Module Title: Interest Rate Risk
Learning Objectives: After reading this chapter you will be able to :
• Identify opportunities to reduce interest rate exposure
• Evaluate ways to manage interest rate risk with forward rate agreements, futures, and
swaps
• Assess the use of interest rate options, including swaptions
Module Outline:
Interest rate risk is more difficult to manage than the risk arising from market variables
such as equity prices, exchange rates, and commodity prices. One complication is that there are
many different interest rates in any given currency (Treasury rates, interbank borrowing and
lending rates, swap rates, and so on). Although these tend to move together, they are not
perfectly correlated. Another complication is that we need more than a single number to describe
the interest rate environment. We need a function describing the variation of the interest rate
with maturity. This is known as the term structure of interest rates or the yield curve.
A key risk management activity for a bank is the management of net interest income. The
net interest income is the excess of interest received over interest paid. It is the role of the assetliability management function within the bank to ensure that the net interest margin, which is net
interest income divided by income- producing assets, remains roughly constant through time.
This section considers how this is done.
Types of Rates
In this section, we explain a number of interest rates that are important to financial institutions.
1. Treasury rates are the rates an investor earns on Treasury bills and Treasury bonds.
These are the instruments used by a government to borrow in its own currency. Japanese
Treasury rates are the rates at which the Japanese government borrows in yen, U.S.
Treasury rates are the rates at which the U.S. government borrows in U.S. dollars, and
so on.
2. LIBOR is short for London interbank offered rate. It is an unsecured short-term borrowing
rate between banks. LIBOR rates are quoted for a number of different currencies and
borrowing periods. The borrowing periods range from one day to one year. LIBOR rates
are used as reference rates for hundreds of trillions of dollars of trans- actions throughout
the world. One popular and important derivative transaction that uses LIBOR as a
reference interest rate is an interest rate swap.
3. LIBOR vs. Treasury Rates - Risk-free rates are important in the pricing of financial
contracts. Treasury rates might be thought to be natural rates to use as risk-free rates,
but in practice they are regarded as artificially low because:
1. The amount of capital a bank is required to hold to support an investment in
Treasury bills and bonds (typically zero) is substantially smaller than the capital required
to support a similar investment in other very-low-risk instruments.
2. In the United States, Treasury instruments are given a favorable tax treatment
com- pared with most other fixed-income investments because they are not taxed at the
state level.
4. The OIS Rate An overnight indexed swap (OIS) is a swap where a fixed interest rate for
a period (e.g., one month, three months, one year, or two years) is exchanged for the
geometric average of overnight rates during the period.4 The relevant overnight rates are
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the rates in the government-organized interbank market where banks with excess
reserves lend to banks that need to borrow to meet their reserve requirements.
United States – Fed fund rate
Europe - EONIA (Euro OverNight Index Average)
UK - SONIA (Sterling OverNight Index Average)
5. Repo Rates Unlike LIBOR and federal funds rates, repo rates are secured borrowing
rates. In a repo (or repurchase agreement), a financial institution that owns securities
agrees to sell the securities for a certain price and to buy them back at a later time for a
slightly higher price. The financial institution is obtaining a loan, and the interest it pays is
the difference between the price at which the securities are sold and the price at which
they are repurchased. The interest rate is referred to as the repo rate.
6. SOFR (the secured overnight financing rate) - s an interest rate set based on the cost of
overnight borrowing for banks as defined by U.S. Treasury repurchase agreements – also
called repos. It’s the front runner being recommended by the Alternative Reference Rates
Committee (ARRC) to serve as the replacement for the London Interbank Offered Rate
(LIBOR), which is being phased out at the end of 2021 as a result of a manipulation
scandal.
Exposure Reduction
Although it might be possible to manage interest rate exposure without derivatives, legal,
tax, and regulatory ramifications must be taken into consideration, particularly in foreign
countries or for cross-border transactions. These may prohibit such transactions or reduce or
eliminate the benefit. The following techniques have been used to reduce interest rate exposure
and the resulting need for derivatives:
• Global cash netting/inhouse bank
In regard to financial markets, the purpose is essentially to minimize transactions and
distinguish remuneration in multiparty agreements
• Intercompany lending
- is an amount lent or advance given by one company (in a group of companies) to
another company (in the same group of companies) for various purposes, including to
help the cash flow of the borrowing company or to fund the fixed assets or to fund the
normal business operations of the borrowing company, which gives rise to interest
income to lending company & interest expense to borrowing company.
• Embedded options in debt
- An embedded option is a feature of a financial instrument that lets issuers or holders
take specified actions against the other party at some future time. Embedded options
are provisions included in some fixed-income securities that allow investors or the
issuer to do specific actions, such as call back (redeem) the issue early.
• Changes to payment schedules
- Changes to payment schedules may permit an organization to maintain cash balances
for longer periods, reducing the need for funding and therefore exposure to interest
rates:
1. Changes to supplier/vendor payment schedules may permit a longer payment
cycle, reducing the need for borrowing. Alternatively, payments may be made on
behalf of other parts of the organization, which may permit netting to be used.
2. Changes to customer payment schedules may increase the speed with which
funds are collected, reducing the need for borrowing. Changing the methods used
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by customers to pay, such as encouraging electronic alternatives to paper checks,
may also speed collections.
3. Changes to contractual long-term payments, such as royalties and license
agreements, to quarterly from annually.
• Asset–liability management
- Asset–liability management involves the pairing or matching of assets (customer loans
and mortgages in the case of a financial institution) and liabilities (customer deposits)
so that changes in interest rates do not adversely impact the organization. This practice
is commonly known as gap management and often involves duration matching.
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Asset/liability management is the process of managing the use of assets and cash flows
to reduce the firm’s risk of loss from not paying a liability on time. Well-managed assets
and liabilities increase business profits. The asset/liability management process is
typically applied to bank loan portfolios and pension plans. It also involves the economic
value of equity.
Derivative Transaction use to Mitigate Risk for Interest rates
1. Forward Rate Agreements
A forward rate agreement (FRA) is an over-the-counter agreement between two parties,
similar to a futures contract, to lock in an interest rate for a short period of time. The period is
typically one month or three months, beginning at a future date.
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Borrower buys an FRA to protect against rising interest rates
Lender sells an FRA to protect against declining interest rates
How does it work?
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At the beginning of the period covered by the FRA, the reference rate is compared
to the FRA rate.
If the reference rate is higher, the FRA seller pays a compensating payment (the
settlement amount) to the FRA buyer.
If the reference rate is lower, the FRA buyer pays the FRA seller.
The notional contract amount is used for calculating the settlement amount but is
not exchanged.
Payment of the settlement amount usually occurs at the beginning of the contract
term, ergo, settlement amount is discounted and the present value of the interest
rate differential is paid.
The following information applies to FRAs:
1. The forward term of an FRA is the time prior to the beginning of the FRA.
2. The contract term is the time covered by the FRA.
3. FRA reference rates are posted on major market information services and commonly are
LIBOR (London interbank offered rate).
4. The settlement amount is the payment to the FRA seller or buyer, based on the differential
between the reference rate and the FRA rate at the beginning of the contract period,
prorated over the term of the FRA, and usually discounted.
5. The maturity of the FRA is the end of the contract term.
Closing Out a Forward Rate Agreement
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FRAs can be closed out at current market value. Since both parties have an obligation
under an FRA, closing out the contract involves unwinding it through an offsetting transaction.
The buyer of an FRA will sell an offsetting FRA, while the seller of an FRA will buy an offsetting
FRA, with a resultant gain or loss.
2. Interest Rate Futures
Interest rate futures are exchange-traded forwards. They permit an organization to
manage exposure to interest rates or fixed income prices by locking in a price or rate for a future
date. Transacted through a broker, there are commissions to buy or sell and margin
requirements. The risk of dealing with other counterparties is replaced with exposure to the
exchange clearinghouse
1. Bond Futures - is a contractual obligation for the contract holder to buy or sell a Bond on
a specified date at a predetermined price. The buyer (long position) of a Bond Future is
obliged to buy the underlying Bond at the agreed price on expiry of the future. The seller
(short position) of a Bond Future is obliged to deliver the underlying bond at the agreed
price on expiry of the Future.
Examples :
US Treasury Notes Futures , Australian Bond Futures
Closing Out a Futures Contract
At expiry, a futures contract can be settled by offsetting it with another futures contract, or by
delivering or accepting delivery of the underlying, as permitted. For delivery against bond futures
contracts, since deliverable bonds have different coupons and maturities, a conversion factor is
used. Exchanges list deliverable bonds and their conversion factors.
Prior to delivery, a purchased futures contract can be closed out by selling a futures contract
with the same delivery date. Similarly, a sold futures contract can be offset by buying a futures
contract with the same delivery date.
3. Interest Rate Swaps
An interest rate swap is an agreement to exchange (swap) interest payment streams of
differing characteristics denominated in the same currency. The interest payments are calculated
by reference to an agreed amount of notional principal, although at no time is this amount
exchanged between the counterparties.
Assumptions:
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When interest rates are expected to fall, market participants move to floating
interest rates, and there is downward pressure on swap spreads.
When interest rates are expected to rise, market participants will move to borrow
at fixed interest rates, putting upward pressure on swap spreads.
 Asset Swaps
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o swap to transform an asset’s income stream
o it allows investors to change the interest rate structure of their revenue streams
without changing the structure of the underlying asset.
o An asset swap is a derivative contract between two parties that swap fixed and
floating assets.
o In an asset swap, an investor will pay a fixed rate to the bank and receive a
floating rate in return.
o Asset swaps serve to hedge against different risks on the reference asset.
Let’s break the swap down into two steps.
There are two main parties involved: 1) the buyer/investor, and 2) the bond seller.
Step 1: To start, the bond buyer buys the bond from the bond seller for the “dirty price” (full price
at par plus accrued interest).
Step 2: The bond buyer and seller will negotiate a contract that results in the buyer paying fixed
coupons to the seller equivalent to the bond coupon rates in exchange for the seller providing
the buyer with LIBOR-based floating coupons. The value of the swap would be the spread that
the seller pays over or under LIBOR. It is based on two things:
The coupon values of the asset compared to the market rate.
The accrued interest and the clean price premium or discount compared to par value.
The swap shares the same maturity as the original coupon. It means that in the event of the
bond defaulting, the buyer will still receive the LIBOR-based floating coupon +/- the spread from
the seller.
Let’s look at a specific example with actual numbers. We are looking at a risky bond with the
following information.
Currency: USD
Issue: March 31, 2020
Maturity: March 31, 2025
Coupon: 7% (annual rate)
Price (Dirty)*: 105%
Swap Rate: 6%
Price Premium: 0.5%
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Credit Rating: BBB
*Dirty Price: The cost of a bond that includes accrued interest based on the coupon rate.
Let us break down our example with the steps listed above.
Step 1: The buyer will pay 105% of the par value, in addition to 7% fixed coupons. We assume
the swap rate is 6%. When the buyer enters into the swap with the seller, the buyer will pay the
fixed coupons in return for the LIBOR +/– spread.
Step 2: The asset swap price (the spread) is calculated through the fixed coupon rate, the swap
rate, and the price premium. Here, the fixed coupon rate is 7%, the swap rate is 6%, and the
price premium during the swap’s lifetime is 0.5%.
Asset Spread = Fixed Coupon Rate – Swap Rate – Price Premium
Asset Spread = 7% – 6% – 0.5% = 0.5%
Steps 1 and 2 will result in a net spread of 0.5%. The asset swap will be quoted as LIBOR +
0.5% (or LIBOR plus 50 bps).
Let us say, for example, that the bond defaults in 2022 even though there are still three years
left until maturity in 2025. Remember that the swap shares the same maturity as the coupon. It
means that although the bond will no longer pay coupons, the seller will continue paying the
buyer with the LIBOR + 0.5% until 2025. It an example of the buyer successfully hedging against
credit risk.
https://corporatefinanceinstitute.com/resources/derivatives/asset-swap/
 Basis Swaps
A basis swaps is an interest rate swap that involves the exchange of two floating
rates, where the floating rate payments are referenced to different bases. Both legs of a
basis swap are floating but derived from different index rates (e.g. LIBOR 1 month vs 3
month). Basis swaps are settled in the form of periodic floating interest rate payments.
They are quoted as a spread over the reference index. For example, 3-month LIBOR is
frequently used as a reference. Spreads are quoted over it.
A basis swap can be used to limit interest rate risk that a firm faces as a result of
having different lending and borrowing rates. Basis swaps help investors to mitigate basis
risk that is a type of risk associated with imperfect hedging. Firms also utilize basis swaps
to hedge the divergence of different rates. Basis swaps could involve many different kinds
of reference rates for the floating payments, such as 3-month LIBOR, 1-month LIBOR, 6month LIBOR, prime rate, etc. There is an active market for basis swaps. This
presentation gives an overview of interest rate basis swap product and valuation model.
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Zero-Coupon Swaps
A zero-coupon swap is a cash flow exchange in which the stream of floating
interest-rate payments is made periodically, as it would be in a standard swap, but the
stream of fixed-rate payments is made as a single lump-sum payment at the swap’s
maturity date, rather than on a periodic basis throughout the swap’s life.
When a zero-coupon swap contract matures, the fixed side of the swap is paid in
one single payment. The variable side of the swap continues to make periodic payments,
just as it would in a standard swap. Because the fixed leg is paid in one lump sum,
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evaluating a zero-coupon swap requires calculating the present value of those cash flows
using the implied interest rate of a zero-coupon bond.
A zero-coupon swap is a type of derivative contract in which two parties sign into
an agreement. One party provides floating payments that fluctuate in response to the
future publication of the interest rate index on which the rate is based (e.g. LIBOR,
EURIBOR, etc.). The other party pays the other party interest at an agreed-upon fixed
rate.
The fixed-rate is linked to a zero-coupon bond, which pays no interest during the
bond’s life but is projected to make a single payment at maturity. In practice, the fixedrate payment is determined by the swap’s zero-coupon rate. The bondholder on the fixed
leg of a zero-coupon swap is responsible for a single payment at maturity, whereas the
party on the floating leg is responsible for periodic payments during the swap’s contract
term. Zero-coupon swaps, on the other hand, can be structured in such a way that both
variable and fixed-rate payments are made in one lump sum.
https://payrollheaven.com/define/zero-coupon-swap/
4. Forward Interest Rate Swaps
A Forward interest swap is an agreement whereby two parties exchange or swap
assets or cash flows from investments at a specified date in the future. The unique aspect
of a forward swap is that the exchange takes place at some point in the future - as
opposed to at the time of signing the swap agreement.
Forward interest swaps are commonly used in interest rate swap agreements. This
is because investors may have a different projection about what interest rates will do in
the future.
(https://thebusinessprofessor.com/en_US/investments-trading-financialmarkets/forward-swap-definition)
Closing Out an Interest Rate Swap
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Interest rate swaps must be settled at market value to be terminated.
The market value of a swap at any time after its commencement is the net present value
of future cash flows between the counterparties.
There are several ways to alter or eliminate an existing interest rate swap:
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Offset the swap with another that will produce the required payment streams.
Cancel the existing swap by paying or receiving a lump sum representing the net
present value of remaining payments. This may require a cash payment if the swap has
a negative value.
Extend the swap by blending it with a new one (blend-and- extend). This embeds the
cost of closing out the swap in the new periodic swap payments.
Assign the swap to another party that will continue to make and receive payments under
the original swap agreement until maturity. The counterparty assigning the swap will
either pay to, or receive from, the new counterparty a lump sum that reflects the net
present value of all remaining payment streams.
5. Interest Rate Options
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An interest rate option gives a buyer the time-limited right to take delivery of an
interest rate product at a pre-set rate in the future, in exchange for a premium. Common
types include: swaptions, which give the holder the right to enter an interest rate swap;
caps and floors, where the buyer receives payments when the rate is above or below the
pre-set strike price; and bond options, which give the holder the right to buy or sell a
physical bond.
IRO premiums are determined by the same factors that affect other options:
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current market rate of the underlying
strike price or rate
time until expiration
market volatility, and
whether it is a call or put.
A call, sometimes called a borrowers' option, increases in value as interest rates
rise; a put, sometimes called a lenders' option, increases in value if interest rates fall. The
expiry date is when the option can be exercised, which is 2 days before the settlement
date, sometimes known as the value date, unless the currency is sterling, in which case
the option is exercised on the settlement date.
Interest-rate options differ from equity options in that they generally cover an extended
duration rather than a single date. Furthermore, because interest rates have a major effect on
the economy, central banks prevent interest rates from reaching extremes, so the variation of
interest rates is much less than what could possibly occur with equities or other types of options.
The strike of most options are referred to a strike prices, but the strike of interest-rate options
are often called strike rates, since these options go into the money if the interest rate rises above
or below the strike rate, depending on the option type.
 Caps and Floors
o interest-rate cap sets a maximum interest rate
o interest-rate floor sets a minimum interest rate
o One of these contracts in a cap is called a caplet
o a single contract in a floor is a floorlet
o Interest rate caps are sometimes called interest-rate calls because they go into
the money if interest rates rise above the strike rate; likewise, interest-rate floors
are sometimes called interest-rate puts because they go into the money when
interest rates decline below the strike rate
 Interest Rate Collar
o interest-rate collar sets both a maximum and minimum interest rate by combining
a cap and a floor
o Collars are often used when caps (or floors) are deemed too expensive.
o Interest-rate collars are generally bought as a package from an option dealer.
o If the reference rate is above the cap rate, then the dealer pays the buyer the net
difference between interest rates; if the reference rate is below the floor, then the
buyer must pay the dealer the difference between the floor rate and the market
rate at expiration multiplied by the notional principal; if the reference rate falls
between the floor and the cap, then no payment is made by either party.
Example: Calculating the Price of a Caplet
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If:
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notional principal = $100 million
strike rate = 5% per annum
contract period = 6-month term
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expiration: 6 months after purchase
premium rate = 0.25% per annum
Then:
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Caplet Premium = $100 million × 0.25%/2 = $125,000
If, at the expiration of the European option, the US dollar libor rate is 6%, then this must be
paid:
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Settlement Sum = $100 Million × (6% − 5%)/2 = $500,000
If the libor rate were 4% instead of 6%, then the option holder would simply let the option expire.
https://thismatter.com/money/options/interest-rate-options.htm
 Swaptions
o A Swaption provides you with the right but not the obligation to enter into an
Interest Rate Swap at a predetermined interest rate on a fixed date in the future.
o Swaption premium is paid by the swaption buyer to the swaption seller, typically
as a percentage of the notional amount of the swap.
 The terms receiver and payer refer to the fixed rate payment stream in a
swap:
 The buyer of a payer swaption has the right to enter a pay- fixed
(receive floating) swap at the strike rate.
 The buyer of a receiver swaption has the right to enter a receivefixed (pay floating) swap at the strike rate.
 Exchange-Traded Options
o Exchange-traded options may have a futures contract as the underlying interest
o interest rates or options on interest rate futures can be used to construct an interest
rate cap, floor, or collar
o Options may be settled in cash or with the underlying asset or futures contract,
depending on exchange rules.
Closing Out an Interest Rate Option
In general, if an interest rate option is no longer required and there is time remaining to expiry,
it can be sold at market value. For a strategy involving several purchased options, market value
is the total of the options that comprise it, and the maximum loss is the cost of the options.
o In the Money – Gain - The phrase in the money (ITM) refers to an option that
possesses intrinsic value.
o Out of the Money – Loss - A call option is OTM if the underlying price is trading
below the strike price of the call. A put option is OTM if the underlying's price is
above the put's strike price
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o At the Money - have a strike price that is equal to its underlying stock's market
price. At-the-money options have no intrinsic value, but because they have time
value, they could potentially earn profits before they expire
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