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Trading Strategies Involving Options
──選擇權交易策略
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Hypothesis
The underlying asset is a stock Other underlying assets can apply to similar results
The options used in the strategies are European
American option may probably be exercised early that leading to different profit outcome
Ignore the time value of money To Simplify the exposition
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Hypothesis
Initial cost premium( 權利金 )-long side margin( 保證金 )-short side
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Types of Strategies
Hedge holding single option on a stock and the stock itself
Spread taking a position in two (or more) options of the same type.
Combination Taking a position in both calls and puts on the same stock
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Hedge strategy
Covered call( 備兌買權 )
Protective call( 保護性買權 )
Protective put ( 保護性賣權 )
Covered put ( 備兌賣權 )
holding single option on a stock and the stock itself
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Put – Call Parity
S + P = C + Ke-r*T + D
S : stock price ; P : the price of put ; C : the price of call ; K : strike price / exercise price ; r : risk-free interest rate ; T : the time to maturity ; D : the present value of the dividends
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Covered call long a stock & short a callS-C=Ke-rf*T+D–P
K
Profit
ST
+S
-C
C+C
-(K-C)
K-C
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Protective callshort a stock & long a call-S+C=-Ke-rf*T-D+P
K
Profit
ST
-S
+C
C
K-C
-C
K-C
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Protective putlong a stock & long a putS+P=Ke-rf*T+D+C
K
Profit
ST
+S
+P-P
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Covered putshort a stock & short a put-S-P=-Ke-rf*T-D-C
K
Profit
ST
-S
-P+P
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Spread trading strategy
Bull Spreads( 多頭價差 ) Bear Spreads( 空頭價差 ) Box Spreads( 箱形價差 ) Butterfly Spreads( 蝶形價差 ) Calendar Spreads( 時間價差 / 行事曆價差 /…) Diagonal Spreads( 對角價差 )
taking a position in two (or more) options of the same type (i.e., two calls or two puts)
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Definition
Type: two types—call & put Option series:1.options of the same type
2.different expiration dates, the same strike price;
different strike prices, the same expiration date.
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Bull spread
Both options have the same expiration date Hoping that the stock price will be up↑ Limit both the upside profit potential and the downsi
de risk i.e. limiting both sides Three types of bull spreads can be distinguished 1. both calls are initially out of the money 2. one call is initially in the money ; the other call is initially out of the money 3. both calls are initially in the money
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Bull Spread Using CallsBuy a call with a lower strike price and sell a call with a higher strike price
Profit
STK1
+C
K2-C
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Payoff from a bull spread created using callsStock price range
Payoff from long call option
Payoff from short call option
Total payoff
ST K≧ 2 ST - K1 -(ST – K2) K2 - K1
K1 < ST < K2 ST - K1 0 ST - K1
ST K≦ 1 0 0 0
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Example
An investor buys for $3 a call with a strike price of $30 and sells for $1 a call with a strike price of $35
The profit is therefore as follows:
Stock price range Profit
ST ≦ 30 -2
30 < ST < 35 ST – 32
ST ≧ 35 3
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Bull Spread Using PutsBuy a put with a lower strike price and sell a put with a higher strike price
Profit
STK1
+P
K2
-P
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Bear Spreads
Both options have the same expiration date Hoping that the stock price will decline Limit both the upside profit potential and the d
ownside risk
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Bear Spread Using PutsSell a put with a lower strike price and buy a put with a higher strike price
Profit
STK1
-P
K2
+P
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Payoff from a bear spread created using putsStock price range
Payoff from long put option
Payoff from short put option
Total payoff
ST K≧ 2 0 0 0
K1 < ST < K2 K2 - ST 0 K2 - ST
ST K≦ 1 K2 - ST -(K1 – ST) K2 - K1
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Example
An investor buys for $3 a put with a strike price of $35 and sells for $1 a put with a strike price of $30
The profit is therefore as follows:
Stock price range Profit
ST ≦ 30 3
30 < ST < 35 33 - ST
ST ≧ 35 -2
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Bear Spread Using CallsSell a call with a lower strike price and buy a call with a higher strike price
Profit
STK2
+c
K1
-c
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Box Spread
A combination of a bull call spread with strike prices k1 and k2 and a bear put spread with the same two strike prices
If all options are European a box spread is worth the present value of the difference between the strike prices( (K2 - K1)e-rT ) ; If they are American this is not necessarily so.
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Box Spread
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Box Spread
If the market price of the box spread is too low(high),it is profitable to buy(sell) the box,called
“long box” or “short box” Commissions are important to be considered
when implementing this strategy coz the small profit may be easily offset by commissions
Alligator spread
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Butterfly Spread
Involves positions in options with three different strike prices
K1 : a relatively low strike price
K3 : a relatively high strike price
K2 : halfway between K1 and K3 , close to the current stock price
Large stock price moves are unlikely
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Butterfly Spread Using CallsBuy a call option with a relatively low K1 , buy a call option with a relatively high K3 , and sell two call options with K2
Profit
STK1
+C
K3
+C
K2
-C
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Payoff from a butterfly spread
Stock price range
Payoff from first long call
Payoff from second long call
Payoff from short calls
Total payoff
ST < K1 0 0 0 0
K1 < ST < K2 ST - K1 0 0 ST - K1
K2 < ST < K3 ST - K1 0 -2(ST – K2) K3 - ST
ST > K3 ST - K1 ST - K3-2(ST – K2) 0
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Example
The stock price is $61.An investor buys for $10 a call with a strike price of $55,$5 a call with a strike price of $65 and sells for $7 two puts with a strike price of $60
The profit is therefore as follows:
Stock price range Profit
ST < 55 -1
55 < ST < 60 ST - K1 -1
60 < ST < 65 K3 - ST -1
ST > 65 -1
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Butterfly Spread Using PutsBuy a put option with a relatively low K1 , buy a put option with a relatively high K3 , and sell two put options with K2
Profit
STK1
+P
K3
+P
K2
-P
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Calendar Spread
The options have the same strike price and different expiration dates
Neutral calendar spread : A strike price close to the current stock price is chosen
Bullish calendar spread : Involves a higher strike price
Bearish calendar spread : Involves a lower strike price
Reverse calendar spread : Buys a short-maturity option and sells a long-maturity option
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Calendar Spread Using CallsBuy a longer-maturity call option and Sell a call option with the same strike price
Profit
STK
+C
-C
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Calendar Spread Using PutsBuy a longer-maturity put option and Sell a put option with the same strike price
Profit
STK
+P
-P
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Brief Summary
Bull and Bear spreads: different strike prices and the same expiration date Calendar spreads: the same strike price and different expiration date
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Diagonal Spread
Both the expiration date and the strike price of the calls are different
Increases the range of profit patterns that are possible
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Diagonal Bull Spread
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Diagonal Bear Spread
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Combinations
Taking a position in both calls and puts on the same stock
Straddle( 跨式價差 ) Strips( 紙帶價差 ) Straps( 皮帶價差 ) Strangles( 勒式價差 )
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Straddle
Bottom straddle (straddle purchase) : Buying a call and put with the same strike price and expiration date ; expecting a large move in a stock price but does not know in which direction the move will be
Top straddle (straddle write) : Selling a call and put with the same strike price and expiration date ; large stock price moves are unlikely
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Bottom straddle
Profit
STK
+C
+P
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Payoff from a bottom straddle
Stock price range
Payoff from long call
Payoff from long put
Total payoff
ST ≤ K 0 K - ST K - ST
ST > K ST - K 0 ST - K
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Strip & Strap
Strip : Buy one call and two puts with the same strike price and expiration date ; Considers a decrease in the stock price to be a more likely than an increase
Strap : Buy two calls and one put with the same strike price and expiration date ; Considers a increase in the stock price to be a more likely than an decrease
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Strip & Strap
call put
Strip 1 2
Strap 2 1
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Strip & Strap
Profit
K ST
Profit
K ST
Strip Strap
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Strangle
Bottom vertical combination : Buy a put and a call with the same expiration date and different strike prices
Top vertical combination : Sell a put and a call with the same expiration date and different strike prices
The stock price has to move farther in a strangle than in a straddle for the investor to make a profit ; The downside risk is less than a straddle
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Bottom vertical combination
K1 K2
Profit
ST
+C
+P
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K1 K2
Profit
ST
+C
+P
Profit
STK
+C
+P
The stock price has to move farther in a strangle than in a straddle for the investor to make a profit ;
The downside risk is less than a straddle
Strangle
Straddle
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Payoff from a bottom vertical combination
Stock price range
Payoff from long call
Payoff from long put
Total payoff
ST K≦ 1 0 K1 - ST K1 - ST
K1 < ST < K2 0 0 0
ST K≧ 2 ST - K2 0 ST - K2
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Other Payoffs
All payoff functions (at time T) can be found:if Euro options can expire (at time T) with every single
possible strike price
Profit
STK1 K2 K3