1) Derivatives such as financial futures contracts, options, swaps, caps, floors and collars are used to manage interest rate risk. 2) Financial futures contracts work by establishing an agreement between a buyer and seller to deliver an underlying asset at a future date at a set price, allowing investors to hedge against interest rate fluctuations. 3) The basis risk of hedging with futures is the difference between the cash price of the underlying asset and the futures price, which can vary over time and impact hedging effectiveness. Managing the basis is important for successful hedging.

1. Chapter Eight
Risk Management:
Financial Futures, Options, Swaps, and Other
Hedging Tools in Asset-Liability Management
1

2. Key Topics
• The Use of Derivatives
• Financial Futures Contracts: Purpose and
Mechanics
• Short and Long Hedges
• Interest-Rate Options: Types of Contracts and
Mechanics
• Interest-Rate Swaps
• Caps, Floors, and Collars
2

3. Derivatives
A derivative is any instrument or contract that
derives its value from another underlying
asset, instrument, or contract, such as
treasury bills and bonds and eurodollar
deposits
3

4. Managing Interest Rate Risk
• Derivatives used to manage interest rate risk
– Financial futures contracts
– Forward rate agreements
– Interest rate swaps
– Options on interest rates
– Interest rate caps
– Interest rate floors
– Interest rate collars
4

5. Cash & Future Markets
• Cash Markets: Financial assets are exchanged
between buyers and sellers for cash at the
time the price is set.
• Future Markets: Buyers and sellers exchange a
contract calling for delivery of the underlying
asset at a specified date in the future. Futures
markets is the organized exchanges where
futures contracts are traded.

6. Financial Futures Contract
• An agreement between a buyer and a seller
which calls for the delivery of a particular
financial asset at a set price at some future
date
6

7. Financial Futures Contracts
7
TA
TL
*D-DD LA
IS Gap = IS Assets – IS Liabilities
and
Recall what happens when interest rates rise? Fall?
One of the most popular methods for neutralizing these gap risks is to
buy and sell financial futures contracts

8. Background on Financial Futures
• Buyers
– A buyer of a futures contract is said to be long
futures
– Agrees to pay the underlying futures price or take
delivery of the underlying asset
– Buyers gain when futures prices rise and lose
when futures prices fall
8

9. Background on Financial Futures
• Sellers
– A seller of a futures contract is said to be short
futures
– Agrees to receive the underlying futures price or
to deliver the underlying asset
– Sellers gain when futures prices fall and lose when
futures prices rise
9

10. The Purpose of Financial Futures
To Shift the Risk of Interest Rate Fluctuations
from Risk-Averse Investors to Speculators
10

11. The World’s Leading Futures and Option
Exchanges
• Chicago Board of
Trade (CBT)
• Chicago Board
Options Exchange
• Singapore Exchange
LTD. (SGX)
• Chicago Mercantile
Exchange (CME)
• Euronext.Liffe (Eurex)
• Sydney Futures
Exchange
• Toronto Futures
Exchange (TFE)
• South African Futures
Exchange (SAFEX)
11

12. Nepal’s Futures and Option Exchanges
• Commodities & Metal exchange Nepal Ltd.
(COMEN)
• Nepal Derivative Exchange (NDEX)
• Mercantile Exchange (MEX)
12

13. Futures vs. Forward Contracts
– Futures Contracts
• Traded on formal exchanges (CBOT, CME, etc.)
• Involve standardized instruments
• Positions require a daily marking to market
– Forward Contracts
• Terms are negotiated between parties
• Do not necessarily involve standardized assets
• Require no cash exchange until expiration
• No marking to market
13

14. Marking in market
• Future contract sell on August, 1
• Future contract for Treasury Bond having face
value Rs. 100,000 at the opining price of 97-27
• The initial margin requirement is Rs. 2,500
• Maintenance margin is Rs. 2000
(additional funds deposited is called variation
margin)

15. SellingCase

16. Date
Settlement
Price
Settlement
Price (Rs.)
Marked to
market
Margin call Final equity
Opening price 97-27 97,843.75 2,500 2500
1-Aug 97-13 97,406.25 437.50 2,937.50
4-Aug 97-25 97,781.25 (375.00) 2,562.50
5-Aug 96-18 96,562.50 1,218.75 3,781.25
6-Aug 96-07 96,218.75 343.75 4,125.00
7-Aug 97-05 97,156.25 (937.50) 3,187.50
8-Aug 99-03 99,093.75 (1,937.50) 1,250.00
11-Aug 101-01 101,031.25 (1,937.50) 1,250.00 562.50
12-Aug 99-25 99,781.25 1,250.00 1,937.50 3,750.00
13-Aug 101-01 101,031.25 (1,250.00) 2,500.00
14-Aug 100-25 100,781.25 250.00 2,750.00
15-Aug 100-25 100,781.25 - 2,750.00
18-Aug 100-16 100,500.00 281.25 (3,031.25) -
Buy back the contract. Total deposited 5,687.50
Amount withdrawan (3,031.25)
Net loss 2,656.25
Selling (Short Position)

17. Buying (Long Position)
Date
Settlement
Price
Settlement
Price (Rs.)
Marked to
market
Margin call Final equity
Opening price 97-27 97,843.75 2,500 2500
1-Aug 97-13 97,406.25 (437.50) 2,062.50
4-Aug 97-25 97,781.25 375.00 2,437.50
5-Aug 96-18 96,562.50 (1,218.75) 1,218.75
6-Aug 96-07 96,218.75 (343.75) 1281.25 2,156.25
7-Aug 97-05 97,156.25 937.50 3,093.75
8-Aug 99-03 99,093.75 1,937.50 5,031.25
11-Aug 101-01 101,031.25 1,937.50 6,968.75
12-Aug 99-25 99,781.25 (1,250.00) 5,718.75
13-Aug 101-01 101,031.25 1,250.00 6,968.75
14-Aug 100-25 100,781.25 (250.00) 6,718.75
15-Aug 100-25 100,781.25 - 6,718.75
18-Aug 100-16 100,500.00 (281.25) (6,437.50) -
Contract Sold back Total deposited 3,781.25
Amount withdrawan (6,437.50)
Net Profit 2,656.25

18. Most Common Financial Futures Contracts
• U.S. Treasury Bond Futures Contracts
• Three-Month Eurodollar Time Deposit Futures
Contract
• 30-Day Federal Funds Futures Contracts
• One Month LIBOR Futures Contracts
18

19. Notation
F0 = Future price today
S0 = Spot price today
Ft = Future price at time t
St = Spot price at time t
FT = Future price at expiration
ST = Spot Price at expiration
T = Time to expiration
t = Time period prior to expiration

20. S0
F0
St
Ft
ST
FT

21. F0=95
Ft=105
Ft=90
Short Position Or Sell
(Market interest rate is expected to rise)
Loss =10
Gain =5
F0=95
But, Interest rate
fall and price rise
Interest rise and price
fall as expected

22. F0=105
Ft=115
Ft=90
Long Position Or Bye
(When interest fall)
Gain =10
Loss =15
F0=105
Interest rate fall and
price rise as expected
But, Interest rate rise
and price fall

25. Solution:
Price Index at 21 Nov, 2005 is 112-06 which equals to:
(112+6/32)*100,000/100 = 112,187.50
Settlement price at 6 Jan, is 113-16 which equals to:
(113+16/32)*100,000/100 = 113,500
Profit = 113,500 – 112,187.50 = 1312.50

26. Equity Account Balance
= Initial margin + Profit
=$1150 + $1312.50 = $2462.50

28. A. Annualized Discount Yield Based on the Low
IMM index = 100 - 95.1300 = 4.87
B. (95.175 – 95.1400) × 100 × 25 × 15 = $1312.50
C. MTM Value of Equity account at settlement
= $1312.50 + $700 = $2012.50

29. Hedging with Futures Contracts
Avoiding Higher
Borrowing Costs
Use a Short Hedge: Sell
Futures Contracts and
then Purchase Similar
Contracts Later
Avoid Declining Asset
Values
Use a Short Hedge: Sell
Futures Contracts and
then Purchase Similar
Contracts Later
Avoiding Lower Than
Expected Yields from
Loans and Securities
Use a long Hedge: Buy
Futures Contracts and
then Sell Similar
Contracts Later


29


30. Short Futures Hedge Process
• Today – contract is sold through an exchange
• Sometime in the future – contract is purchased
through the same exchange
• Results – the two contracts are cancelled out by the
futures clearinghouse
• Gain or loss is the difference in the price purchased for
(at the end) and price sold for (at the beginning)
• Profit will be made on futures trading, which will offset
some or all of the loss in the value of any bonds still
held.
30

31. Long Futures Hedge Process
• Today – contract is purchased through an exchange
• Sometime in the future – contract is sold through the
same exchange
• Results – the two contracts are cancelled by the
clearinghouse
• Gain or loss is the difference in the price purchase for
(at the beginning) and the price sold for (at the end)
• The resulting profit from trading in financial futures
will offset some or all the loss in revenue due to lower
interest rates on loans.
31

32. Hedging Deposit Costs
• Suppose market interest rate is rising at least one-half
percent point from 10% p.a., over the next three months.
• If a bank needs to raise $100 million from sale of deposits
over the 90 days.
• Then, the deposit cost at 10% rate is:
=$100 million X 10% X 90 ÷ 360 = $2,500,000
• If the deposit interest climb to 10.5%, the deposit cost
would be:
=$100 million X 10.5% X 90 ÷ 360 = $2,625,000
• The amount of potential loss in profit :
= $2,625,000 - $2,500,000 = $125,000

33. To counteract the potential profit loss :
• Today sell 100 90-day Eurodollar future contract trading
at IMM index of 91.5
The price per $100 = 100-((100-IMM index) X90/360)
= 100-((100-91.5) X90/360) = 97.875
Price for $100 m = $100 m X 97.875/100 = $97,875,000
• Within next 90 days, buy 100 90-day Eurodollar futures at
an IMM Index of 91.
The price per $100 = 100-((100-91.0) X90/360)
=97.75
Price for $100 m = $100 m X 97.75/100 = $97,750,000
Profit on buy and sell of future = $97,875,000-$97,750,000
=$125,000

36. Basis Risk
The basis is the cash price of an asset minus the
corresponding futures price for the same asset at a
point in time
▫ For financial futures, the basis can be calculated as the spot rate
minus the futures rate
▫ It may be positive or negative, depending on whether futures
rates are above or below spot rates
▫ May swing widely in value far in advance of contract expiration
Basis=Cash-market price (or interest rate) – futures
market price (or interest rate)
Or
Basis = C0 – F0 or Ct - Ft
36

37. Short Hedge
C0 =97
F0 =96
Ct =90
Ft =89
Loss on Cash market =Ct – C0 = 90 – 97 = -7
Gain on Future market =F0 – Ft = 96 – 89 = 7
Net dollar return on trading = (Ct – C0)+(F0 – Ft )= -7+7 =0
Or Net dollar return on trading = (Ct – Ft) - (C0 - F0)

38. Realized Return from Combining Cash and
Futures Market Trading
=Closing Basis Between Cash and Futures Market
-Opening Basis Between Cash and Futures Market
Or
Dollar Return = Basis at termination of hedge
– Basis at initiation of hedge
Or
= Return Earned in the Cash Market
+/- Profit or Loss from Futures Trading
38

39. Long Hedge
C0 =101
F0 =103
Ct =106
Ft =108
Loss on Cash market =C0 –Ct = 101 – 106 = -5
Gain on Future market =Ft –F0 = 108 – 103 = 5
Net dollar return on trading = (C0 –Ct )+(Ft –F0 )= -5+5 =0
Or Net dollar return on trading = (C0 - F0) - (Ct – Ft)

40. Realized Return from Combining Cash and
Futures Market Trading
= Opening Basis Between Cash and Futures Market
-Closing Basis Between Cash and Futures Market
Or
Dollar Return = Basis at initiation of hedge
– Basis at termination of hedge
Or
= Return Earned in the Cash Market
+/- Profit or Loss from Futures Trading
40

42. F0 = 109+5/32 = 109.1563×100,000/100 = 109156.25
Ft = 100+3/32 =100.0938 ×100,000/100 = 100093.75
F0 for 11 contracts = 109156.25 × 11 = 1200718.8
Ft for 11 contracts = 100093.75 × 11 = 1101031.3
Gain on Future Market = F0 - Ft
=1200719 – 1101031 = 99687.5
Given,
C0 = 1,100,000 and Ct = 1,000,000
Loss on Cash Market = Ct - C0
= 1,000,000 - 1,100,000 = 100,000

43. Gain or Loss from Combined Cash and Future Market
= Gain from Future market - Loss from Cash Market
= 99687.5 – 100000 = - 312.50
Basis at initiation = C0 – F0 = 1,100,000 – 1,200,718.8
= -100,718.75
Basis at termination = Ct – Ft = 1,000,000 – 1,101,031.3
= -101,031.3
Gain/Loss = (Ct – Ft)- (C0 – F0) = -101,031.3- (-100,718.75)
= - 312.5

44. Change in the Market Value of the
Futures Contract
44

45. i)(1
i
-D
F
FF
0
0t




i)(1
i
F-DFF 00t



Or
i)(1
i
D-
P
P





46. Example
Suppose a $100,000 par value TB futures
contract is traded at a price of $99,700 initially
but then interest rates on TB increase a full
percentage point 7 to 8%, If the TB has a
duration of nine years, then change in the value
of TB is:
= -9 yrs. X $99,700X0.01/(1+0.07) = -$8,385.98

47. Solution
Value of Future Contract
= (113+6/32)×$100,000/100
= $113,187.50
Change in value
= -10.48 x $113,187.50 x.01/ (1+.05)
= -$11,297.19

48. i)(1
i
F-DFF 00t


 ………. (i)


















 TL
i)(1
i
D--TA
i)(1
i
D-NW LA
………. (ii)
If we set the change in net worth equal to the change
in the N number of futures position value, then
N
i)(1
i
FD- 0 


 

















 TL
i)(1
i
D--TA
i)(1
i
D- LA
(Ft – F0)×N = ΔNW
Or

49. Or
0
LA
FD
TA)
TA
TL
D-(D


N
Where Dis duration of Future and Nis Number of Future Contract Needed

50. Example
Suppose, a bank has an average asset duration
of four years, an average liability duration of
two years, total assets of $500 million, and total
Liabilities of $460 million. The bank plans to
trade in T-Bond futures contracts. The T-Bond
named in the future contracts have a duration
of nine years and the T-bonds current price is
$99,700 per $100,000 contract. Calculate
number of contracts needed.

51. Number of Futures Contracts Needed
$99,7009yrs
$500m)
$500m
m$460
yrs2-(4yrs


N
51
≈ 1,200 contracts

52. Solution
Number of Future Contracts Needed:
574
25.531,11236.10
000,000,120]3
120
97
8[





53. Questions for Discussion
• What are financial futures contracts? Which
financial institutions use futures and other
derivatives for risk management?
• How can financial futures help financial service
firms deal with interest rate risk?
• What futures transactions would most likely be
used in a period of rising interest rates? Falling
interest rates?
53

54. What types of Future you use When:
• Yield on assets decline?
• Borrowing costs increase?
• Value of interest earning assets decline?

55. Option
• Option means ‘The freedom to choose’
• Definition: A contract that gives its buyer the
right but not obligation to buy or sell an asset
at a fixed price on or before a given date.
• Buyer of Option is also called HOLDER or
OWNER of option.
• Seller is also called WRITER of option.

56. Option contd..
• The seller of the option grants the buyer of
the option the Right, but not the
OBLIGATION, to purchase from or sell to the
seller something.
• The Writer grants this right to the buyer in
exchange for a certain sum of money, which is
called Option Price or Option Premium.

57. Types of Options
Call Option: Call option if contract that gives its
owner the right but not obligation to buy the
specified asset at a pre-specified price before
or given date.
Put Option: Put option is a contract that gives its
owner the right but not obligation to sell the
specified asset at a pre-specified price.

58. Types of Options contd..
Naked Option: Naked option is an option in
which an investor writes the option on the
stock not already owned.
Covered Option: Covered option is a option in
which an investor writes the option on the
stock already owned.

59. Option Terminologies
Option Price: The initial entry fee of the option is
the option price or option premium.
Exercise/Strike Price: The fixed price specified at
which the option buyer has right to
buy or sell an asset specified in an
option contract is called the option’s
Exercise Price or Strike Price.

60. Option Terminologies contd…
Expiration Date: The date after which an option
no longer be exercised.
Underlying Asset: An underlying asset is the
asset to be exchanged on or before expiration
date in the option contract.
Exercising the Option: Exercising the option is
the act of actually buying or selling the
underlying asset as per option contract.

61. Option Terminologies contd…
In-the-Money Option: Option is said to be in-the-
money option if it is worth exercising.
• If the price of an underlying asset is higher than
the exercise price, call option is in-the-money. If
asset price is substantially higher than exercise
price, call option is said to be deep-in-the-money.
• If the price of an underlying asset is lower than
the exercise price, put option is in-the-money. Put
option is the deep-in-the-money if stock price is
substantially lower then exercise price.

62. Option Terminologies contd…
Out-of-the-Money Option: Option is said to be out-
of-the-money option if it is not worth exercising.
• If the price of an underlying asset is lower than
the exercise price, call option is out-of-the-
money. If asset price is substantially lower than
exercise price, call option is said to be deep-out-
of-in-the-money.
• If the price of an underlying asset is higher than
the exercise price, put option is in-the-money. Put
option is the deep-in-the-money if stock price is
substantially higher then exercise price.

63. Asset
Price
Option
Exercise
Price
Call Option Put Option
In-the-
money
Out-of-
the-
money

64. Asset
Price
Option
Exercise
Price
Put Option Call Option
In-the-
money
Out-of-
the-
money

65. Option Terminologies contd…
At-the-Money Option: Option is at the money
option when the market price of an
underlying asset is equal to exercise price.
Option Position: The buyer of the asset is called
long position and seller of asset is called short
position.

66. Most Common Option Contracts Used By
Banks
• U.S. Treasury Bond Futures Options
• Eurodollar Futures Option
66

67. The option buyer can:
1. Exercise the option,
2. Sell the options to another buyer,
3. Simply allow the option to expire.

68. Principal Uses of Option Contracts
1. Protecting a security portfolio through the use of put options to
insulate against falling security prices (rising interest rates);
however, there is no delivery obligation under an option contract
so the user can benefit from keeping his or her securities if
interest rates fall and security prices rise
2. Hedging against positive or negative gaps between interest-
sensitive assets and interest- sensitive liabilities;
for example,
a. put options can be used to offset losses from a negative gap
when interest rates rise,
b. call options can be used to offset a positive gap when interest
rates fall.
68

69. Fall Interest Rate when Gap is Positive
• When interest rate fall, the price of security
rises,
• Buy call option at low price and sell or exercise
before expiration at high price,
• The gain on option will offset the loss in NIM
ISA 10 million
ISL 7 million
IS Gap 3 million
Suppose,
Interest rate fall by 1% point (9 to 8%)
Then,
Loss of potential profit
=3 million X 1% = 30,000

70. Rise Interest Rate when Gap is -ve
• When interest rate rise, the price of security
decline,
• Buy put option in current price and buy back the
option future before expiration at low price,
• The gain on option will offset the loss in NIM
ISA 10 million
ISL 12 million
IS Gap -2 million
Suppose,
Interest rate rise by 1% point (9 to 10%)
Then,
Loss of potential profit
=2 million X 1% = 20,000

72. Explanation
• When interest rate falls, yields on assets also
fall. Falling on yields is LOSS.
• On the other hand, price of assets increase.
• Loss due to falling in yield on asset can be
offset through buying call option.

74. Explanation
• When interest rate rise, deposit and
borrowing costs also rise. Increase in deposit
cost is LOSS.
• On the other hand, price of assets decline.
• Loss due to rising in deposit cost can be offset
through buying put option.

79. Profit/Loss Computation
Before tax profit on put option
= [S0-(Ft X 100)] X 25-Option Premium
Where,
S0 = Option strike price
Ft = Future market price
Before tax profit on call option
= Security market price – Strike price – Opt. premium
Note: The option is allowed to be expired, If it is out of
money. Then, the loss or gain is only option premium.

83. Interest Rate Swap
A contract between two parties to
exchange interest payments in an effort
to save money and hedge against
interest-rate risk
Swaps are often employed to deal with
asset-liability maturity mismatches.
83

84. Interest Rate Swap
Firm
US Dollar
Rate
(in US)
British Pound
Rate
(in UK)
US Firm 10.0% 9.0%
British Firm 11.0% 8.0%

85. U.S.A. U.K.
Lender Lender
$10,000 m
£6,250 m
US Firm
US Firm
British Firm
British Firm

86. U.S.A. U.K.
Lender Lender
$10,000 m
£6,250 m
US Firm
US Firm
British Firm
British Firm
@10%
@11%
@8%
@9%
@10%
@8%

87. 87
Interest –Rate Swap

88. Quality Swap
• Borrower with lower credit rating pays fixed
payments of borrower with higher credit
rating
• Borrower with higher credit rating pays short-
term floating rate payments of borrower with
lower credit rating
88

90. Parties to the
SWAP
Fixed interest
rates parties
must pay if
they issue
long-term
bonds
Floating
interest rates
parties must
pa if they
receive a
short-term
loan
Potential
interest rate
savings of
each borrower
A lower credit-
rated borrower
11.50% Prime+1.75% 0.50%
A higher credit-
rated borrower 9.00%
Prime interest
rate
0.25%
Difference in
interest rates due
to differences in
borrowers’ credit
ratings (quality
spread)
2.50% 1.75% 0.75%

91. Swaps can reduce risk by matching asset-liability
maturity mismatch.
Bank A
Short-
term
asset
with
flexible
yields
Long-term
liability with
Carrying
fixed interest
rate
Bank B
Short-term
liabilities
with
flexible
interest
Long-term
asset with
fixed interest
rate
Risk in decreasing
interest rate
Risk in rising
interest rate

92. Risks of Interest Rate Swaps
• Substantial Brokerage Fees
• Credit Risk
▫ The counterparty may default on the exchange of
the interest payments
▫ Only the interest payment exchange is at risk, not
the principal
• Basis Risk
▫ A swap’s reference interest rates are not the same
as those attached to all the assets and liabilities
(LIBOR, bond rates, etc.), so rates do not change
exactly the same -> some risk remains
92

93. Netting
• The swap parties only swap the net difference
between the interest payments.
• This reduces the potential damage if one party
defaults on its obligation
93

94. Interest Rate Cap
• Protects the holder from rising interest rates.
• For an up front fee borrowers are assured
their loan rate will not rise above the cap rate
94

95. Interest Rate Floor
A contract setting the lowest interest rate a
borrower is allowed to pay on a flexible-rate
loan
95

96. Interest Rate Collar
A contract setting the maximum and minimum
interest rates that may be assessed on a
flexible-rate loan. It combines an interest rate
cap and floor into one contract.
96

97. Quick Quiz
• What is a call option?
• Suppose market interest rates were expected
to rise. What type of option would normally
be used?
• If rates were expected to fall, what type of
option would a financial institution’s manager
be likely to employ?
97