Chapter 15
Other Derivative
Assets
1
© 2004 South-Western Publishing
Outline
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Futures options
Pricing futures options
Warrants
Other derivative assets
Futures Options
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3
Characteristics
Speculating with futures options
Spreading with futures options
Basis risk with spreads
Hedging with futures options
Speculators and hedging
Early exercise of futures options
Characteristics
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4
Are futures options “uniquely worthless”?
Futures options give users of the futures
market an enhanced ability to tailor their
risk/return exposure to individual needs
Futures options provide an opportunity for
the speculator to avoid the potentially
unlimited losses associated with futures
contracts
Characteristics (cont’d)
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Futures options are relatively new
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–
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Commodity Futures Trading Commission
Act of 1974
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5
Non-agricultural futures since 1982
Agricultural futures since 1984
Futures options must not be “contrary to the
public interest”
Futures options must serve legitimate hedging
purposes
Characteristics (cont’d)
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Futures options are no different from listed
options
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6
Futures calls give the right to go long
Call writer has the obligation to go short if the
call holder exercises
Futures puts give the right to go short
Put writer has the obligation to go long if the put
holder exercises
Characteristics (cont’d)
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7
The underlying security is the futures
contract, not the physical commodity
represented by the futures contract
The option holder decides if and when to
exercise
Exercise of a futures call does not result in
delivery of the underlying commodity
Characteristics (cont’d)
Futures Prices
February 10, 2004
S&P 500
Index
8
Open
High
Low
Settle
Change
MAR
1138.30
1146.50
1137.60
1143.20
+330
JUN
1137.00
1145.00
1137.00
1142.30
+340
SEP
….
….
….
1141.40
+320
DEC
1139.00
1141.20
1139.00
1141.20
+350
Characteristics (cont’d)
Futures Options Prices
February 10, 2004
S&P 500
Index
9
Calls
Puts
Strike
Price
FEB
MAR
APR
FEB
MAR
APR
1140
11.60
22.50
30.20
8.40
19.30
27.90
1150
6.60
17.00
24.80
13.40
23.80
32.50
1160
3.30
12.60
20.00
20.10
29.40
37.60
1170
1.45
9.00
15.80
28.20
35.80
….
1180
0.65
6.20
12.40
37.40
….
….
Characteristics (cont’d)
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Like other puts and calls, futures options
have both intrinsic value and time value
Expiration
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10
The option month refers to the futures contract
delivery month
Depending on the commodity, the option may
expire on a specific date in the preceding month
The actual expiration date varies by commodity
Some futures options have a serial expiration
feature
Speculating With Futures
Options
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Speculation principles for futures options
are the same as for equity options
Buying futures options involves a
predetermined, known, and limited
maximum loss, just as with options on
other assets
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11
The option premium is the most the option
buyer can lose
Speculating With Futures
Options (cont’d)
Money At Risk Example
In early September, a speculator anticipates lower
demand for soybeans and anticipates a drop in the
price of soybeans. She decides to buy a put option
on soybean futures. Specifically, she purchases 3
APR 8300 puts at a listed price of 25.25 cents. The
money at risk is
3 contracts x 5,000bu/contract x $0.2525/bu = $3,787.50
12
Spreading With Futures Options
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Used by speculators in futures options to
reduce their money at risk
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13
E.g., construct a bullspread
Spreading With Futures Options
(cont’d)
Bullspread Example
Consider MAR 8600 and 8700 calls on
soybeans with settlement prices of 7 cents
and 5 cents per bushel, respectively. The
table on the next slide shows the profit and
loss summary for a soybean bullspread.
14
Spreading With Futures Options
(cont’d)
Bullspread Example
Futures Settlement Price (cents per bushel)
15
858
860
862
864
866
Buy 8600
call @ $.07
-7
-7
-5
-3
-1
Write 8700
call @ $.05
+5
+5
+5
+5
+5
Net
-2
-2
0
+2
+4
Basis Risk With Spreads
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If the basis of two futures contracts
underlying a long position in futures
options and a short position in futures
options are different, it is possible that both
contracts will move against you
Hedging With Futures Options
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There are as many ways to hedge with
futures options as there are with equity or
index options
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Any hedge serves to limit risk with some
tradeoff in potential return
In the commodities market, there can be several
levels of hedging
Hedging With Futures Options
(cont’d)
Hedging Example
William Bob operates a 1,500-acre farm in the midwest and
plans on harvesting 50,000 bushels of soybeans. To hedge
price risk, Bob could go short 10 soybean contracts, covering
50,000 bushels. However, to protect himself against
unexpected problems with the crop (such as tornadoes), Bob
could hedge by only going short 9 soybean contracts. This
reduces the inconvenience and cost of having to either close
out some contracts at a financial loss or acquire soybeans in
the cash market to deliver against the short contracts.
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Speculators and Hedging
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Futures options are particularly useful to
speculators of interest rate of stock index
futures
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If a speculator buys an S&P 500 index futures
contract, a market decline results in a reduced
account balance as the contract is marked to
market each day
Puts on the S&P futures would provide some
protection against the potentially large losses
Early Exercise of Futures
Options
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Listed call options on equity securities or
indexes will not normally be exercised early
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This would result in an abandonment of the
remaining time value of the option
Early Exercise of Futures
Options (cont’d)
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With futures options, there are
circumstances in which it is optimal to
exercise a call early
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E.g., exercising a call allows the speculator to
go long in futures and to earn interest with the
futures contract
Pricing Futures Options
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Futures option pricing model
Disposing of valuable options
Futures option deltas
Implied volatility
Futures Option Pricing Model
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Black’s futures option pricing model for
European call options:
C  e  RT FN ( a )  KN (b)
2
F

 
ln   
T
K
2

where a 
 T
and
23
b  a  T
Futures Option Pricing Model
(cont’d)
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Black’s futures option pricing model for
European put options:
P  e  RT KN (b)  FN(a)

Alternatively, value the put option using
put/call parity:
P  C e
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 RT
(F  K )
Disposing of Valuable Options
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The holder of a futures option has three
alternatives:
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Keep the option
Exercise the option
Sell the option
The risk of holding onto the option is that
prices may move adversely
Disposing of Valuable Options
(cont’d)
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The early exercise of option is normally
suboptimal
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Deep-in-the-money options have little time value
and it is often advantageous to exercise them
early
Selling the option has the merit of capturing
the remaining time value and converts the
intrinsic value to cash
Futures Option Deltas
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Slightly different from delta for equity or
index options
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Call delta:
e  RT N (a)
–
Put delta:
e
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 RT
N (b)
Implied Volatility
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Implied volatility is the standard deviation
of returns that will cause the pricing model
to predict the actual option premium
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Calculating implied volatility must be done
via trial and error
Warrants
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Characteristics
Pricing
Hedging with stock warrants
Characteristics
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A warrant is a non-dividend-paying security
giving its owner the right to buy a certain
number of shares at a set price directly
from the issuing company
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Warrants are relatively rare
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Traded on the New York Stock Exchange, the
American Stock Exchange, and Nasdaq
Characteristics (cont’d)
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Warrants are really long-term call options
Warrants give the owners the right to
purchase a set number of shares of stock
directly from the issuing company
There is a predetermined exercise price and
expiration date
Characteristics (cont’d)
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Warrants pay no dividends and their
owners have no voting rights
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Investors like them because they provide
leverage and let them assume a bullish position
with a low investment
Warrants can have very unusual exercise
terms and conditions
Characteristics (cont’d)
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The vast majority of warrants are from
small, relatively risky firms, often issued in
conjunction with an IPO
Pricing
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Primary factor is the relationship between
the price of the underlying common stock
and the exercise price
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When the stock price rises above the exercise
price, the warrant is in-the-money
Pricing (cont’d)
Actual
Warrant
Price
Maximum
value
warrant
price
Minimum
value
Exercise
price
Stock price
35
Pricing (cont’d)
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The theoretical maximum price of a warrant
is equal to the stock price
The theoretical minimum value is the
warrant’s intrinsic value
The gap between the market price of the
warrant and its minimum value is largest
when the stock price equals the exercise
price
Pricing (cont’d)
New York Stock Exchange Warrants
February 11, 2004
Issuer
Symbol
Exercise
price
Expiration
Warrant
price
Stock
price
Chiquita
Brands
CQB
$19.23
3-19-09
$8.00
$23.23
Collegiate
Pacific
BOO
$5.00
5-26-05
$5.15
$10.05
IW
$12.00
4-5-05
$0.05
$4.40
Image Ware
Systems
37
Hedging With Stock Warrants
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A warrant hedge is similar to covered call
writing
Warrant hedging involves the warrant
lender
An investor buys shares of stock and
simultaneously sell short warrants on the
same company
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To short sell, investor borrows warrants
Hedging With Stock Warrants
(cont’d)
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If the stock price is below the exercise price
at warrant expiration, the warrants are
worthless
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Short seller owes lender nothing and keeps
short sale proceeds
Loss in value of the underlying stock is reduced
by warrant proceeds
Hedging With Stock Warrants
(cont’d)
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Warrants are exercised if stock price rises
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Investor must repay the lender the loan
Investor’s profit is limited to the exercise price
plus the proceeds from the short sale
Other Derivative Assets
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Foreign currency options
When-issued stock
Foreign Currency Options
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Foreign currency options began trading in
1982
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Commercial banks arrange most currency
option trading
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Contracts guaranteed by Options Clearing
Corporation
Foreign Currency Options
(cont’d)
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Different from options on foreign currency
futures
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Currency call gives you the right to buy the
foreign currency
Currency futures call gives you the right to go
long the futures contract
Foreign Currency Options
(cont’d)
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A foreign currency call is equivalent to a
dollar put on the currency
The contract size is one-half the size of the
futures contract
Unlike futures, options must be paid in full
or a significant margin posted
The Black-Scholes model does not work
well with foreign currency options
When-Issued Stock
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The NYSE permits investors to trade shares
of stock issued in conjunction with a stock
split even before new shares are distributed
to existing shareholders
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Both the new shares and the old shares
trade simultaneously
When-Issued Stock (cont’d)
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The old shares will go ex-distribution on
the second business day before the date of
record
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Purchase after this date is a purchase with a due
bill for the additional shares
Holders of the due bill are entitled to the new
shares when they are issued