Lecture 8
Options on Futures
Primary Text
Edwards and Ma: Chapters 18, 19, & 20
Options on Futures
Call
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The structure of a futures option is very similar to an option on
the physical. For both instruments, an option owner has the right
to exercise, and the seller has a duty to perform upon exercise.
Upon exercising a futures option, a call holder receives a long
position in the underlying futures at the settlement price
prevailing at the time of exercise, plus a payment that equals the
futures settlement price (FPT) minus the exercise price (SPT) of
the futures option.
The call writer receives a short position in the underlying futures
at the settlement price prevailing at the time of exercise and
makes a payment to the call holder that equals the futures
settlement price (FPT) minus the exercise price (SPT) .
Options on Futures
Put

Upon exercising a put option on futures, a put holder receives
a short position in the underlying futures at the settlement
price prevailing at the time of exercise.

The put holder also receives a payment that equals the
exercise price of the futures option (SPT) minus the futures
settlement price (FPT).

The put writer receives a long position in the underlying
futures at the settlement price prevailing at the time of
exercise and makes a payment to the put holder equal to the
strike price (SPT) minus the futures settlement price (FPT).
Options on Futures
Call and Put Payoffs

In every exercise, the option holder and writer receive a futures
position. The traders may offset the futures position or continue
to hold the positions. For both the call and put, the purchaser
originally paid the option premium to the seller.
Futures Position and Cash Flow upon Exercise
Initial
Position
Immediate
FPT < SP
Cash Flow Futures Position
FPT > SP
Cash Flow
Futures Position
Cash Flow
Long Call
− Cf
No Exercise
0
Long Futures
FPT − SP
Short Call
+ Cf
No Exercise
0
Short Futures
−(FPT − SP)
Long Put
− Pf
Short Futures
SP − FPT
No Exercise
0
Short Put
+ Pf
Long Futures
−(SP − FPT)
No Exercise
0
Options on Futures
Profit/Loss from Call and Put
Upon Exercise of the option:

Profit/Loss of the Call Holder = Max (FPT −SPT, 0) − Cf

Profit/Loss of the Call Writer = Cf − Max (FPT −SPT, 0)

Profit/Loss of the Put Holder = Max (SPT −FPT, 0) − Pf

Profit/Loss of the Put Writer = Pf − Max (SPT −FPT, 0)

Note that, in addition to the profit or loss upon exercise of
the option, option holder and writer obtain futures
positions which need to be offset before expiration
Options on Futures
Profit Potentials and Risk Exposure

Consider three simple trading strategies in S&P 500 futures:

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a simple long position of a S&P 500 futures purchased at $300 per share
a long call option position in a S&P 500 futures with strike price $300
and premium $10 per share, and
a short put option position in a S&P 500 futures with strike price $300
and premium $10 per share.
Upon exercise of any of these contracts, the trader receives a
long position in S&P 500 index futures contract (with 500
shares) at the settlement price prevailing at the time of exercise.
The ultimate profits or losses associated with these positions
depend on the value of the S&P 500 futures contract at
expiration.
Options on Futures
Profit Potentials and Risk Exposure
Potential profits and losses from these positions for alternative hypothetical
futures prices at expiration, ranging from $280 to $330 per share.
Potential Profit/Loss from Long Futures, Long Call, and Short Put
20
Long Futures
Long Call
Short Put
15
Profit/Loss (1000 Dollars)

10
5
0
-5
-10
-15
280
290
300
310
Futures Price at Expiration
320
330
Options on Futures
Profit Potentials and Risk Exposure

Consider three simple trading strategies with S&P 500 futures:

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a short position (500 shares) at $300 per share,
a short call option position with strike price $300 and premium $10 per
share, and
a long put option position with strike price $300 and premium $10 per
share.
Upon exercise of any of these contracts, the trader receives a
short position in S&P 500 index futures contract (with 500
shares) at the settlement price prevailing at the time of exercise.
The ultimate profits or losses associated with these positions
depend on the value of the S&P 500 futures contract at
expiration.
Options on Futures
Profit Potentials and Risk Exposure
Potential profits and losses from these positions for alternative hypothetical
futures prices at expiration, ranging from $280 to $330 per share.
Potential Profit/Loss from Short Futures, Short Call, and Long Put
15
Short Futures
Short Call
Long Put
10
Profit/Loss (1000 Dollars)

5
0
-5
-10
-15
-20
280
290
300
310
Futures Price at Expiration
320
330
Options on Futures
Profit Potentials and Risk Exposure
Results of Futures Option Exercises
Initial
Position
Position upon
Profit
Risk
Exercise
Potential
Exposure
Long Futures
Long Futures
Unlimited
Unlimited
Long Call
Long Futures
Unlimited
Limited
Short Put
Long Futures
Limited
Unlimited
Short Futures
Short Futures
Unlimited
Unlimited
Short Call
Short Futures
Limited
Unlimited
Long Put
Short Futures
Unlimited
Limited
Options on Futures
Put-Call Parity Relationship for Futures Options

The put-call parity relationship for futures options:
Pf = Cf + SP - FP
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Pf = Put option premium
Cf = Call option premium
SP = Strike Price of the Call and Put options
FP = Futures settlement price
The put-call parity relationship states that put premium will be equal
to the call premium plus the difference between the strike price and
underlying futures price (i.e., SP – FP).
Since at-the-money calls and puts have no intrinsic value (i.e., SP =
FP, or SP – FP =0), their premiums are identical.
The relationship can also be expressed as Cf = Pf + FP - SP
Options on Futures
The Black Model for Futures Option Pricing

Fischer Black developed the following futures option pricing model:
C f  [ N ( d 1 )  FP  N ( d 2 )  SP ]  e
d1 
 FP 
ln 

 SP 

f




T
f
2
T
d 2  d1  



 rT
f
T
Cf = Call option premium ▪ SP = Strike Price of the Call and Put options
FP = Futures settlement price ▪ R = riskless interest rate
T = time to maturity of the option in years
σf = expected annualized volatility of the futures returns
N(d) = the probability that a random draw from a standard normal
distribution will be less than d
Options on Futures
Determinants of Futures Option Premiums
Determinants of Futures Options Premiums - effect of an increase in each factor.
Effect of an increase in each pricing factor on the option value,
holding other factors constant
Pricing Factors
Call Premium (Cf )
Put Premium (Pf )
Futures price (FP t )
(↑)
Increase (↑)
Decrease (↓)
Strike Price (SP t )
(↑)
Decrease (↓)
Increase (↑)
Time to Expiration (T − t )
(↑)
Increase (↑)
Increase (↑)
Interest Rate (r )
(↑)
Decrease (↓)
Decrease (↓)
Volatility (σ f )
(↑)
Increase (↑)
Increase (↑)
Options on Futures
Speculating with Futures Options


Strategies for speculating with options based on price change can be
categorized into two major groups: simple and complex.
Simple Speculation Strategies:
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
Long or short call
Long or short put
Complex Speculations Strategies:
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Covered Option Strategies:
 Covered call writing = short call + long futures
 Covered put writing = short put + short futures
Synthetic Option Strategies:
 Synthetic (long) call = long put + long futures
 Synthetic (long) put = long call + short futures
Options on Futures
Simple Speculation Strategies


Bullish: If a trader believes that stock or futures price will rise, she will adopt
a long call position (bullish strategy);
Bearish: If she believes that the stock or futures price will fall, she will adopt
a long put position (bearish strategy).
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The more bullish or bearish a trader is, the more attractive it will be to purchase an
out-of-the-money call or put option. Such options are cheaper, and provide greater
leverage with no additional downside risk.
Bearish to neutral: A trader who believes that stock or futures price will
either fall or remain constant (bearish to neutral) can earn income from
writing call (short call)
Bullish to neutral: A trader who believes that the stock or futures price will
either rise or remain constant (bullish to neutral) can earn income from
writing puts (short put).

Speculators who strongly hold these beliefs (bearish to neutral or bullish to neutral)
will want to write in-the-money options.
Options on Futures
Simple Speculation Strategies
Speculation with Futures Options - Simple Call and Put Strategies
Nature of the
Speculation
Trader's Belief
Belief
Strategy
FP will rise
Bullish
Long Call
FP will fall
Bearish
Long Put
FP will rise or remain constant
Bullish to Neutral
Short Put
FP will fall or remain constant
Bearish to Neutral
Short Call
Options on Futures
Complex Speculation Strategies
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Covered Call Writing: Selling a call option against a long futures (or stock)
position is known as covered call writing. This strategy permits a trader to
receive the call option premium in return for giving up some or all of the
upside profit potential due to an increase in the futures price. It is a desirable
strategy if futures prices are expected to remain fairly stable.
Example: Covered call writing strategy with S&P 500 futures purchased at
$300 per share and a short call option position in a S&P 500 futures with
strike price $300 and premium $10 per share.
If the S&P 500 futures price falls below or stays at $300, the call holder does
not exercise her right and let the call to expire − the speculator’s net profit or
loss is equal to the call premium minus the loss from the futures transaction.
If the S&P 500 futures price rise above $300, the call holder exercises her
right and the call writer receives a short position in S&P 500 futures, which is
offset by her long position in S&P 500 futures - the speculator’s net profit is
equal to the call premium
Options on Futures
Covered Call Writing – Profit or Loss
Speculation with Options - Covered Call Writing (Short Call plus Long Futures)
FP T < SP
Trader
Activity/Position
Call Holder
Do not exercise
Net Profit/Loss
Long Call (SP )
Speculator (Call Writer)
FP T > SP
Activity/Position
Exercise (receive futures position)
Long Futures
Offset futures position
Receive futures position
Short Futures
Short Futures
Short Call (SP )
Long Futures (FP t = SP )
Net Profit/Loss
Speculation with Options - Covered Call Writing
FP T < SP
Trader
Activity/Position
Call Holder
Do not exercise
Speculator (Call Writer)
−
Net Profit/Loss
− C f + (FP T − SP)
Long Futures
Receive futures position
C f − (FP T − SP)
Cf
FP T − SP
FP T − SP
Short Futures
C f + FP T − SP
−
Cf
Speculation with Options - Covered Call Writing
20
Long Futures
15
Profit/Loss (1000 US$)
−Cf
−
Short Futures
Activity/Position
Exercise (receive futures position)
Offset futures position
Short Call (SP )
Long Futures (FP t = SP )
Net Profit/Loss
−
Long Call (SP )
FP T > SP
Short Call
Short Call plus Long Futures
10
5
0
-5
-10
-15
280
290
300
310
Futures Price
320
330
Options on Futures
Complex Speculation Strategies
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Covered Put Writing: Selling a put option against a short futures (or stock)
position is known as covered put writing. This is an income augmenting
strategy, since the trader receives the put premium. This strategy again is
attractive if futures prices are expected to be fairly stable, since in the event
of declining futures price the short futures position will not be profitable
because the put holder will exercise her right.
Example: Short a put option in S&P 500 futures with strike price $300 and
premium $10 per share and short S&P 500 futures at $300 per share.
If the S&P 500 futures price falls below $300, the put holder will exercise her
right and receives a short position in the futures − the speculator’s net profit
or loss is equal to the put premium.
If the S&P 500 futures price rise above $300, the put holder will not exercise
the option, and the speculator will have to offset the short futures position by
purchasing the futures contract - the speculator’s net profit/loss is equal to the
put premium minus the loss from the futures transaction
Options on Futures
Covered Put Writing – Profit or Loss
Speculation with Options - Covered Put Writing (Short Put plus Short Futures)
FP T < SP
FP T > SP
Trader
Activity/Position
Net Profit/Loss
Activity/Position
Put Holder
Exercise (receive futures contract)
Do not exercise
Long Put (SP )
Speculator (Put Writer)
Net Profit/Loss
Short Futures
Receive futures position
Offset futures position
Short Put (SP )
Short Futures (FP t = SP ) Long Futures
Long Futures
Table 17: Speculation with Options - Covered Put Writing
FP T < SP
FP T > SP
Trader
Activity/Position
Put Holder
Exercise (receive futures contract)
Long Put (SP )
Short Futures
Speculator (Put Writer)
Activity/Position
− P f + SP − FP T
Long Futures
Short Futures (FP t = SP )
Cash Flow
Do not exercise
−
Receive futures position
Short Put (SP )
−Pf
Offset futures position
P f − (SP − FP T )
−
SP − FP T
−
Pf
−
Pf
− (FP T − SP )
Long Futures
−
P f + SP − FP T
Figure 12: Speculation with Options - Covered Put Writing
15
Short Futures
10
Profit/Loss (1000 US$)
Cash Flow
Short Put
Short Put plus Short Futures
5
0
-5
-10
-15
-20
280
290
300
310
Futures Price
320
330
Options on Futures
Complex Speculation Strategies
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Synthetic Options: Synthetic options are created by combining the purchase of
a call or put option with an outright short or long futures (or stock) position.
Synthetic option positions are generally used either as an efficient way to alter
the risk-return profile of an existing speculative position, perhaps because of a
change in a speculator’s price expectation, or as a way to lock in unrealized
speculative profits.
Synthetic Calls: Long futures plus a long put option on the futures contract
 A synthetic call strategy enables an investor to assume a position that has a
risk and return profile similar to an outright long call position.
 This strategy may be used by speculators who hold a long futures position
and, while confident that futures prices will rise in the long or even
intermediate term, fear an interim price decline.
 Buying the put protects them against potential losses associated with a
large price decline. In effect, the trader is placing a stop loss order on his
long futures position.
Options on Futures
Synthetic Calls – Profit or Loss

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Example: Long a put option in S&P 500 futures with strike price $300 and
premium $10 per share along with a long S&P 500 futures at $300 per share.
If the S&P 500 futures price falls below $300, the put holder will exercise
her right and receives a short position in the futures, plus a cash inflow equal
to the amount of (300 – FPT). She also incurs a loss from her long futures
position equal to the amount of (300 – FPT). Thus, upon exercise of the put
option, the speculator’s futures positions and cash flows are offset, and her
maximum loss is equal to the put premium (Pf = 10).
If the S&P 500 futures price rise above $300, the put holder will not exercise
her right and let the put option to expire, incurring a loss equal to the
premium paid (Pf = 10). But, she makes profit by offsetting her long futures
position (i.e., by selling the futures contract) equal to the amount of (FPT –
300).
Options on Futures
Synthetic Calls – Profit or Loss
Speculation with Options - Synthetic Call (Long Put plus Long Futures)
FP T < SP
Trader
Activity/Position
Speculator (Put Holder)
Exercise (receive futures position)
Long Put (SP )
Cash Flow
Short Put (SP )
Activity/Position
Do not exercise
Short Futures
Long Futures (FP t = SP )
Put Writer
FP T > SP
Short Futures
Receive futures position
Long Futures
Do nothing
Cash Flow
Speculation with Options - Synthetic Call
FP T < SP
FP T > SP
Trader
Activity/Position
Speculator (Put Holder)
Exercise (receive futures position)
Long Put (SP )
Short Futures
Long Futures (FP t = SP )
Put Writer
Net Profit/Loss
− P f + SP − FP T
−
− (SP − FP T )
−
−Pf
Receive futures position
Short Put (SP )
Long Futures
P f − (SP − FP T )
Activity/Position
Net Profit/Loss
Do not exercise
−
−Pf
Short Futures
−
FP T − SP
− P f + FP T − SP
Do nothing
−
Pf
Speculation with Options - Synthetic Call
Profit/Loss (1,000 US$)
20
Long Futures
Long Put
15
10
5
0
-5
-10
-15
280
290
300
310
Futures Price
320
330
Options on Futures
Synthetic Puts
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Synthetic Puts: Short futures plus a long call option on the futures contract
 This strategy insulates the speculator from losses due to a large price
increase, but still permits him to profit from declining prices.
 This strategy allows the speculator either to lock in an unrealized profit or
limit the loss on the short futures position. The profit/loss profile of this
position is similar to that of a long put.
Example: Long a call option in S&P 500 futures with strike price $300 and
premium $10 per share along with a short S&P 500 futures at $300 per share.
If the S&P 500 futures price falls below $300, the speculator will not exercise
the call option but offsets the short futures position. Her net profit is equal to
the gain from futures transaction (300 – FPT) minus the call premium.
If the S&P 500 futures price rise above $300, the speculator will exercise the
call option and receive a long position in S&P 500 futures which is offset
against her short futures position. Her net loss from the synthetic put strategy is
equal to the call option premium paid.
Options on Futures
Synthetic Puts – Profit or Loss
Speculation with Options - Synthetic Put (Long Call plus Short Futures)
FP T < SP
Trader
Activity/Position
Speculator (Call Holder)
Do not exercise
Long Call (SP )
Net Profit/Loss
FP T > SP
Activity/Position
Net Profit/Loss
Exercise (receive futures position)
Long Futures
Short Futures (FP t = SP ) Long Futures
Call Writer
Short Call (SP )
Do nothing
Receive futures position
Short Futures
Table 19: Speculation with Options - Synthetic Put
FP T < SP
Trader
Activity/Position
Speculator (Call Holder)
Do not exercise
Short Futures (FP t = SP )
Activity/Position
−Cf
Long Futures
− C f + (FP T − SP )
(SP − FP T )
−
− (FP T − SP )
− C f + (SP − FP T )
−
−Cf
Do nothing
Receive futures position
−
Short Call (SP )
Net Profit/Loss
Exercise (receive futures position)
Long Futures
−
Call Writer
Net Profit/Loss
−
Long Call (SP )
FP T > SP
Cf
Short Futures
C f − (FP T − SP )
Speculation with options - Synthetic Put
15
Profit/Loss (1,000 US$)
Short Futures
Long Call
Long Call plus Short Futures
10
5
0
-5
-10
-15
-20
280
290
300
310
Futures Price
320
330
Options on Futures
Speculations with Futures Options – Complex Strategies
Speculation with Futures Options - Complex Strategies
Nature of the
Speculation
Trader's Belief
Belief
Strategy
Resemblance
FP will rise
Bullish
Synthetic Call
Long Call
FP will fall
Bearish
Synthetic Put
Long Put
FP will rise or remain constant Neutral to slightly Bullish Covered Call Writing
Short Put
FP will fall or remain constant Neutral to slightly Bearish Covered Put Writing
Short Call
Options on Futures
Option Spreads



Option spreads are a way to speculate on relative price changes.
These strategies involve the simultaneous purchase and sale of different
options, creating a price spread that widens or narrows according to what
happens to underlying asset prices.
Common option spreads are categorized in three major types:

Vertical Spreads – An option spread in which the two legs of the spread
have different strike prices but have the same expiration date
 Horizontal Spreads – An option spread in which the two legs of the
spread have different expiration dates but the same strike price

Diagonal Spreads – An option spread in which the two legs of the spread
have both different strike prices and different expiration dates
 Diagonal spreads are hybrids of vertical and horizontal spreads

The appropriate spreading strategies differ depending on the market trend
in the prices of underlying futures (or assets).
Options on Futures
Option Spreads


Bullish Vertical Option Spreads – Bullish option spreads are strategies that
yield a profit when underlying asset prices rise. Such spreads are established
by purchasing an option with a low strike price and selling an option with a
high strike price, both with the same expiration date.
Bull Vertical Call Option Spreads - A bull vertical call option spread is
created by buying a call option with a relatively low strike price (SPL) and
selling a call option with a relatively high strike price (SPH), both with the
same expiration date.

To initiate this spread, the speculator has to invest a cash amount equal to
the difference between the low strike premium (CL) and the high strike
premium (CH), which is commonly known among the option traders as
the net debit.

Net Debit = − call premium paid + call premium received
= − CL + CH < 0 (because CL > CH)
Options on Futures
Bull Vertical Call Option Spreads



If, upon expiration, the underlying futures price (FP) is less than or equal to
the lower of the two strike prices, both options will expire out-of-the-money.
In this case, the speculator will lose the difference between the premiums.
Maximum Loss = − CL + CH = Net debit (remember, CL > CH)
If prices rise prior to expiration and the futures price (FP) exceeds the higher
strike price, both options will be in-the-money and exercised. In this case, the
speculator’s maximum profit will be equal to the difference between the two
strike prices (SPH−SPL) less the net debit (− CL + CH)
Maximum Profit = (SPH−SPL) − CL + CH = Strike price diff. - Net debit
If prices rise prior to expiration and the futures price (FP) lies between the two
strike prices, long call with the lower strike price will be in-the-money and the
short call with the higher strike price will still be out-of-the-money. In this case
the speculator will exercise the long call and the higher strike call holder will
let the option to expire.
Profit/Loss = − CL + CH + (FP−SPL) = Net debit + Diff. in FP and SPL
Options on Futures
Bull Vertical Call Option Spreads
Profit-Loss Profile of a Bull Vertical Call Spread
Bull Vertical
Call Spread
FP ≤ SP L
Activity
Cash Flow
SP H ≤ FP
SP L < FP < SP H
Activity
Cash Flow
Activity
Long Call (SP L ) Let Expire
Exercise
Exercise
Short Call (SP H ) Let Expire
Let Expire
Exercise
Profit/Loss
Cash Flow
Spreading with Options: Bull Vertical Call Spreads
Table 21: Profit-Loss Profile of a Bull Vertical Call Spread
FP ≤ SP L
Bull Vertical
Call Spread
Activity
SP H < FP
SP L < FP < SP H
Cash Flow
Activity
Cash Flow
Activity
Cash Flow
Long Call (SP L ) Let Expire
− CL
Exercise
− C L + (FP − SP L )
Exercise
− C L + (FP − SP L )
Short Call (SP H ) Let Expire
CH
Let Expire
CH
Exercise
C H − (FP − SP H )
(FP −SP L ) − C L +C H
− CL + CH
Profit/Loss
(SP H −SP L ) − C L +C H
S&P 500 Futures $300-320 (premium $10 and $5) Bull Vertical Call Spread
Profit/Loss per contract ($1,000)
8
6
4
2
0
-2
-4
280
290
300
310
Futures Price
320
330
340
Options on Futures
Option Spreads


Bull Vertical Put Option Spreads - A bull vertical put spread is created by
purchasing a put option with a low strike price (SPL) and selling a put option
with a higher strike price (SPH) , both with the same expiration date.
 The premium paid to purchase the lower strike put option (PL) will always
be less than the premium received from the sale of the higher strike put
(PH), so that the net premium will generate a cash inflow, which is
commonly known among the option traders as the net credit.

Net Credit = − Put premium paid + Put premium received
= − PL + PH > 0 (because PL < PH)
If, at expiration, the underlying futures price (FP) is less than or equal to the
lower of the two strike prices, both options will be in-the-money and will be
exercised. In this case, the speculator incurs a net loss equal to the difference
of the two strike prices (SPL – SPH) plus the net credit (− PL + PH).
Maximum Loss= (SPL − SPH) − PL + PH = − Strike price diff. + Net credit
Options on Futures
Bull Vertical Call Option Spreads


If prices rise prior to expiration and the futures price (FP) exceeds the higher
strike price, both options will expire out-of-the-money and are not likely to be
exercised. Thus, the speculator maximum profit will be equal to the net credit
(− PL + PH).
Maximum Profit = − PL + PH = Net credit (remember, PL < PH)
If prices rise prior to expiration and the futures price (FP) lies between the two
strike prices, long put with the lower strike price will be out-of-the-money
(will not be exercised) and the short put with the higher strike price will be inthe-money (will be exercised). In this case, the speculator’s net profit or loss
will be equal to the difference between the futures price and higher strike price
(FP−SPH) plus the net debit (− PL + PH), which may be less than, or equal to,
or higher than zero.
Profit/Loss = (FP−SPH) − PL + PH = Diff. in FP and SPH + Net Credit
Options on Futures
Bull Vertical Put Option Spreads

Like a bull vertical call spread, bull vertical put spreads have limited profit and
loss potentials. The major distinction is that a call spread results in a net debit
(cash outflow), while a bull vertical put spread results in a net credit (cash
inflow). A vertical put spread can be profitable even if futures (or asset) price do
not rise, as long as they do not fall. Some traders, therefore, prefer a bull put
spread to a bull call spread.
Profit-Loss Profile of a Bull Vertical Put Spread
FP ≤ SP L
Bull Vertical
Activity
Cash Flow
SP H ≤ FP
Put Spread
Activity
Long Put (SP L )
Exercise
Let Expire
Let Expire
Short Put (SP H )
Exercise
Exercise
Let Expire
Profit/Loss
Cash Flow
SP L < FP < SP H
Activity
Cash Flow
Spreading with Options: Bull Vertical Put Spreads
Table 22: Profit-Loss Profile of a Bull Vertical Put Spread
FP ≤ SP L
Bull Vertical
SP H ≤ FP
SP L < FP < SP H
Put Spread
Activity
Cash Flow
Activity
Cash Flow
Activity
Cash Flow
Long Put (SP L )
Exercise
− P L + (SP L − FP )
Let Expire
− PL
Let Expire
− PL
Short Put (SP H )
Exercise
P H − (SP H − FP )
Exercise
P H − (SP H − FP )
Let Expire
PH
(SP L −SP H ) − P L +P H
Profit/Loss
(FP −SP H ) − P L +P H
− PL + PH
S&P 500 Futures $300-320 (premium $5 and $10) Bull Vertical Put Spread
Profit/Loss per contract ($1,000)
4
2
0
-2
-4
-6
-8
280
290
300
310
Futures Price
320
330
340
Options on Futures
Option Spreads


Bearish Vertical Option Spreads – Bearish option spreads are strategies that
yield a profit when underlying futures (or asset) prices decline. Such spreads
are established by purchasing an option with a high strike price and selling an
option with a low strike price, both with the same expiration date.
Bear Vertical Call Option Spreads - A bear vertical call options spread is
created by buying a call option with a relatively high strike price (SPH) and
selling a call option with a relatively low strike price (SPL), both with the
same expiration date.

Initiating this spread, the speculator receives a cash inflow equal to the
difference between the low strike premium (CL) and the high strike
premium (CH), which is commonly known among the option traders as
the net credit.

Net Credit = Call premium received − Call premium paid
= CL − CH > 0 (because CL > CH)
Options on Futures
Bear Vertical Call Option Spreads



If, upon expiration, the underlying futures price is less than or equal to the
lower of the two strike prices, both options will expire out-of-the-money. In
this case, the speculator will earn the difference between the premiums.
Maximum Profit = CL − CH = Net Credit (remember, CL > CH)
If prices rise prior to expiration and the futures price exceeds the higher strike
price, both options will be in-the-money and exercised. The maximum loss in
that case will be the net premium earned (CL − CH) minus the difference
between the strike prices of the tow options (SPH−SPL).
Maximum Loss = CL − CH − (SPH−SPL) = Net Credit − Strike price diff.
If prices rise prior to expiration and the futures price lies between the two
strike prices, long call with the lower strike price will be in-the-money
(exercised) and the short call with the higher strike price will still be out-ofthe-money (expire).
Profit/Loss = CL − CH − (FP−SPL) = Net credit − Diff. in FP and SPL
Options on Futures
Bear Vertical Call Option Spreads
Profit-Loss Profile of a Bear Vertical Call Spread
Bull Vertical
Call Spread
FP ≤ SP L
Activity
Cash Flow
SP H < FP
SP L < FP < SP H
Activity
Cash Flow
Activity
Short Call (SP L ) Let Expire
Exercise
Exercise
Long Call (SP H ) Let Expire
Let Expire
Exercise
Profit/Loss
Cash Flow
Spreading with Options: Bear Vertical Call Spreads
Table 23: Profit-Loss Profile of a Bear Vertical Call Spread
FP ≤ SP L
Bull Vertical
Call Spread
Activity
SP H < FP
SP L < FP < SP H
Cash Flow
Activity
Cash Flow
Activity
Cash Flow
Short Call (SP L ) Let Expire
CL
Exercise
C L − (FP − SP L )
Exercise
C L − (FP − SP L )
Long Call (SP H ) Let Expire
− CH
Let Expire
− CH
Exercise
− C H + (FP − SP H )
CL − CH
Profit/Loss
C L − C H − (FP−SP L )
C L −C H − (SP H −SP L )
S&P 500 Futures $300-320 (premium $10 and $5) Bear Vertical Call Spread
Profit/Loss per Contract ($1,000)
4
2
0
-2
-4
-6
-8
280
290
300
310
Futures Prices
320
330
340
Options on Futures
Option Spreads


Bear Vertical Put Option Spreads - A bear vertical put spread is created by
purchasing a put option with a relatively higher strike price (SPH) and selling a
put option with a lower strike price (SPL) , both with the same expiration date.
 The premium paid to purchase the higher strike put option (PH) will
always be higher than the premium received from the sale of the lower
strike put (PL), so that the net premium will generate a cash outflow,
which is commonly known among the option traders as the net debit.

Net Debit = Put premium received − Put premium paid
= PL − PH < 0 (because, PL < PH)
If futures price (FP) declines to a level lower than the lower strike price, both
options will be in-the-money and exercised. The maximum profit in that case
will be the net premium paid (net debit, PL − PH ) plus the difference between
the strike prices of the two options
Maximum Profit = PL − PH + (SPH − SPL) = Net debit +Strike Price Diff.
Options on Futures
Bear Vertical Put Option Spreads

If futures price rise to a level greater than the higher strike price, both options
will expire out-of-the-money. In this case, the spreader incurs a net loss equal
to the net debit (− PH + PL).
Maximum Loss= PL − PH = Net debit < 0

If the futures price lies between the two strike prices, the (short) put option
with the higher strike price will be in-the-money and exercised, and the (long)
put with the lower strike price will be out-of-the-money and expire
unexercised. In this case, the spreader’s net profit or loss will be equal to the
net debit (PL − PH) plus the difference between the higher strike price and
futures price (SPH− FP).
Profit/Loss = PL − PH + (FP−SPH) = Net debit + Diff. in FP and SPH
Options on Futures
Bear Vertical Put Option Spreads

The difference between bear vertical call and put spread strategies is that a
vertical call spread will be profitable even if asset prices do not decline, as long
as prices do not rise. A vertical put spread will not be profitable unless prices
actually decline. Therefore, speculators often prefer bear vertical call spreads to
bear vertical put spreads.
Profit-Loss Profile of a Bear Vertical Put Spread
FP ≤ SP L
Bull Vertical
Activity
Cash Flow
SP H ≤ FP
Put Spread
Activity
Short Put (SP L )
Exercise
Let Expire
Let Expire
Long Put (SP H )
Exercise
Exercise
Let Expire
Profit/Loss
Cash Flow
SP L < FP < SP H
Activity
Cash Flow
Spreading with Options: Bear Vertical Put Spreads
Table 24: Profit-Loss Profile of a Bear Vertical Put Spread
FP ≤ SP L
Bull Vertical
SP H ≤ FP
SP L < FP < SP H
Put Spread
Activity
Cash Flow
Activity
Cash Flow
Activity
Cash Flow
Short Put (SP L )
Exercise
P L − (SP L − FP )
Let Expire
PL
Let Expire
PL
Long Put (SP H )
Exercise
− P H + (SP H − FP )
Exercise
− P H + (SP H − FP )
Let Expire
− PH
P L − P H + (SP H −SP L )
Profit/Loss
P L − P H + (SP H −FP )
PL − PH
S&P 500 Futures $300-320 (prem. $5 and $10) Bear Vertical Put Spread
Profit/Loss per Contract ($1,000)
8
6
4
2
0
-2
-4
280
290
300
310
Futures Prices
320
330
340
Options on Futures
Horizontal or Time Spreads





Horizontal or Time Spreads:
If an investor believes that underlying asset prices will be stable for a
foreseeable period of time, he or she can attempt to profit from the declining
time value of options by setting up a horizontal option spread.
A horizontal option spread is created by selling an option with a relatively
short time to expiration and buying an option of the same time with a longer
time to expiration, both with the same strike prices.
In general, the time value of a short-maturity option will decline at a faster rate
than will the time value of a longer maturity option.
Thus, as long as the underlying asset price remains stable, or does not move
significantly against the investor, he or she can make profit from “riding
down” the time value of the near-term option, since the loss on the longer-term
option will be less than the profit on the near-term option.
Options on Futures
Straddles and Strangles







Straddles:
Like spreads, straddles involve the simultaneous sale and purchase of options.
Unlike spreads, straddles entail the purchase of a call and put (a long straddle),
or the sale of a call and put (a short straddle).
This strategy is often used by speculators who believe that asset prices either
will move substantially in one direction or the other (but are uncertain as to
which direction) or will remain fairly constant.
Long Straddle:
A long straddle is formed by buying an equal number of calls and puts with
the same strike price and with the same expiration date.
This strategy will be profitable if underlying asset prices move substantially in
either direction.

If prices fall – the put option will become profitable

If prices rise – the call option will become profitable
Options on Futures
Long Straddle
FPT <SP
Trader
Activity
Profit/Loss
FPT >SP
Activity
Long Call
Do not exercise
Exercise
Long Put
Exercise
Do not exercise
Net Returns
Profit/Loss
Options on Futures
Long Straddle


The maximum loss from the straddle: The cost of the straddle, that is the
sum of call and put premiums paid, −(Cf + Pf) – which will occur if the futures
price at expiration is the same as the strike price of the option.
The maximum profit from the straddle: Unlimited. To the extent that the
gain on the profitable option exceeds the total premium cost of establishing
the straddle, there will be a net profit.
FPT <SP
Trader
Activity
Long Call
Do not exercise
− Cf
Exercise
−Cf + (FPT −SP )
Long Put
Exercise
−Pf + (SP − FPT)
Do not exercise
−Pf
Net Returns
Profit/Loss
FPT >SP
−(Cf +Pf) + (SP−FPT)
Activity
Profit/Loss
−(Cf +Pf) +(FPT −SP )
Options on Futures
Long Straddle
Long Straddle: S&P 500 Futures, Call and Put with strike price 300
and premium 10 per share
6,000
4,000
2,000
0
-2,000
-4,000
-6,000
-8,000
-10,000
-12,000
270
280
290
300
310
320
330
Options on Futures
Short Straddles




Short Straddle:
A short straddle is formed by selling an equal number of calls and puts with
the same strike price and with the same expiration date.
This strategy will be profitable if underlying asset prices remain stable.
If futures prices move substantially in either direction, the trader incurs loses

If prices fall – the put option will be exercised by the holder

If prices rise – the call option will be exercised by the holder

The maximum profit from short straddle: Limited to the premiums received
from selling the call and put options, that is (Cf + Pf)

The maximum loss from short straddle: Unlimited. To the extent that the
loss from the exercised option exceeds the total premium received, there will
be a net loss.
Options on Futures
Short Straddle
FPT < SP
Trader
Activity
Profit/Loss
FPT > SP
Activity
Short Call
Call holder does
not exercise
Call holder
exercises
Short Put
Put holder
exercises
Put holder does
not exercise
Net Returns
Profit/Loss
Options on Futures
Short Straddle


Short straddles are more popular of the two strategies.
These are employed to take advantage of the declining time value of
options in markets where asset prices are expected to remain constant
FPT <SP
Trader
FPT >SP
Activity
Profit/Loss
Activity
Profit/Loss
Short Call
Call holder does
not exercise
Cf
Call holder
exercises
Cf − (FPT −SP )
Short Put
Put holder
exercises
Pf − (SP − FPT)
Put holder does
not exercise
Pf
Net Retuns
Cf +Pf − (SP−FPT)
Cf +Pf − (FPT −SP )
Options on Futures
Short Straddle
Short Straddle: S&P 500 Futures, Call and Put with strike price 300 and
premium 10 per share
12,000
10,000
8,000
6,000
4,000
2,000
0
-2,000
-4,000
-6,000
270
280
290
300
310
320
330
Options on Futures
Straddles and Strangles







Strangles:
A strangle is a straddle in which the two legs do not share a common strike
price – that is the call and put have different strike prices.
A long strangle is used to profit from a volatile price scenario.
A short strangle is used to profit from a stable price scenario.
Long Strangle:
A long strangle is formed by buying an equal number of calls and puts with
different strike prices but with the same expiration date.
This strategy will be profitable if underlying asset prices move substantially in
either direction.

If prices fall – the put option will become profitable

If prices rise – the call option will become profitable
Options on Futures
Long Strangle


Consider a out-of-the-money strangle: established by purchasing a call with
higher strike price (SPC) and a put with lower strike price (SPP) .
SPC > SPP
FPT < SPP< SPC
Activity
Profit/Loss
SPP < SPC < FPT
Trader
Activity
Long Call
(SPC)
Do not
exercise
Do not
exercise
Exercise
Long Put
(SPP)
Exercise
Do not
exercise
Do not
exercise
Net
Returns
Profit/Loss
SPP< FPT < SPC
Activity
Profit/Loss
Options on Futures
Long Strangle


The maximum loss from the strangle: The cost of the strangle, that is the
sum of call and put premiums paid, −(Cf + Pf). The net returns profile is
characterized by a broad flat zone of losses – between the two strike prices.
The maximum profit from the straddle: Unlimited.
FPT < SPP< SPC
SPP< FPT < SPC
SPP < SPC < FPT
Trader
Activity
Profit/Loss
Activity
Profit/Loss
Activity
Profit/Loss
Long Call
(SPC)
Do not
exercise
−Cf
Do not
exercise
− Cf
Exercise
− Cf +
Long Put
(SPP)
Exercise
−Pf +
Do not
exercise
−Pf
Do not
exercise
Net
Returns
(SPP − FPT)
−(Cf +Pf ) +
(SPP − FPT)
−(Cf +Pf )
(FPT − SPC )
−Pf
−(Cf +Pf ) +
(FPT−SPC )
Options on Futures
Long Strangle
Long Strangle: S&P 500 Futures, Call with SP 320 premium 15 and Put with
SP300 and premium 10
4,000
2,000
0
-2,000
-4,000
-6,000
-8,000
-10,000
-12,000
-14,000
270
280
290
300
310
320
330
340
350
Options on Futures
Strangles




Short Strangle:
A short strangle is formed by selling an equal number of calls and puts with
different strike prices but with the same expiration date.
This strategy will be profitable if underlying asset prices remain fairly stable.
If futures prices move substantially in either direction, the trader incurs loses

If prices fall – the put option will be exercised by the holder

If prices rise – the call option will be exercised by the holder

The maximum profit from short strangle: Limited to the premiums received
from selling the call and put options, that is (Cf + Pf)

The maximum loss from short strangle: Unlimited. To the extent that the
loss from the exercised option exceeds the total premium received, there will
be a net loss.
Options on Futures
Short Strangle


Consider a out-of-the-money strangle: established by selling a call with higher
strike price (SPC) a put with lower strike price (SPP) .
SPC > SPP
FPT < SPP< SPC
Activity
Profit/Loss
SPP < SPC < FPT
Trader
Activity
Short Call
(SPC)
Holder does
not exercise
Holder does
not exercise
Holder
Exercises
Short Put
(SPP)
Holder
Exercises
Holder does
not exercise
Holder does
not exercise
Net
Returns
Profit/Loss
SPP< FPT < SPC
Activity
Profit/Loss
Options on Futures
Short Strangle


Short strangles are more popular of the two strategies.
These are employed to take advantage of the declining time value of options in
markets where asset prices are expected to remain constant
FPT < SPP< SPC
Trader
Activity
Short Call
(SPC)
Short Put
(SPP)
Net
Returns
SPP< FPT < SPC
SPP < SPC < FPT
Profit/Loss
Activity
Profit/Loss
Activity
Profit/Loss
Holder
does not
exercise
Cf
Holder
does not
exercise
Cf
Holder
Exercises
Cf −
(FPT − SPC )
Holder
Exercises
Pf −
(SPP − FPT)
Holder
does not
exercise
Pf
Holder
does not
exercise
Pf
(Cf +Pf ) −
(SPP − FPT)
Cf + P f
(Cf +Pf ) −
(FPT−SPC )
Options on Futures
Short Strangle
Short Straddle: S&P 500 Futures, Call with SP 320 premium 15 and Put
with SP300 and premium 10
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
-2,000
-4,000
270
280
290
300
310
320
330
340
350
Options on Futures
Hedging with Options on Futures

Hedgers using futures basically attempt to lock in a specific price. In
contrast, hedgers using options seek to set a specific floor or ceiling
price.

Hedging with futures allows hedgers to lock in a specific price
but restricts them to benefit from favorable price movements.

hedging with options allows hedgers to lock in a floor or ceiling
price at the expense of option premiums.

A futures hedger generally assumes a futures position opposite that of
his cash position, hoping to offset any cash market loss with a profit
on futures position.

An option hedger, however, can establish a floor price (with a long put
position), or a ceiling price (with a long call position), and still retain
the possibility of profiting from favorable price movement.
Options on Futures: Short Hedge
Hedging with Options on Futures

Assume that on 24 April 2010, a US soybean farmer plants soybean in her
farmland with an expectation of harvesting 50,000 bushels of soybean in
October 2010.

The cash price for soybeans in the local spot market is $10.00 per bushel
(60 pounds) during plantation.

The farmer is worried that cash prices for soybeans will decrease during
the fall months, and she may not be able to recover her production costs.

In order to minimize her price risk, the farmer considers the potentials of
hedging with futures and options. The two simple ways of hedging are:
1. Sell November 2010 Soybean futures contract, and
2. Purchase put option on November 2010 Soybean futures contract.
Options on Futures
Hedging with Options on Futures

On 24 April 2010, the November 2010 Soybean futures price is $10.40
per bushel, resulting in a basis – $0.40 per bushel.

Assume that cash, futures, and options prices are highly correlated with
each other.

Also assume that the basis remains constant from April through
September.

Consider two cash price scenarios at the time of harvest:

cash price for soybeans declines to $9.00 per bushel, and

cash price for soybeans increases to $11.00 per bushel.

Since the basis is assumed to remain constant, the futures prices for
these scenarios will be $9.40 and $11.40 per bushel, respectively.
Hedging with Futures: Short Hedge
Soybeans: Planted in April and Harvested in September
Date
24 April 2010
Cash (soybeans)
Futures (soybeans)
US$ 10.00 per bushel
(Basis is − 0.40)
Price Decline
30 Sep 2010
Sell 50,000 bushels @
US$ 9.00 per bushel
(Basis is − 0.40)
Gain/Loss =
Effective price
Price Increase
30 Sep 2010
Sell 50,000 bushels @
US$ 11.00 per bushel
(Basis is − 0.40)
Effective price
Gain/Loss =
Hedging with Futures: Short Hedge
Table 25: Hedging with Futures.
Date
24-Apr-10
Cash
US$ 10.00 per bushel
Futures
Short 10 soybean futures contracts @
US$ 10.40 per bushel
Price Decline
30-Sep-10
Sell 50,000 bushels of soybeans @
Long 10 soybean futures contracts @
US$ 9.00 per bushel
US$ 9.40 per bushel
Gain = US$1.00 per bushel
Effective sales price (US$/bushel))
10.00
Price Increase
30-Sep-10
Sell 50,000 bushels of soybeans @
Long 10 soybean futures contracts @
US$ 11.00 per bushel
US$ 11.40 per bushel
Loss = −1.00 (US$) per bushel
Effective sales price (US$/bushel))
10.00
Hedging with Options on Futures: Short Hedge
Soybeans: Planted in April and Harvested in September
Date
24 April 2010
Cash (soybeans)
Options (soybeans)
US$ 10.00 per bushel
(Basis is − 0.40)
Price Decline
30 Sep 2010
Sell 50,000 bushels @
US$ 9.00 per bushel
(Basis is − 0.40)
Gain/Loss =
Effective price
Price Increase
30 Sep 2010
Sell 50,000 bushels @
US$ 11.00 per bushel
(Basis is − 0.40)
Effective price
Gain/Loss =
Hedging with Options: Short Hedge
Table 26: Hedging with Options on Futures.
Date
24-Apr-10
Cash
US$ 10.00 per bushel
Options
Buy put on 10 soybean futures with Strike
price $ 11.00 at premium $0.5 per bushel
Price Decline
30-Sep-10
Sell 50,000 bushels of soybeans @
Soybean futures contracts price is $9.4
US$ 9.00 per bushel
Exercise the put option
Gain = (11.0 − 9.4) − 0.5 = $ 1.10/bushel
Effective sales price (US$/bushel))
10.10
Price Increase
30-Sep-10
Sell 50,000 bushels of soybeans @
Soybean futures contracts price is $11.4
US$ 11.00 per bushel
Do not exercise the put option
Loss = −0.50 (US$) per bushel
Effective sales price (US$/bushel))
10.50
Options on Futures: Long Hedge
Hedging with Options on Futures

Assume that on 24 April 2010, a US soybean oil producer estimates that
she will need 50,000 bushels of soybean in October 2010 for full capacity
utilization of her processing plant.

The cash price for soybeans in the local spot market is $10.00 per bushel
(60 pounds) in April.

The soybean crusher is worried that cash prices for soybeans may
increase during the fall months.

In order to minimize her price risk, the soybean crusher considers the
potentials of hedging with futures and options. The two simple ways of
hedging are:
1. Buy November 2010 Soybean futures contract, and
2. Buy a call option on November 2010 Soybean futures contract.
Options on Futures: Long Hedge
Hedging with Options on Futures

On 24 April 2010, the November 2010 Soybean futures price is $10.40
per bushel, resulting in a basis – $0.40 per bushel.

Assume that cash, futures, and options prices are highly correlated with
each other.

Also assume that the basis remains constant from April through
September.

Consider two cash price scenarios at the time of harvest:

cash price for soybeans declines to $9.00 per bushel, and

cash price for soybeans increases to $11.00 per bushel.

Since the basis is assumed to remain constant, the futures prices for
these scenarios will be $9.40 and $11.40 per bushel, respectively.
Hedging with Futures: Long Hedge
Soybeans: Planted in April and Harvested in September
Date
24 April 2010
Cash (soybeans)
Futures (soybeans)
US$ 10.00 per bushel
(Basis is − 0.40)
Price Decline
30 Sep 2010
Buy 50,000 bushels @
US$ 9.00 per bushel
(Basis is − 0.40)
Gain/Loss =
Effective cost
Price Increase
30 Sep 2010
Buy 50,000 bushels @
US$ 11.00 per bushel
(Basis is − 0.40)
Effective cost
Gain/Loss =
Hedging with Futures: Long Hedge
Table 25: Hedging with Futures.
Date
24-Apr-10
Cash
US$ 10.00 per bushel
Futures
Long 10 soybean futures contracts @
US$ 10.40 per bushel
Price Decline
30-Sep-10
Buy 50,000 bushels of soybeans @
Short 10 soybean futures contracts @
US$ 9.00 per bushel
US$ 9.40 per bushel
Loss = −$1.00 per bushel
Effective cost (US$/bushel))
($9.00 + $1.00=) 10.00
Price Increase
30-Sep-10
Buy 50,000 bushels of soybeans @
Short 10 soybean futures contracts @
US$ 11.00 per bushel
US$ 11.40 per bushel
Gain = 1.00 (US$) per bushel
Effective cost (US$/bushel))
($11.00 − $1.00 =) 10.00
Hedging with Options on Futures: Long Hedge
Soybeans: Planted in April and Harvested in September
Date
24 April 2010
Cash (soybeans)
Options (soybeans)
US$ 10.00 per bushel
(Basis is − 0.44)
Price Decline
30 Sep 2010
Buy 50,000 bushels @
US$ 9.00 per bushel
(Basis is − 0.44)
Gain/Loss =
Effective cost
Price Increase
30 Sep 2010
Buy 50,000 bushels @
US$ 11.00 per bushel
(Basis is − 0.44)
Effective cost
Gain/Loss =
Hedging with Options: Long Hedge
Table 26: Hedging with Options on Futures.
Date
24-Apr-10
Cash
US$ 10.00 per bushel
Options
Long a call on 10 soybean futures with
Strike price $ 9.50 at premium $0.5/bushel
Price Decline
30-Sep-10
Buy 50,000 bushels of soybeans @
Soybean futures contracts price is $9.4
US$ 9.00 per bushel
Do not exercise the call option
Loss = − $0.5/bushel
Effective cost (US$/bushel))
($9.00 + 0.50 =) $9.50
Price Increase
30-Sep-10
Buy 50,000 bushels of soybeans @
Soybean futures contracts price is $11.4
US$ 11.00 per bushel
Exercise the call option
Gain = (11.40 - 9.50) − 0.50 = 1.40 $/bu.
Effective cost (US$/bushel))
(11 − 1.40 =) 9.60 $/bushel