Interest-rate risk substantially affect the values of the assets and liabilities of most corporations and is often a dominant factor affecting the values of pension funds, banks and many other financial intermediaries.

1. Interest -Rate Risk and Hedging with
Derivative Instruments.
Interest-rate risk substantially affects the values of the assets and liabilities of
most corporations and is often a dominant factor affecting the values of
pension funds, banks and many other financial intermediaries.
How Does Interest -Rate Risk Arise?
Interest rate risk is the risk that value of a fixed income security held by an
institution will change, as a result of a change in market interest rates.
As rates go up in the wider market. the value of owing an instrument offering a
fixed rate of interest naturally falls (Compared to the value of owning newly
issued fixed-income securities that pay a higher coupon).To the extent that the
position is not perfectly offset by changes in the value of other instruments in
the institution's portfolio- the firm will suffer an economic loss. Open
positions arise most often from differences in the maturities, nominal values.
and rate reset dates between instruments and cash flows that are asset like
longs, and those that are liability-like shorts).A major mismatch between the
maturities of assets and liabilities can lead to liquidity risk. The degree to
which such exposures threaten a firm depends not only on the amount held
and each position's sensitivity to interest-rate changes. But also on the degree
to which these sensitivities are correlated within portfolio and more broadly
across trading desks and business lines.

2. Even when instruments seem first sight to large offset each other economic
exposure, an imperfect correlation between offsetting instrument both within
the same maturity for different issuers and across the yield curve, can generate
significant risks, The yield curve, often called the term structure of interest
rates, measures the relationship between the discount rates, and the time to
maturity of bonds.
Risk Managers often refer to something that they call " curve risk" curve risk
arises in portfolios when long and short positions of different maturities are
effectively hedged against a parallel shift in yields, but are not hedged against
a change in the shape of the yield curve. Parallel shifts occur when a shock in
the market has an equal effect on yield of instrument with different maturity
dates, conversely, the yield curve is said to "change Shape" when a shock in
the market has a stronger effect on, say the returns of shorter-dated
instruments than it has on the returns of longer dated instruments . this may
affect the slope of the yield curve and its curvature.
Curve risk is not the only worry. Even if offsetting positions have the same
maturity, "basis" risk can arise if the rates of the positions are imperfectly
correlated. For example, three month Euro dollar instruments and three
month treasury bills both naturally pay three month interest rates. However,
these rates are not perfectly correlated with each other. And spread between
their yields may vary over time. As a result, a three month Treasury bill funded
by three months Eurodollar Deposit Represents an imperfectly Hedged
position.

3. Bond Price And Yield To Maturity
Bond portfolio managers and fixed income derivatives traders keep a close eye
on their screens for moves in the yield curve that effect the value of bonds and
other fixed-income securities. The pay close attention to financial
announcements. Such as comments from the Government Federal Reserve.
That may signal a change in the fed funds rate, which in turn, will change the
shape of the yield curve and drive bond prices up or down.
The Pricing of Bonds is based on the present value concept. That is we need to
work out the value that the future cash flows associated with a security might
have today. This clearly involves discounting the future cash flows to reveal
their present values but what discount rate should we use? The problem is
complicated because different discount rates may apply to different kinds of
bonds with different maturities. interest rates vary, and usually are an
increasing function of time to maturity, another factor that effects the relevant
discount rates is the risk of the bond and especially, its credit risk, the
probability of a default and the extent of the loss that is expected in such an
event. A further factor that affects bond prices is liquidity risk .The risk that
the market for the bond might not be liquid enough for the seller to receive a
"Fair" price at the time of sale.
let us start with the valuation of say a 10 year government bond , this helps to
clarify the problem, because government bonds can essentially be regarded as
being free of credit risk. The bondholder is promised an annual fixed coupon
and the payment of the principal amount at the maturity of bond. So if the
notional amount (Principal) is $1000 and the coupon rate is 5%, the

4. bondholder will receive $50 per year for the first nine years and the end of the
10 year period the sum of the last coupon and the principal $1050.
The problem we face in assessing the present value of the bond is that $50
received after, say eight years is necessarily worth less than $50 received at the
end of the first year, if only because of the opportunity cost associated with
obtaining cash later rather than earlier.
The value of bond can therefore be found by discounting all the expected
future payments by the relevant discount factors.(these discount factors are
also referred to as "zero-coupon rates" referring to zero coupon bonds, which
have only a single bullet payment at maturity).
The Risk factor Sensitivity Approach
At the trading desk level and for specific financial market, traders long ago
developed specialized measures of the sensitivity of an instrument to changes
in the value of primary risk factors. Depending on the market such primary
risk factors might take the form of interest rates, yield to maturity, volatility,
stock price, and so on. In the case of fixed income products a popular risk
measure among traders ins DV01 also known as "value of an 01" DVO1 is a
trader abbreviation for the change in the value of a security after a change in
yield or a change in interest rate of 1 basis point this is 1 percent of a
percentage point, .0001.
The DV01 measure is consistent with the conventional “duration" analysis of
bond, which is often thought of as the average life of bond. more formally it is

5. weighted average of the dates (expressed in years) of each cash flow, where the
weights are the present value of the cash payment divided by the sum of
weights. i.e., the price of bond itself.
The modified duration of a bond a measure often used in bond calculation is
the duration divided by 1 plus the yield to maturity of the bond.
Consider, for example a bond trading a $90 with a yield to maturity of 5% and
modified duration of eight years. According to this approximation, a 5- basis
point increase in yield result in a price decline of .05% x 8= .04%
the longer the maturity of the bond, the higher its duration and the more
sensitive the price of bond to a change yield.
Instrument for Hedging Interest Rate Risk
What kind of instrument and strategies can be used to manage the risks that
we have measured the answer off course lies in the world of derivatives
contracts? Such as swaps, forwards, futures, and options, whose values are
derived from various underlying assets or rates?
Over the years, and especially since the 1970s, many different kinds of
derivative instruments with varying levels of complexity and customization
have been invented to hedge financial risk. Some instruments are traded on
formal exchange around the world. Such as the Treasury bond futures traded.
These exchange traded derivatives are fairly simple and standardization
contracts, backed by a clearinghouse to ensure contract integrity. but

6. most derivatives are not traded on exchanges, but instead are private bilateral
contracts between a dealer and a customer knows as over the counter or OTC
derivatives. Such OTC derivative contracts can be highly customized to the
needs of a customer the drawback is that they are less liquid than exchange
traded futures. And their execution is backed only by the capital of the
provider or dealer. This is why the key player in the OTC derivatives market
are all financial institutions with a good credit standing. Interest rate swaps,
swaptions, forward rate agreements caps, floors and collars. The key
derivative instruments used by investors, corporations, and financial
institutions to manage interest rate risk are all traded over the counter.
The size of government debt, on a worldwide basis, is enormous. Coupled with
corporate bonds and bank loan portfolios, it gives rise to a huge pool of assets
and liabilities that are sensitive to changes in interest rates. so it is not
surprising to find that the OTC market for interest rate derivatives is also very
sizable. Press headlines tend to concentrate on risk management failures and
speculation in the derivative markets, there is no doubt that interest rate
derivatives are an essential tool for managing risk. The greater use of
derivatives by banks to shift their interest rate risk, and they have added
significantly to the banking sector's strength.
Forward and Futures Contracts
Forward contracts allow its buyer to lock in today the future price of an asset
such as an interest rate linked security, a currency a stock or a commodity.
The buyer has to pay the agreed-upon price on the settlement date. Whether
or not the rate or the price of the underlying asset has moved in his or her

7. favor. The seller is also required to deliver the asset on the settlement date,
whatever the asset's price on the spot market. There is no upfront fee to pay in
a forward transaction and no cash changes hands before the settlement date.
Forward contracts are essentially OTC instruments, and therefore can be
highly customized. Some contracts are settled through the delivery of the
underlying asset against payment of the agreed upon price (forward
price).Other contracts, such as interest rate risk forwards are cash settled. i.e.
one party has to pay the other the difference between the contract value of the
forward and its spot value at the maturity date.
A future contract is simply a forward contract that is traded on an exchange.
Unlike forwards, futures have standardized terms, such as the underlying cash
instrument or rate. The notional amount. And maturities.(this standardization
is essential if the exchange market in the contract is to be liquid) At its
initiation, a futures contract has zero value. But anyone buying a future
contract must deposit an initial payment. Called margin, with the
clearinghouse of exchange. The every day, the contract is "market to Market"
and daily installments, positive or negative, that correspond to the change in
the daily value of the futures price (determined in the marketplace) are paid.
The total of the daily installment and the payment at maturity equal the
futures price set when the contracts was initiated.
Both forward and futures allow investors to protect open positions from
adverse price movements any losses and gains on the open positions are offset
by the payoff of the derivatives contracts. In the case of interest-rate- forwards
or futures, if the actual interest rate at the maturity of the contracts is different

8. from the predetermined rate, money is paid or received, depending on
whether the difference is positive or negative.
In practice there is slight wrinkle in the definition of contracts on short-term
interest rates. For example, a futures contract on a one year T-bill rate is
defined as 100 minus the promised interest rate. Thus if the predetermined
future rate is 2.5 percent, then the contract is on a predetermined price of 97.5
, if at the end of the year ,the actual rate on a one year T-bill is 3.2 percent, the
realized value is then 96.8. In such a case the holder of the long position will
be paid by the seller of the contract the sum of 97.5 - 96.8=.7 per unit of
contract.
Such a contract allows a company to hedge a "one-period" rate change and is
similar to the forward rate agreement (FRA) contracts that are traded on the
OTC markets. FRA contracts are very popular with short term borrowers who
are trying to fix today the effective interest rate they will have to pay at a
future date.
The contracts just described are all "Cash Settled" at maturity meaning that
cash is paid by the losing party to the gaining party. In the case of some
futures contracts on long term rates. However, settlement is made by
delivering specific long-term bonds.
Futures, forwards, and FRA contracts offer the investor many opportunities to
hedge future rate changes, and to fix future rates at the present time. They are
traded in very competitive markets, and the bid/offer spread for these OTC
contracts is usually very narrow.

9. Swaps
Another simple instrument for hedging interest-rat risk, and possibly the most
frequently used. Is the interest rate swap. A swap is an OTC agreement
between two parties to exchange the cash flows of two different securities
throughout the life of the contract. It can be viewed as a series of forwards and
as with forwards, the contracts is binding on both sides of the transaction
(Whether or not the contracts has evolved in one party's favor).
Interest rate swaps are very flexible hedging instruments. They are used by
treasurers in asset and liability management and by bond portfolio managers
to reduce or extend the duration of an open position.
The most common form of interest rate swap is the fixed floating interest rate
swap, where the fixed side pays a fixed interest rate on a notional amount $1
million, quarterly or semiannually, and the floating side pays a floating rate on
the same notional amount. The reference rate on the floating side might be
LIBOR, the rate in the commercial paper market or any other reference agreed
upon by the parties to the contracts. There is no exchange of principal, as the
principal on both sides of the swap cancels out both at the inception and at the
maturity of the contract.
In a currency swap, on the contrary, both sides of the transaction exchange the
principal amount. Denominated in difference currencies, both at the start and
at the maturity of the transaction. The exchange rate for the two currencies is
decided when the swap is initiated, so that both sides are locked into the
future exchange rate. At intervals (monthly, quarterly, semiannually and so

10. on) throughout the life of the currency swap both sides, exchange interest rate
payments either fixed or floating ,denominated in the relevant currencies.
As is the case with forwards and futures, no up-front fee is payable when a
swap is initiated, as ll swap transactions are priced initially so that the net
present value (NPV) of both legs of the swap is the same. As times goes on and
interest rates vary, the NPV of both legs of the swap varies and the difference
between the NPVs can become negative or positive. If interest rates rise, the
cash flows on the floating leg increase. As does the contracts NPV, conversely
the NPV of the fixed leg declines.
Interest rate swaps are used by corporations or financial institutions to change
the nature of their payments on loans either from fixed to variable rates or
from variable to fixed rates, depending on the nature of the corporation's
income stream. Swaps are a convenient tool for managing the interest-rate
risks implied by the company's forecasts of interest-rate behavior, if interest
rates are expected to rise sharply, the company will try to fix interest
payments, in a declining interest rate environment, and the company will tend
to convert fixed rates into variable rates.
For example, imagine that parties A and B enter into a five-year interest rate
swap with a notional value of $100 million. Party A will pay party B each year,
at year-end, a sum equal to $100 million times a fixed interest rate. say 4
percent and will receive from party B a sum equal to $100 million times the
one year T-Bill rate plus a spread of say 1%.so each year a fixed amount of $4
million to party B, while party B pays an amount determined by the variable
rate (T-bill rate at the beginning of the period plus 1 percent)
In practice, there is a netting procedure, and only the difference is paid, so it
the T-bill rate at the beginning of the year is less than 3 percent. Party A pays

11. party B the difference between 4 percent and the T-bill rate plus 1 percent
times $100 million. for example, if the one year T-bill rate is 2.5 percent. Party
A will pay party B [.04-(.025-.01)] x $1 million= $500000, if the one -year T-
bill rate is 3.8 percent, then party B will pay Party A the sum of [(.038+.010) -
.04] x $1 million =$800000
Swap transactions are often used by corporate treasurers as a way of bridging
the gap that tends to exist between the particular needs of a company and the
needs of the market. For example, a treasurer may for practical reason issue a
five year bond denominated in Swiss francs, paying a fixed coupon, also in
Swiss francs, although his preferred exposure might be in U.S.dollars floating
with a LIBOR reference. His preferred exposure can be achieved by means of
a currency swap. On one side of the transaction, the treasurer receives the
cash flows of the bond issued in Swiss francs on the other side of the
transaction he pays floating LIBOR.
Interest rate and currency swap are the major components of the OTC
derivatives market. But the basic principle of swapping has been applied to all
assets classes, such as equities and commodities. Asset swap have become very
popular, as they allow investors to transfer the cash flows and the risk
associated with various kind of assets to other market players in exchange for
floating interest payments, usually based on LIBOR.

12. Options: Calls, Puts, and Exotics
Call options are contracts that allow the buyer to purchase the underlying
instrument (say a particular bond) at a predetermined price (the striking or
exercise price) during a given period or at the maturity date. An option that
can be exercised only at the maturity of the contract is termed a “European"
option. while one that can be exercised at any time up to and including
maturity date, is termed an "American" option. Call options give the buyer the
right to exercise the option when the future prices movement of the
underlying bond or rate is favorable to the buyer i.e. when the price of the
underlying instrument at the exercise time is above the predetermined
exercise price. But the purchaser of an option, unlike the counter party to a
forward, future, or swap, may allow the contract to expire without exercise.
For this one-sided right, the buyer must pay a premium.
It is important to emphasize the difference between purchasing a call option
and purchasing a future or forward contract. The futures must be executed at
maturity at the agreed-upon terms. Whereas the call may end exercised if the
price goes against the buyer. Another important difference is that while the
buyer of a call pays the seller of the contract a price that reflects the value of
the right. Futures and forward contracts have zero value at initiation. the
futures price for the futures transaction is set at such a level that the contract
has a zero present value.
A Put option is the opposite of a call, it gives the holder the right to sell the
underlying bond at a predetermined price, at any time up to (American put) or
exactly and only at (European put) the maturity date. A stand alone put option

13. on a bond is therefore a bet on the decline in the value of the bond (
or equivalently, a bet on an increase in interest rates) put option also allow
the holder of an open position to insure against a loss of value. The open
position and the option "hedge" offset each other. In this case we can view the
exercise price of the option contract relative to the current value of the bond.
As the insurance "deductible”, that is the amount of value that the bond must
lost before the option insurance take effect.
It can be show that buying a future contract is similar to simultaneously
buying a call option and selling a put option on the same underlying bond,
where the exercise price of the call and the put are equal to the forward price
of the bond. In the same way, one can create a synthetic call option by buying
a forward contract and a put option on the same underlying instrument.
A huge number of strategies for hedging interest-rate-risks can be put in place
by buying and selling call and put options at different exercise prices for
different maturities. In effect "slices" of the future probability distribution of
the prices of the underlying instruments can be priced via options and can be
traded. The different strategies are characterized by various risk-return trade-
offs hopefully in line with the risk appetite of the investor.
Buying a put and a call with the same exercise price is called a straddle and
represents a bet on increased volatility, that is, sharp moves up or down in
price of the underlying asset. An investor can therefore " sell volatility" in
interest rates by selling a straddle, i.e., by selling a put and a call contract
simultaneously that have the same exercise price and maturity. Traders often
use straddles when an announcement about a change in interest rate is

14. expected and when the outcome of the announcement is uncertain or before
some other major macroeconomic decision by a government or central bank.
On the other side of the deal, an investor who purchases a straddle is really
inuring against a major increase or a major decrease in the price of the
underlying asset during the life of the option.
Volatility can be purchased more cheaply by buying a put and a call option at
different exercise prices. With both options out of the money. for example, if
the bond price is 100, one might buy a put option with an exercise price of 95
and a call with an exercise price of 105. Such a "strangle" much cheaper than
an at the money straddle with an exercise price of 100.
Caps, Floors, and Collars
The huge market in the United States for adjustable-rate mortgages (ARMs) as
an intuitive way to explore caps, floors and Collars. About half of the entire
new mortgage loan has adjustable rates, rather than a rate that is fixed over
the life of the mortgage.
The Adjustable rate on an ARM might be based on the rate of six-month
Treasury bill, over the next six months, the borrower will pay the rate plus a
spread of , say 2% per annum often adjustable rate borrowers are offered a
“Cap” on the interest rate of their long-term loans, so that when short-term
interest rates rise above a predetermined rate, say 5% , the borrower does not
pay more than the 5 percent cap plus the add-on (for a total of 7%)

15. This cap is clearly an attractive feature for the borrower, and its costs money
to put it in place, In order to reduce the cost of the Cap, the borrower might
also be offered a “Floor”. A Floor sets a minimum interest payment per period,
even when shot-term interest rate decline substantially, the borrower wont
benefit from the reduction in rates below this floor. In numerical example, if
the floor is set at a T-bill rate of 2% the borrower will pay a minimum of 4%
(i.e. the 2% floor plus the 2 percent add-on).
Now the floor and the cap can be set at such levels that their premiums exactly
offset each other. Such an arrangement is often termed a “zero-cost collar” or
“zero –cost Cylinder”
We can see caps and floors and their combinations used in many different risk
management markets. For example, the collar or cylinder, as a combination of
a ceiling and floor agreement on periodic payments, is a very popular way to
hedge foreign currency positions.
Swaptions
Options on a swap are referred to as “swaptions” and represent the right to
enter into a swap on or before a specified date at currently determined terms.
Such options may be either European or American in style. If the buyer of the
swaption has the right to pay a fixed rate in swap upon exercise, it is called a
payer’s swaption. If the buyer of the swaption has the right to receive a fixed
rate. It is called a receiver’s swaption. Such options may structure with fixed
and floating legs in different currencies. A swaption clearly offers more

16. flexibility than a straight swap. But the purchaser must pay an option
premium for that added benefit.
Exotic Options
So far we’ve considered straightforward or “plain vanilla” options. Options
with more complicated terms are known as exotic options. One of the most
popular is an option that has as its reference the average price of the
underlying instrument over some agreed-upon period of time. For example
one might purchase a call contract from a major bank that entitles the owner
to receive the difference. if positive between the average price of a 30-year
bond, say one month before maturity date and and exercise price agreed upon
in advance (say ,100), the volatility of an average rate option is smaller than
the volatility of the corresponding vanilla Option.
Knock-in and knock-out options are also quite common. These options may be
exercised or expire during an agreed-upon time period before the formal
maturity date of the option contract if the price of the underlying instruments
“hits” a certain predetermined price level. These options, like most exotics
options are “path dependent”, their value is dependent on certain paths that
the price of the underlying instrument may take .there is an endless list of
exotics options (more are invented every year) with names such as Himalayan
,octopus, ratchet, chooser, look back, and barrier options.
Pricing and hedging exotic options rely on complex mathematical models that
are prone to model risk. Some of these exotic structures. Such as barrier

17. options, can expose the seller of the options to significant risks, as there is no
perfect hedge for them.
Financial Engineering
Forwards, swaps, and options are the main building block of financial
engineering. They can be used separately to hedge specific risks, or combined
to form complex structures that meet the needs of customers.
In particular derivatives allow investors and institutions to break apart or
“segment” risks (or, conversely, to handle them together). Take, for example, a
U.S fund manager who holds a bond denominated in Euros. The fund
manager is exposed to interest rate-rate risk in the euro fixed-income market
to changes in the dollar/euro exchange rate. The manager can hedge both
risks by means of a currency swap. Alternatively, she can hedge the foreign
exchange exposure through a currency forward or currency option. the fund
manager could also avoid the trouble of hedging only the currency exposure by
entering into a so-called quanto swap. Under this structure, she would receive
the coupon of the bond in dollars at a prearranged exchange rate and pay U.s
LIBOR floating.
There is almost no limit to the imagination of the structures in banks who are
responsible for devising complex instruments intended to match the
risk/return appetite of their clients. But financial engineering is not by itself
risk management, and in the world of derivatives, often there is a fine line
between hedge and speculation. Firms can be tempted to enter into complex
transactions that enhance portfolio returns. Enhancing returns always means

18. taking on more risk is some form or other.often, it means marginally
increasing returns in the present in exchange for assuming an unlikely but
potentially very severe loss in the future, too often the risk embedded in
complex structures is not fully understood by corporations entering into
complex derivative transactions or is not fully communicated to senior
managers or other stakeholders.
The board as well as the senior management of corporations needs to
understand the natural risk the corporation is runnig.senior management
needs to deploy robust policies and risk measures that tie the firm’s use of
derivatives to its risk appetite and to the business strategy it has
communicated to stakeholders.