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Options, Futures, and Other Derivatives 6th
Edition, Copyright John C. Hull 2005 10.1
Trading StrategiesInvolving Options
Chapter 10
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Edition, Copyright John C. Hull 2005 10.2
Types of Strategies
Covered Strategies: Take a position inthe option and the underlying
Spread Strategies: Take a position in 2or more options of the same type (Aspread)
Combination Strategies: Take a position
in a mixture of calls & puts (Acombination)
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Options, Futures, and Other Derivatives 6th
Edition, Copyright John C. Hull 2005 10.4
Types of Strategies
These symbols imply the following:
NC or NP or NS > 0 implies buying (going long)
NC orNP orNS < 0 implies selling (going short)
The Profit Equations Profit equation for calls held to expiration
4 = NC[Max(0,ST - X) - C]
For buyer of one call (NC = 1) this implies
4 = Max(0,ST - X) - C For seller of one call (NC = -1) this implies
4 = -Max(0,ST - X) + C
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Options, Futures, and Other Derivatives 6th
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Types of Strategies
The Profit Equations (continued)
Profit equation for puts held to expiration
4 = NP[Max(0,X - ST) - P] For buyer of one put (NP = 1) this implies 4 = Max(0,X
- ST) - P
For seller of one put (NP = -1) this implies 4 = -Max(0,X - ST) + P
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Types of Strategies
The Profit Equations (continued)
Profit equation for stock
4 = NS[ST - S0] For buyer of one share (NS = 1) this implies 4 = ST - S0 For short seller of one share (NS = -1) this implies 4 = -ST
+ S0
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Options, Futures, and Other Derivatives 6th
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Positions in an Option & the
Underlying (Figure 10.1, page 224)
Profit
STK
Profit
ST
K
Profit
ST
K
Profit
ST
K
(a)(b)
(c) (d)
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Options, Futures, and Other Derivatives 6th
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Bull Spread Using Calls(Figure 10.2, page 225)
Bull Spread Using Calls: Buying a call option on a stock with aparticular strike price and selling a call option on the same stockwith a higher strike price.
Payoff from a Bull Spread:
Stock priceRange
Payoff fromLong CallOption
Payoff fromShort CallOption
Total Payoff
ST K2K1 < ST < K2ST K1
ST - K1ST - K10
K2 - ST0
0
K2 - K1ST K20
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Options, Futures, and Other Derivatives 6th
Edition, Copyright John C. Hull 2005 10.9
Bull Spread Using Calls(Figure 10.2, page 225)
Ex: An investor buys $3 a call with a strike price of $30 and sellsfor $1 a call with a strike price of $35.
Payoff from a Bull Spread:
Stock priceRange
Payoff fromLong CallOption
Payoff fromShort CallOption
Total Payoff
ST $35
$30 < ST < $35
ST $30
ST - $30 - $3
ST - $30 -$3
0 - $3
$35 - ST +$1
0+$1
0+$1
$3
ST - $32
-$2
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Options, Futures, and Other Derivatives 6th
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Bull Spread Using Calls(Figure 10.2, page 225)
K1
K2
Profit
ST
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Options, Futures, and Other Derivatives 6th
Edition, Copyright John C. Hull 2005 10.11
Bull Spread Using PutsFigure 10.3, page 226
K1
K2
Profit
ST
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Options, Futures, and Other Derivatives 6th
Edition, Copyright John C. Hull 2005 10.13
Bear Spread Using CallsFigure 10.5, page 229
Bear Spread: Buying a call option on a stock with a particular strike priceand selling a call option on the same stock with a lower strike price.
Stock priceRange
Payoff fromLong CallOption
Payoff fromShort CallOption
Total Payoff
ST K2K1 < ST < K2ST K1
ST - K20
0
K1 - STK1 - ST0
-(K2 - K1)
-(ST K1)
0
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Options, Futures, and Other Derivatives 6th
Edition, Copyright John C. Hull 2005 10.14
Bear Spread Using CallsFigure 10.5, page 229
Example: An investor buys a call for $1 with a strike price of $35 and sellsfor $3 a call with a strike price of $30.
Stock priceRange
Payoff fromLong CallOption
Payoff fromShort CallOption
Total Payoff
ST $35
$30 < ST < $35
ST $30
ST - $35
0
0
$30 - ST$30 - ST0
-($35 - $30)
-(ST $30)
0
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Options, Futures, and Other Derivatives 6th
Edition, Copyright John C. Hull 2005 10.15
Bear Spread Using CallsFigure 10.5, page 229
K1
K2
Profit
ST
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Options, Futures, and Other Derivatives 6th
Edition, Copyright John C. Hull 2005 10.16
Box Spread
A combination of a bull call spread and abear put spread
If all options are European a box spread isworth the present value of the differencebetween the strike prices
If they are American this is not necessarilyso. (See Business Snapshot 10.1)
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Butterfly Spread Using Calls
Butterfly Spread: buying a call option with a relative lowstrike price, K1,, buying a call option with a relative highstrike price. K3, and selling two call options with a strikeprice halfway in between, K2.
Stock priceRange
Payofffrom FirstLong CallOption
Payoff fromSecondLong CallOption
Payoff fromShort Calls
Total Payoff
ST
K3
K2 < ST < K3K2 < ST < K3ST K1
ST
- K1ST - K1
ST - K10
ST
- K30
0
0
-2(ST
- K2)
-2(ST - K2)
0
0
0
K3 - STST - K10
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Edition, Copyright John C. Hull 2005 10.18
Butterfly Spread Using Calls
Example: Call option prices on a $61 stock are: $10 for a $55 strike, $7for a $60 strike, and $5 for a $65 strike. The investor could create abutterfly spread by buying one call with $55 strike price, buying a call witha $65 strike price, and selling two calls with a $60 strike price.
Stock priceRange
Payofffrom FirstLong CallOption
Payoff fromSecondLong CallOption
Payoff fromShort Calls
Total Payoff
ST
$65
$60 < ST
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Options, Futures, and Other Derivatives 6th
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Butterfly Spread Using CallsFigure 10.6, page 231
K1
K3
Profit
ST
K2
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Calendar Spread Using CallsFigure 10.8, page 232
Profit
ST
K
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Edition, Copyright John C. Hull 2005 10.22
Calendar Spread Using PutsFigure 10.9, page 233
Profit
ST
K
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Edition, Copyright John C. Hull 2005 10.23
A Straddle CombinationFigure 10.10, page 234
Straddle:Buying a call and a put with the same strike price and expirationDate.
Stock priceRange
Payoff from Call Payoff from Put Total Payoff
ST K
ST < K
ST K
0
0
K - ST
ST - K
K - ST
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Options, Futures, and Other Derivatives6
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Edition, Copyright John C. Hull 2005 10.25
A Straddle CombinationFigure 10.10, page 234
Profit
ST
K
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Options, Futures, and Other Derivatives 6th Edition, Copyright John C. Hull 200510.26
Strip & Strap
Strip: combining one long call with two long putsStrap: combining two long calls with one long put
Profit
K ST
Profit
K ST
Strip Strap
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A Strangle Combinationbuying one call with a strike price of K2 and buying one put with a
strike price of K1
K1
K2
Profit
ST
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