском.

Форвард-форвардные ставки

Во многих случаях для хеджирования на случай изменения процентных ставок в более долгосрочной перспективе используются стрипы контрактов FRA. Стрип (strip) – это ряд последовательных контрактов.

Например, для хеджирования периода продолжительностью 12 месяцев может быть использован стрип из четырех контрактов FRA: 1 х З; 3 x 6; 6 x 9; 9 x 12.

Возникает вопрос, какой будет эффективная ставка за весь период при использовании стрипа FRA, когда каждый из контрактов FRA имеет свою ставку?

Допустим, стрип из двух FRA охватывает два периода: от 0 до n и от 0 до N. Доходность периода от n до N можно определить по формуле на основе процента к платежу за указанные временные периоды:

Отсюда:

Определить эффективную годовую процентную ставку можно по следующей формуле:

где:

  • L 0 х 3 –текущая ставка LIBOR или ставка-ориентир
  • L 3 х 6, L 6 х 9, L 9 х 12 – ставки FRA для периода 3 х 6, 6 х 9, 9 х 12

Пример 3:

Руководство Компании желает захеджировать процентные ставки в течение 6-месячного периода, который начинается через 6 месяцев, то есть защита форвардной позиции 6 x 12.

В этом случае, руководство Компании может использовать для этого соглашение о будущей процентной ставке 6 x 12.

Однако стрип из двух 3-х месячных FRA (6 x 9 и 9 x 12) обеспечивает большую гибкость, так как при необходимости он может изменить условия хеджа для периода, начинающегося через 9 месяцев. Стрип также ограничивает котировку FRA 6X12.

Компании через 6 месяцев потребуется заём в $5 000 000 на 6 месяцев. По мнению руководства к моменту заимствования процентные ставки должны вырасти. Оно анализирует котировки банков, предлагающих FRA со ставками на основе 3-х месячной LIBOR.

FRA Банк А Банк А

6 х 9 (91 день)6,21 – 6,156,23 – 6,18
9 х 12 (92 дня)6,28 – 6,226,30 – 6,25

Руководство Компании принимает цены бид банка А, поскольку они ниже, и покупает стрип из двух FRA: 6 x 9 плюс 9 x 12. Это позволяет зафиксировать процентные ставки на 6 месяцев, то есть на весь заёмный период.

Эффективная ставка FRA для стрипа рассчитывается по формуле 15:

Источник: http://finmarkets.info/4-3-raschjoty-po-soglashenijam-o-budushhej-procentnoj-stavke/

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