2. The nature of options on financial
futures
An option
…an agreement between two parties in which
one gives the other the right, but not the
obligation, to buy or sell a specific asset at a
set price for a specified period of time.
The buyer of an option
…pays a premium for the opportunity to decide
whether to effect the transaction (exercise the
option) when it is beneficial.
The option seller (option writer)
…receives the initial option premium and is
obligated to effect the transaction if and when
the buyer exercises the option.
3. Two types of options
1. Call option
…the buyer of the call has the right to buy the
underlying asset at a specific strike price for
a set period of time.
the seller of the call option is obligated to
deliver the underlying asset to the buyer when
the buyer exercises the option.
2. Put option
…the buyer has the right to sell the
underlying asset at a specific strike price for
a set period of time.
the seller of a put option is obligated to buy
the underlying asset when the put option
buyer exercises the option.
4. Options versus futures
In a futures contract, both parties are obligated
to the transaction
An option contract gives the buyer (holder) the
right, but not the obligation, to buy or sell an
asset at some specified price:
call option, the right to buy
put option, the right to sell
Exercise or strike price
…the price at which the transaction takes
place
Expiration date
…the last day in which the option can be used
5. Option valuation
Theoretical value of the option:
Vo = Max( Va - E, 0)
where Va = market price of the asset
E = Strike or exercise price.
Example: Option to buy a house at $100,000
If market value is $120,000:
Vo= Max( 120,000 - 100,000, 0) = 20,000
If market value is 80,000, Vo = 0
6. Options, market prices and strike prices
…as long as there is some time to expiration, it is
possible for the market value of the option to be
greater than its theoretical value.
Call Options Put Options
Out of the Money Out of the Money
Market price < Strike price Market price > Strike price
At the Money At the Money
Market price = Strike price Market price = Strike price
In the Money In the Money
Market price > Strike price Market price < Strike price
7. Option value: time and volatility
The longer the period of time to expiration, the
greater the value of the option:
more time in which the option may have value
the further away is the exercise price, the
further away you must pay the price for the
asset
The greater the possibility of extreme
outcomes, the greater the value of the option
volatility
8. Options on 90-day Eurodollar futures,
April 2, 2002
Each option's price, the
premium, reflects the
Option Premiums* consensus view of the value of
Strike Calls Puts the position.
Price June Sept. June Sept. Intrinsic value equals the dollar
value of the difference between
9700 0.53 0.25 0.02 0.41 the current market price of the
9725 0.30 0.14 0.08 0.56 underlying Eurodollar future
9750 0.18 0.09 0.19 0.73 and the strike price or zero,
9775 0.09 0.05 0.28 0.93 whichever is greater.
9800 0.02 0.01 0.49 1.17
The time value of an option
Monday volume: 31,051 calls; 40,271 puts equals the difference between
Open interest: the option price and the
Monday, 4,259,529 calls; 3,413,424 puts intrinsic value.
90-Day Eurodollar Futures Prices (Rates), Consider the time values of the
April 2, 2002 June 2002 call from 97.25 to
98.00 strike prices, the time
June 2002: 97.52 (2.48%)
values are $75, $400, $225, and
September 2002: 96.83 (3.17%) $50, respectively, or 3, 16, 9,
and 2 basis points.
9. Option premium
…equals the intrinsic value of the option plus the
time value:
premium = intrinsic value + time value
The intrinsic value and premium for call
options with the same expiration but different
strike prices, decreases as the strike price
increases.
the higher is the strike price, the greater is the
price the call option buyer must pay for the
underlying futures contract at exercise.
The time value of an option increases with the
length of time until option expiration
the market price has a longer time to reach a
profitable level and move favorably.
10. The intrinsic value of a put option is the greater of
the strike price minus the underlying asset’s
market price, and zero.
The time value of a put also equals the option premium
minus the intrinsic value.
June put option at 97.50 was slightly out of the money
--the June futures price, 97.52, was above the strike
price.
The 19 basis point premium represented time value.
Put options with the same expiration, premiums increase
with higher strike prices
Example: the buyer of a June put option at 98.00 has
the right to sell June 2002 Eurodollar futures at a price
$1,200 (48 x $25) over the current price.
Option is in the money with an intrinsic value of $1,200 and a
time value of $25 (one basis point).
Example: the September put options, the premiums
rise as high as 117 basis points for a deep in the
money option.
The time value is greatest for at the money put options, and
11. Buying or selling a futures position
Institutional traders buy and sell futures
contracts to hedge positions in the cash
market.
As the futures price increases, corresponding
futures rates decrease.
Both buyers and sellers can lose an unlimited
amount,
given the historical range of futures price
movements and the short-term nature of the
futures contracts, actual prices have not varied
all the way to zero or 100.
12. Profit or loss in a futures position
A. Futures Positions
Profit Profit
Futures Futures
0 0
97.52 Price 97.52 Price
Loss Loss
1. Buy June 2002 Eurodollar Futures at 97.52. 2. Sell June 2002 Eurodollar Futures at 97.52.
Value of the Asset --------->
13. Trading call options
Buying a call option
the buyer’s profit equals the eventual futures
price minus the strike price and the initial call
premium
compared with a pure long futures position, the
buyer of a call option on the same futures
contract faces less risk of loss if futures prices
fall yet realizes the same potential gains if
prices increase
Selling a call option
the seller’s profit is a maximum of the premium
less the eventual futures price minus the strike
price
compared with a pure short futures position,
the seller of a call option faces less potential
gain if futures prices fall yet realizes the same
potential losses if prices increase
14. Trading put options
Buying a put option
a put option limits losses to the option
premium, while a pure futures sale exhibits
greater loss potential
comparable to the direct short sale of a futures
contract, the buyer of a put option faces less
risk of loss if futures prices increase yet
realizes the same potential gains if prices fall
Selling a put option
a put option limits gains to the option premium,
while a pure futures sale exhibits greater gain
potential
comparable to pure long futures position, the
buyer of a put option faces less potential gain if
futures prices increase yet realizes the same
potential loss if prices fall
15. Profit or loss in an options position
B. Call Options on Futures
Profit Profit
0.93
97.50 Futures 97.75 Futures
0 0
97.68 Price Price
20.18
98.68
Loss Loss
1. Buy a June 2002 Eurodollar Futures Call 2. Sell a Sept. 2002 Eurodollar Futures Call
Option at 97.50. Option at 97.75.
C. Put Options on Futures
Profit Profit
0.56
97.25 Futures Futures
0 0
Price Price
97.25
20.08 97.17 96.69
Loss Loss
1. Buy a June 2002 Eurodollar Futures Put 2. Sell a Sept. 2002 Eurodollar Futures Put
Option at 97.25. Option at 97.25.
16. The use of options on futures by
commercial banks
Commercial banks can use financial futures
options for the same hedging purposes as they
use financial futures.
Managers must first identify the bank’s
relevant interest rate risk position.
17. Positions that profit from rising
interest rates
Suppose that a bank would be adversely
affected if the level of interest rates increases.
This might occur because the bank has a
negative GAP or a positive duration gap, or
simply anticipates issuing new CDs in the
near term.
A bank has three alternatives that should
reduce the overall risk associated with rising
interest rates:
1. sell financial futures contracts directly
2. sell call options on financial futures
3. buy put options on financial futures
18. Profiting from falling interest rates
Banks that are asset sensitive in terms of earnings
sensitivity or that commit to buying fixed-income
securities in the future will be adversely affected if the
level of interest rates declines.
It can buy futures directly, buy call options on futures,
sell put options on futures, or enter a swap to pay a
floating rate and receive a fixed rate.
Although the futures position offers unlimited gains and
losses that are presumably offset by changes in value of
the cash position, a purchased call option offers the
same approximate gain but limits the loss to the initial
call premium.
The sale of a put limits the gain and has unrestricted
losses. The basic swap, in contrast, produces gains only
when the actual floating rate falls below the fixed rate.
19. Several general conclusions apply to
futures, options and swaps
1. Futures and basic swap positions produce
unlimited gains or losses depending on which
direction rates move and this value change
occurs immediately with a rate move.
Thus, a hedger is protected from adverse rate
changes but loses the potential gains if rates
move favorably.
2. Buying a put or call option on futures limits
the bank’s potential losses if rates move
adversely.
This type of position has been classified as a
form of insurance because the option buyer
has to pay a premium for this protection.
20. Several general conclusions apply to
futures, options and swaps (continued)
3. Determining the best alternative depends on
how far management expects rates to
change and how much risk of loss is
acceptable.
4. Selling a call or put option limits the
potential gain but produces unlimited
losses if rates move adversely.
Selling options is generally speculative and
not used for hedging.
21. Several general conclusions apply to
futures, options and swaps (continued)
5. A final important distinction is the cash flow
requirement of each type of position.
The buyer of a call or put option must
immediately pay the premium.
However, there are no margin requirements for
the long position.
The seller of a call or put option immediately
receives the premium, but must post initial
margin and is subject to margin calls because
the loss possibilities are unlimited.
All futures positions require margin and swap
positions require collateral.
22. Profit and loss potential on futures, options on
futures positions, and basic interest rate swaps
23. Futures versus options positions
… important distinction is the cash flow
requirement of each type of position
The buyer of a call or put option must
immediately pay the premium.
There are no margin requirements for the long
positions.
The seller of a call or put option immediately
receives the premium, but must post initial
margin and is subject to margin calls because
the loss possibilities are unlimited.
All futures positions require margin.
24. Using options on futures to hedge
borrowing costs
Borrowers in the commercial loan market and
mortgage market often demand fixed-rate
loans.
How can a bank agree to make fixed-rate loans
when it has floating-rate liabilities?
The bank initially finances the loan by issuing a $1
million 3-month Eurodollar time deposit.
After the first three months, the bank expects to
finance the loan by issuing a series of 3-month
Eurodollar deposits timed to coincide with the
maturity of the preceding deposit.
4/2/02 7/1/02 9/30/02 12/30/02 4/1/03
Loan yield 8.0%
Issue 3m Issue 3m Issue 3m Issue 3m
Euro 2.04% Euro ? Euro ? Euro?
27. Hedging with options on futures
A participant who wants to reduce the risk
associated with rising interest rates can buy
put options on financial futures.
The purchase of a put option essentially places
a cap on the bank’s borrowing cost.
If futures rates rise above the strike price plus
the premium on the option, the put will produce
a profit that offsets dollar for dollar the
increased cost of cash Eurodollars.
If futures rates do not change much or decline,
the option may expire unexercised and the bank
will have lost a portion or all of the option
premium.
28. A. Buy: September 2002 Put Option; Strike Price = 97.25*
Profit
(3.20%)
Profit diagrams for put options on Eurodollar futures, A[ril 2, 2003
F 1 =96.80 97.25
0 Futures
Prices
96.83= Futures Price (F)
96.69
0.56
- (3.31%)
Loss B. Buy: December 2002 Put Option; Strike Price = 97.25*
Profit
(4.71%)
1
F = 95.29 97.25 Futures
0
F = 96.21 Prices
96.20
1.05
- (3.80%)
Loss C. Buy: March 2003 Put Option; Strike Price = 97.25*
Profit
(5.00%)
1
F = 95.00 97.25 Futures
0
Prices
F= 95.63
1.62
- (4.37%)
Loss
31. Interest rate caps, floors and collars
The purchase of a put option on Eurodollar
futures essentially places a cap on the bank's
borrowing cost.
The advantage of a put option is that for a fixed
price, the option premium, the bank can set a
cap on its borrowing costs, yet retain the
possibility of benefiting from rate declines.
If the bank is willing to give up some of the
profit potential from declining rates, it can
reduce the net cost of insurance by accepting
a floor, or minimum level, for its borrowing
cost.
32. Interest rate caps and floors
Interest rate cap
…an agreement between two counterparties
that limits the buyer's interest rate exposure to
a maximum rate
the cap is actually the purchase of a call option
on an interest rate
Interest rate floor
…an agreement between two counterparties
that limits the buyer's interest rate exposure to
a minimum rate
the floor is actually the purchase of a put option
on an interest rate
33. Interest rate cap
…A series of consecutive long call options
(caplets) on a specific interest rate at the same
strike rate.
To establish a Rate Cap:
the buyer selects an interest rate index
a maturity over which the contract will be in
place
a strike (exercise) rate that represents the cap
rate and a notional principal amount
By paying an up-front premium, the buyer then
locks-in this cap on the underlying interest
rate.
34. The buyer of a cap receives a cash payment from the seller.
The payoff is the maximum of 0 or 3-month LIBOR minus 4% times
the notional principal amount.
A. Cap = Long Call Option on 3-Month LIBOR
Dollar Payout
(3-month LIBOR +C
-4%) x Notional
Principal Amount
• If 3-month LIBOR exceeds
4%, the buyer receives cash
from the seller and nothing
otherwise.
• At maturity, the cap
expires. 3-Month
LIBOR
4 Percent
Rate
B. Cap Payoff: Strike Rate = 4 Percent*
Floating
Rate
4 Percent
Value Value Value Value Value
Date Date Date Date Date
Time
35. The benefits and negatives of buying a cap
Similar to those of buying any option.
The bank, as buyer of a cap, can set a
maximum (cap) rate on its borrowing costs.
It can also convert a fixed-rate loan to a
floating rate loan.
it gets protection from rising rates and retains
the benefits if rates fall.
The primary negative to the buyer is that a cap
requires an up-front premium payment.
The premium on a cap that is at the money or in
the money in a rising rate environment can be
high.
36. Establish a floor
A bank borrower can establish a floor by
selling a call option on Eurodollar futures.
The seller of a call receives the option
premium, but agrees to sell to the call option
buyer the underlying Eurodollar futures at the
agreed strike price upon exercise.
A floor exists because any opportunity gain in
the cash market from borrowing at lower rates
will be offset by the loss on the sold call
option.
In essence, the bank has limited its maximum
borrowing cost, but also established a floor
borrowing cost.
The combination of setting a cap rate and floor
rate is labeled a collar.
37. A buyer can establish a minimum interest rate by buying a floor on an
interest rate index. The buyer of the floor receives a cash payment equal to
the greater of zero the product of 4 percent minus 3-month LIBOR and a
notional principal amount..
Dollar Payout
(4% - 3-month 1P A. Floor = Long Put Option on 3-Month LIBOR
LIBOR) x Notional
Principal Amount
• Thus, if 3-m LIBOR
exceeds 6 %, the buyer of
a floor at 6% receives
nothing.
• The buyer is only paid if
3-m LIBOR is less than 3-Month
6% 4 Percent LIBOR
Rate B. Floor Payoff: Strike Rate = 4 Percent*
Floating
Rate
4 Percent
Value Value Value Value Value
Date Date Date Date Date
Time
38. Interest rate floor
…a series of consecutive floorlets at the
same strike rate
To establish a floor, the buyer of an interest
rate floor selects
an index
a maturity for the agreement
a strike rate
a notional principal amount
By paying a premium, the buyer of the floor, or
series of floorlets, has established a minimum
rate on its interest rate exposure.
39. The benefits and negatives of buying a floor
The benefits are similar to those of any put
option
A floor protects against falling interest rates
while retaining the benefits of rising rates
The primary negative is that the premium may
be high on an at the money or in the money
floor, especially if the consensus forecast is
that interest rates will fall in the future.
40. Interest rate collar and reverse collar
Interest rate collar
…the simultaneous purchase of an interest
rate cap and sale of an interest rate floor on
the same index for the same maturity and
notional principal amount.
The cap rate is set above the floor rate.
The objective of the buyer of a collar is to
protect against rising interest rates.
The purchase of the cap protects against rising
rates while the sale of the floor generates
premium income.
A collar creates a band within which the
buyer’s effective interest rate fluctuates.
41. Zero cost collar
…requires choosing different cap and floor
rates such that the premiums are equal.
Designed to establish a collar where the buyer
has no net premium payment.
The benefit is the same as any collar with zero
up-front cost.
The negative is that the band within which the
index rate fluctuates is typically small and the
buyer gives up any real gain from falling rates.
42. Reverse collar
…buying an interest rate floor and
simultaneously selling an interest rate cap.
The objective is to protect the bank from
falling interest rates.
The buyer selects the index rate and matches
the maturity and notional principal amounts
for the floor and cap.
Buyers can construct zero cost reverse
collars when it is possible to find floor and
cap rates with the same premiums that
provide an acceptable band.
43. Caps and floors premium cost
A. Caps/Floors
Term Bid Offer Bid Offer Bid Offer
Caps 4.00% 5.00% 6.00%
1 year 24 30 3 7 1 2
2 years 81 17 36 43 10 15
3 years 195 205 104 114 27 34
5 years 362 380 185 199 86 95
7 years 533 553 311 334 105 120
10 years 687 720 406 436 177 207
Floors 1.50% 2.00% 2.50%
1 year 1 2 15 19 57 61
2 years 1 6 32 39 95 102
3 years 7 16 49 58 128 137
5 years 24 39 80 94 190 205
7 years 40 62 102 116 232 254
10 years 90 120 162 192 267 297
NOTE: Caps/Floors are based on 3-month LIBOR; up-front
costs in basis points. Figures in bold print represent strike
rates. SOURCE: Bear Stearns
44. The size of cap and floor premiums are
determined by a wide range of factors
The relationship between the strike rate and the
prevailing 3-month LIBOR
premiums are highest for in the money options and
lower for at the money and out of the money options
Premiums increase with maturity.
The option seller must be compensated more for
committing to a fixed-rate for a longer period of time.
Prevailing economic conditions, the shape of the yield
curve, and the volatility of interest rates.
upsloping yield curve -- caps will be more expensive
than floors.
the steeper is the slope of the yield curve, ceteris
paribus, the greater are the cap premiums.
floor premiums reveal the opposite relationship.
45. Protecting against falling interest rates
Assume that a bank is asset sensitive such
that the bank's net interest income will
decrease if interest rates fall.
Essentially the bank holds loans priced at
prime +1% and funds the loans with a 3-year
fixed-rate deposit at 2.75%.
Three alternative approaches to reduce risk
associated with falling rates:
1. entering into a basic interest rate swap to
pay 3-month LIBOR and receive a fixed rate
2. buying an interest rate floor
3. buying a reverse collar
46. Using a Basic Swap to Hedge Aggregate Balance
Sheet Risk of Loss From Falling Rates
Floating Rate Bank Swap Terms:
Loans
Pay LIBOR, Receive 4.55%
Prime +100 3-m LIBOR
Swap
Bank Counterparty
Fixed 2.75 4.55% Fixed
Deposits
47. Buying a floor on a 3-month LIBOR to hedge aggregate
balance sheet risk of loss from falling rates
Floating Rate
Loans Floor Terms:
Prime +100 Buy a 2.0% floor on 3m LIBOR
Swap
Bank Receive when
Counterparty
3-m LIBOR< 2.0%
Fixed 2.75 Fee: (.21%) /yr
Deposits
48. Buying a Reverse Collar to Hedge Aggregate
Balance Sheet Risk of Loss From Falling Rates
Floating Rate Strategy: Buy a Floor on a 3-m LIBOR at
Loans 1.50%, sell a Cap on 3-m LIBOR at 2.50%
Prime +100 Pay when
3-m LIBOR>2.50% Swap
Bank Receive when Counterparty
Fixed 2.75 3-m LIBOR<1.50%
Prem: 0.10% /yr
Deposits
49. Protecting against rising interest rates
Assume that the bank has made 3-year
fixed rate term loans at 7%, funded via 3-
month Eurodollar deposits for which it pays
the prevailing LIBOR minus 0.25%.
The bank is liability sensitive, it is exposed
to loss from rising interest rates
Three strategies to hedge this risk:
1. enter a basic swap to pay 6% fixed-rate and
receive 3-month LIBOR
2. buy a cap on 3-month LIBOR with a 5.70%
strike rate
3. buy a collar on 3-month LIBOR
50. Using a basic swap to hedge aggregate
balance sheet risk of loss from rising rates
Floating Rate
Loans Strategy: Receive 3-m LIBOR, Pay 4.56%
Fixed 7.0%
4.56% Fixed
Swap
Bank
Counterparty
3-m LIBOR −0.25% 3-m LIBOR
Deposits
51. Buying a cap on 3-month LIBOR to hedge aggregate
balance sheet risk of loss from rising rates
Floating Rate
Loans Strategy: Buy a Cap on 3m LIBOR at 3.0%
Fixed 7.0%
Receive when Swap
Bank
3-month LIBOR > 3.00% Counterparty
3-m LIBOR −0.25% Fee: (0.70%) /yr
Deposits
52. Using a collar on 3-month LIBOR to hedge aggregate
balance sheet risk of loss from rising rates
Floating Rate
Loans Strategy: Buy a Cap at 3.0% and Sell a Floor at 2.0%
Fixed 7.0%
Receive when 3-M LIBOR > 3.0%
Swap
Bank
Counterparty
Pay when 3-M LIBOR < 2.0% Fee: (0.30%) /yr
3-m LIBOR −0.25%
Deposits
53. Interest rate swaps with options
To obtain fixed-rate financing, a firm with access to
capital markets has a variety of alternatives:
1. Issue option-free bonds directly
2. Issue floating-rate debt that it converts via a basic
swap to fixed-rate debt
3. Issue fixed-rate callable debt, and combine this with
an interest rate swap with a call option and a plain
vanilla or basic swap
Investors demand a higher rate for callable bonds to
compensate for the risk the bonds will be called
the call option will be exercised when interest rates
fall, and investors will receive their principal back
when similar investment opportunities carry lower
yields
the issuer of the call option effectively pays for the
option in the form of the higher initial interest rate
54. Interest rate swap with a call option
…like a basic swap except that the call option
holder (buyer) has the right to terminate the swap
after a set period of time.
Specifically, the swap party that pays a
fixed-rate and receives a floating rate
has the option to terminate a callable
swap prior to maturity of the swap.
Thisoption may, in turn, be exercised
only after some time has elapsed.
55. Issue fixed-rate debt with an 8-year maturity
Dealer spread: 0.10%
Cash Market Alternatives
8-year fixed rate debt: 8.50% Strategy involves three steps
8-year callable fixed-rate debt: 8.80% implemented simultaneously:
1.issues callable debt at 8.80%
6-month floating-rate debt: LIBOR 2.enters into a callable swap
Interest Rate Swap Terms paying LIBOR and receiving
Basic Swap: 8-year swap without options: 8.90%
pay 8.55% fixed; receive LIBOR 3.enters into a basic swap
pay LIBOR; receive 8.45% paying 8.55%, receiving
Callable Swap: 8-year swap, LIBOR.
callable after 4 yrs:
pay LIBOR; receive 8.90% fixed
Example: Callable Swap
pay 9.00% fixed; receive LIBOR
Net Borrowing Cost after Option Exercise Net Cost of Borrowing
Pay: After Option Exercise in 4 Yrs
cash rate + callable swap rate + basic swap rate Basic swap:
[8.80% + LIBOR + 8.55%] pay 8.55%; receive LIBOR
Receive: callable swap rate + basic swap rate New floating-rate debt:
– [8.90% + LIBOR] pay LIBOR +/- ?
Net Pay =8.45% Net cost = 8.55% +/- spread to LIBOR
56. Interest rate swap with a put option
…A put option gives the holder of a putable swap
the right to put the security back to the issuer
prior to maturity
With a putable bond an investor can get
principal back after a deferment period
Option value increases when interest rates rise
Investors are willing to accept lower yields
With a putable swap, the party receiving the
fixed-rate payment has the option of
terminating the swap after a deferment period,
and will likely do so when rates increase.
57. Putable Bond: 8-yr bond, putable after 4 yrs: 8.05%
Putable Swap: 8-yr swap, putable after 4 yrs:
pay LIBOR; receive 8.20% fixed
pay 8.30% fixed; receive LIBOR
Strategy involves three steps implemented simultaneously:
1. issue putable debt at 8.05%
2. enter into a putable swap to pay LIBOR and receive 8.20%
3. enter into a basic swap to pay 8.55% and receive LIBOR
Net Cost of Borrowing With a Putable Swap for 4 Years
Pay: Put bond rate + Put swap rate + Basic swap rate
[8.05% + LIBOR + 8.55%]
Example: Putable Swap
Receive: Put swap rate + Basic swap rate
− [ 8.20% + LIBOR]
Net cost = 8.40%
Net Cost of Borrowing After Option Exercise in 4 Yrs
Basic swap: pay 8.55%; receive LIBOR
New floating-rate debt: pay LIBOR +/- ?
Net cost = 8.55% +/- spread to LIBOR
