Lecture 8 Options on Futures Primary Text Edwards and Ma: Chapters 18, 19, & 20.

Lecture 8Options on Futures

Primary Text

Edwards and Ma: Chapters 18, 19, & 20

Options on FuturesCall

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 FuturesPut

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).

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.

Options on FuturesCall and Put Payoffs

Futures Position and Cash Flow upon Exercise

Initial Immediate FPT < SP FPT > SP

Position Cash Flow Futures Position

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

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 FuturesProfit/Loss from Call and Put

Options on FuturesProfit Potentials and Risk Exposure

Consider three simple trading strategies in S&P 500 futures: 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.

Potential profits and losses from these positions for alternative hypothetical futures prices at expiration, ranging from $280 to $330 per share.

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280 290 300 310 320 330

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Futures Price at Expiration

Potential Profit/Loss from Long Futures, Long Call, and Short Put

Long Futures Long Call Short Put


Options on Futures

Consider three simple trading strategies with S&P 500 futures: 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.

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.

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280 290 300 310 320 330

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Futures Price at Expiration

Potential Profit/Loss from Short Futures, Short Call, and Long Put

Short Futures Short Call Long Put


Results of Futures Option Exercises

Initial Position upon Profit Risk

Position 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


The put-call parity relationship for futures options:

Pf = Cf + SP - FP 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 FuturesPut-Call Parity Relationship for Futures Options

Fischer Black developed the following futures option pricing model:

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 FuturesThe Black Model for Futures Option Pricing

rTf eSPdNFPdNC ])()([ 21

2

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1

T

T

SPFP

d f

f

Tdd f 12

Options on FuturesDeterminants of Futures Option Premiums

Determinants of Futures Options Premiums - effect of an increase in each factor.

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 (↑)

holding other factors constant

Effect of an increase in each pricing factor on the option value,

Strategies for speculating with options based on price change can be categorized into two major groups: simple and complex.

Simple Speculation Strategies: Long or short call Long or short put

Complex Speculations Strategies: 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 FuturesSpeculating with Futures Options

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).

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 FuturesSimple Speculation Strategies

Options on FuturesSimple 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

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 FuturesComplex Speculation Strategies

Speculation with Options - Covered Call Writing (Short Call plus Long Futures)

Trader Activity/Position Net Profit/Loss Activity/Position Net Profit/Loss

Call Holder Do not exercise Exercise (receive futures position)

Long Call (SP ) Long Futures

Speculator (Call Writer) Offset futures position Receive futures position

Short Call (SP )

Long Futures (FP t = SP ) Short Futures Short Futures

FP T < SP FP T > SP

Options on FuturesCovered Call Writing – Profit or Loss

280 290 300 310 320 330-15000

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-5000

0

5000

10000

15000

20000 Speculation with Options - Covered Call Writing

Long Futures Short Call Short Call plus Long Futures

Futures Price

Pro

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Speculation with Options - Covered Call Writing


Call Holder Do not exercise Exercise (receive futures position)

Long Call (SP ) − − C f Long Futures − C f + (FP T − SP)

Speculator (Call Writer) Offset futures position Receive futures position

Short Call (SP ) − C f C f − (FP T − SP)

Long Futures (FP t = SP ) Short Futures FP T − SP Short Futures FP T − SP

− C f + FP T − SP − C f

FP T < SP FP T > SP

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


Speculation with Options - Covered Put Writing (Short Put plus Short Futures)


Put Holder Exercise (receive futures contract) Do not exercise

Long Put (SP ) Short Futures

Speculator (Put Writer) Receive futures position Offset futures position

Short Put (SP )

Short Futures (FP t = SP ) Long Futures Long Futures

FP T < SP FP T > SP

Options on FuturesCovered Put Writing – Profit or Loss

280 290 300 310 320 330-20000

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0

5000

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15000 Figure 12: Speculation with Options - Covered Put Writing

Short Futures Short Put Short Put plus Short Futures

Futures Price

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Table 17: Speculation with Options - Covered Put Writing

Trader Activity/Position Cash Flow Activity/Position Cash Flow

Put Holder Exercise (receive futures contract) Do not exercise

Long Put (SP ) Short Futures − P f + SP − FP T − − P f

Speculator (Put Writer) Receive futures position Offset futures position

Short Put (SP ) Long Futures P f − (SP − FP T ) − P f

Short Futures (FP t = SP ) − SP − FP T Long Futures − (FP T − SP )

− P f − P f + SP − FP T

FP T < SP FP T > SP

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.


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 FuturesSynthetic Calls – Profit or Loss

Speculation with Options - Synthetic Call (Long Put plus Long Futures)

Trader Activity/Position Cash Flow Activity/Position Cash Flow

Speculator (Put Holder) Exercise (receive futures position) Do not exercise

Long Put (SP ) Short Futures

Long Futures (FP t = SP ) Short Futures

Put Writer Receive futures position Do nothing

Short Put (SP ) Long Futures

FP T < SP FP T > SP

Options on FuturesSynthetic Calls – Profit or Loss

Speculation with Options - Synthetic Call


Speculator (Put Holder) Exercise (receive futures position) Do not exercise

Long Put (SP ) Short Futures − P f + SP − FP T − − P f

Long Futures (FP t = SP ) − − (SP − FP T ) Short Futures FP T − SP

− − P f − − P f + FP T − SP

Put Writer Receive futures position Do nothing

Short Put (SP ) Long Futures P f − (SP − FP T ) − P f

FP T < SP FP T > SP

280 290 300 310 320 330-15000

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5000

10000

15000

20000Speculation with Options - Synthetic Call

Long Futures Long PutLong Put plus Long Futures

Futures Price

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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 FuturesSynthetic Puts

Speculation with Options - Synthetic Put (Long Call plus Short Futures)


Speculator (Call Holder) Do not exercise Exercise (receive futures position)

Long Call (SP ) Long Futures

Short Futures (FP t = SP ) Long Futures

Call Writer Do nothing Receive futures position

Short Call (SP ) Short Futures

FP T < SP FP T > SP

Options on FuturesSynthetic Puts – Profit or Loss

280 290 300 310 320 330-20000

-15000

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5000

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15000Speculation with options - Synthetic Put

Short Futures Long Call Long Call plus Short Futures

Futures Price

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Table 19: Speculation with Options - Synthetic Put


Speculator (Call Holder) Do not exercise Exercise (receive futures position)

Long Call (SP ) − − C f Long Futures − C f + (FP T − SP )

Short Futures (FP t = SP ) Long Futures (SP − FP T ) − − (FP T − SP )

− − C f + (SP − FP T ) − − C f

Call Writer Do nothing Receive futures position

Short Call (SP ) − C f Short Futures C f − (FP T − SP )

FP T < SP FP T > SP

Options on FuturesSpeculations 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 FuturesOption 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).


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


Profit-Loss Profile of a Bull Vertical Call Spread

Bull Vertical

Call Spread Activity Cash Flow Activity Cash Flow Activity Cash Flow

Long Call (SP L ) Let Expire Exercise Exercise

Short Call (SP H ) Let Expire Let Expire Exercise

Profit/Loss

FP ≤ SP L SP L < FP < SP H SP H ≤ FP

Spreading with Options: Bull Vertical Call SpreadsTable 21: Profit-Loss Profile of a Bull Vertical Call Spread

Bull Vertical


Long Call (SP L ) Let Expire − C L Exercise − C L + (FP − SP L ) Exercise − C L + (FP − SP L )

Short Call (SP H ) Let Expire C H Let Expire C H Exercise C H − (FP − SP H )

Profit/Loss − C L + C H (FP −SP L ) − C L +C H (SP H−SP L ) − C L +C H

FP ≤ SP L SP L < FP < SP H SP H < FP

280 290 300 310 320 330 340-4000

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S&P 500 Futures $300-320 (premium $10 and $5) Bull Vertical Call Spread

Futures Price

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$1,0

00)


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


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 in-the-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

Bull Vertical

Put Spread Activity Cash Flow Activity Cash Flow Activity Cash Flow

Long Put (SP L ) Exercise Let Expire Let Expire

Short Put (SP H ) Exercise Exercise Let Expire

Profit/Loss


Spreading with Options: Bull Vertical Put Spreads

280 290 300 310 320 330 340-8000

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S&P 500 Futures $300-320 (premium $5 and $10) Bull Vertical Put Spread

Futures Price

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Table 22: Profit-Loss Profile of a Bull Vertical Put Spread

Bull Vertical


Long Put (SP L ) Exercise − P L + (SP L − FP ) Let Expire − P L Let Expire − P L

Short Put (SP H ) Exercise P H − (SP H − FP ) Exercise P H − (SP H − FP ) Let Expire P H

Profit/Loss (SP L −SP H ) − P L +P H (FP −SP H ) − P L +P H − P L + P H



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-of-the-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


Short Call (SP L ) Let Expire Exercise Exercise

Long Call (SP H ) Let Expire Let Expire Exercise

Profit/Loss


Spreading with Options: Bear Vertical Call Spreads

280 290 300 310 320 330 340-8000

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4000S&P 500 Futures $300-320 (premium $10 and $5) Bear Vertical Call Spread

Futures Prices

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Table 23: Profit-Loss Profile of a Bear Vertical Call Spread

Bull Vertical


Short Call (SP L ) Let Expire C L Exercise C L − (FP − SP L ) Exercise C L − (FP − SP L )

Long Call (SP H ) Let Expire − C H Let Expire − C H Exercise − C H + (FP − SP H )

Profit/Loss C L − C H C L − C H − (FP−SP L ) C L −C H − (SP H −SP L )



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

Profit-Loss Profile of a Bear Vertical Put Spread

Bull Vertical


Short Put (SP L ) Exercise Let Expire Let Expire

Long Put (SP H ) Exercise Exercise Let Expire

Profit/Loss

SP H ≤ FPFP ≤ SP L SP L < FP < SP H

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.

Spreading with Options: Bear Vertical Put Spreads

280 290 300 310 320 330 340-4000

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S&P 500 Futures $300-320 (prem. $5 and $10) Bear Vertical Put Spread

Futures Prices

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Los

s pe

r C

ontr

act

($1,

000)

Table 24: Profit-Loss Profile of a Bear Vertical Put Spread

Bull Vertical


Short Put (SP L ) Exercise P L − (SP L − FP ) Let Expire P L Let Expire P L

Long Put (SP H ) Exercise − P H + (SP H − FP ) Exercise − P H + (SP H − FP ) Let Expire − P H

Profit/Loss P L − P H + (SP H −SP L ) P L − P H + (SP H −FP ) P L − P H

SP H ≤ FPFP ≤ SP L SP L < FP < SP H

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 FuturesStraddles 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

FPT <SP FPT >SP

Trader Activity Profit/Loss Activity Profit/Loss

Long Call

Do not exercise Exercise

Long Put Exercise Do not

exercise

Net Returns

Options on FuturesLong Straddle

FPT <SP FPT >SP


Long Call

Do not exercise

−Cf Exercise −Cf + (FPT −SP )

Long Put

Exercise −Pf + (SP − FPT) Do not exercise

−Pf

Net Returns

−(Cf +Pf) + (SP−FPT)

−(Cf +Pf) +(FPT

−SP )

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.



270 280 290 300 310 320 330-12,000

-10,000

-8,000

-6,000

-4,000

-2,000

0

2,000

4,000

6,000

Long Straddle: S&P 500 Futures, Call and Put with strike price 300 and premium 10 per share

Options on FuturesShort 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.

FPT < SP FPT > SP


Short Call

Call holder does not exercise

Call holder exercises

Short Put

Put holder exercises

Put holder does not exercise

Net Returns

Options on FuturesShort Straddle

FPT <SP FPT >SP


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 )


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


270 280 290 300 310 320 330-6,000

-4,000

-2,000

0

2,000

4,000

6,000

8,000

10,000

12,000

Short Straddle: S&P 500 Futures, Call and Put with strike price 300 and premium 10 per share

Options on FuturesStraddles 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

FPT < SPP< SPC SPP< FPT < SPC SPP < SPC < FPT

TraderActivit

yProfit/Loss

ActivityProfit/Loss

Activity

Profit/Loss

Long Call(SPC)

Do not exercis

e

Do not exercise

Exercise

Long Put(SPP)

Exercise

Do not exercise

Do not exercis

e

Net Return

s

Options on FuturesLong 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


TraderActivit

yProfit/Loss

ActivityProfit/Loss

Activity

Profit/Loss

Long Call(SPC)

Do not exercis

e−Cf

Do not exercise

−CfExercis

e

−Cf + (FPT − SPC )

Long Put(SPP)

Exercise

−Pf + (SPP − FPT)

Do not exercise

−Pf

Do not exercis

e−Pf

Net Return

s

−(Cf +Pf ) +

(SPP − FPT)

−(Cf +Pf ) −(Cf +Pf )

+ (FPT−SPC )


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.


270 280 290 300 310 320 330 340 350-14,000

-12,000

-10,000

-8,000

-6,000

-4,000

-2,000

0

2,000

4,000

Long Strangle: S&P 500 Futures, Call with SP 320 premium 15 and Put with SP300 and premium 10

Options on FuturesStrangles

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.


Trader ActivityProfit/Loss

ActivityProfit/Loss

ActivityProfit/Loss

Short Call (SPC)

Holder does not exercise


Holder Exercises

Short Put(SPP)

Holder Exercises



Net Returns

Options on FuturesShort 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


Trader ActivityProfit/Loss

ActivityProfit/Loss

Activity

Profit/Loss

Short Call (SPC)


Cf


Cf

Holder Exercis

es

Cf − (FPT − SPC )

Short Put(SPP)

Holder Exercise

s

Pf − (SPP − FPT)


Pf

Holder does not

exercise

Pf

Net Returns

(Cf +Pf ) − (SPP − FPT)

Cf +Pf

(Cf +Pf ) − (FPT−SPC )


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


270 280 290 300 310 320 330 340 350-4,000

-2,000

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

Short Straddle: S&P 500 Futures, Call with SP 320 premium 15 and Put with SP300 and premium 10

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 HedgeSoybeans: Planted in April and Harvested in September

Date Cash (soybeans) Futures (soybeans)

24 April 2010 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



Effective price

Hedging with Futures: Short Hedge

Table 25: Hedging with Futures.

Date Cash Futures

24-Apr-10 US$ 10.00 per bushel 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 @


Loss = −1.00 (US$) per bushel


Hedging with Options on Futures: Short Hedge Soybeans: Planted in April and Harvested in September

Date Cash (soybeans) Options (soybeans)


(Basis is − 0.40)

Price Decline



Effective price

Price Increase



Effective price

Hedging with Options: Short Hedge

Table 26: Hedging with Options on Futures.

Date Cash Options

24-Apr-10 US$ 10.00 per bushel 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


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


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 HedgeSoybeans: Planted in April and Harvested in September

Date Cash (soybeans) Futures (soybeans)


(Basis is − 0.40)

Price Decline

30 Sep 2010 Buy 50,000 bushels @US$ 9.00 per bushel


Effective cost

Price Increase



Effective cost

Hedging with Futures: Long Hedge

Table 25: Hedging with Futures.

Date Cash Futures

24-Apr-10 US$ 10.00 per bushel 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 @


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 @


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 Cash (soybeans) Options (soybeans)


(Basis is − 0.44)

Price Decline



Effective cost

Price Increase



Effective cost

Hedging with Options: Long Hedge

Table 26: Hedging with Options on Futures.

Date Cash Options

24-Apr-10 US$ 10.00 per bushel 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

Lecture 8 Options on Futures Primary Text Edwards and Ma: Chapters 18, 19, & 20.

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Transcript of Lecture 8 Options on Futures Primary Text Edwards and Ma: Chapters 18, 19, & 20.