Option Strategies
Purpose:
• Provide background on the basic and advanced
option strategies
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Put-Call Parity
C(S,X,t) + B(X,t) = S + P(S,X,t)
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Covered Call
• S - C(S,X,t) = S - S + B(X,t) - P(S,X,t)
• S - C(S,X,t) = B(X,t) - P(S,X,t)
$
P
0
X
S
X-P
C(S,X,t) = S - B(X,t) + P(S,X,t)
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Protective Put
• S + P(S,X,t) = C(S,X,t) + B(X,t)
$
0
-C
X
S
X+C
C(S,X,t) + B(X,t) = S + P(S,X,t)
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Bull Money Spread
X1 < X 2
• Bull Spread = C(S,X1,t) – C(S,X2,t)
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Bear Money Spread
X1 < X 2
• Bear Spread = P(S,X2,t) – P(S,X1,t)
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Collar
X1 < X 2
•
Collar = S + P(S,X1,t) – C(S,X2,t)
A collar is similar to a bull spread because
• Collar = B(X1,t) + C(S,X1,t) – C(S,X2,t)
C(S,X,t) + B(X,t) = S + P(S,X,t)
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Butterfly Spread
X1 < X2 < X3
•
•
•
•
A Butterfly combines a long bull spread
with another short bull spread
The Long Spread = C(S,X1,t) – C(S,X2,t)
The Short Spread = C(S,X3,t) –
C(S,X2,t)
Resulting Butterfly Spread
C(S,X1,t) – 2C(S,X2,t) + C(S,X3,t)
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Condor
X1 < X2 < X3 < X4
A Condor extends the Butterfly by combining a
long bull spread with another short bull
spread, with a gap between them
• The Long Spread = C(S,X1,t) – C(S,X2,t)
• The Short Spread = C(S,X4,t) – C(S,X3,t)
Resulting Condor Spread
C(S,X1,t)–C(S,X2,t)–C(S,X3,t)+C(S,X4,t)
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Calendar Spread
t1 longer than t2
• Calendar Spread = C(S,X,t1) – C(S,X,t2)
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Long Strangle
X1 < S < X2
• This is a variation on the basic straddle
• To form a strangle, buy both an out-ofthe-money call and an out-of-the-money
put
Strangle = C(S,X2,t) + P(S,X1,t)
$
0
-(P+C)
X1-P-C
X1 X2
S
X2+P+C
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Strap
A strap is a straddle augmented on the
bullish side
Strap = 2C(S,X,t) + P(S,X,t)
$
0
-(P+2C)
X-P-2C
X
S
X+.5P+C
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Strip
A strip is a straddle augmented on the
bearish side
Strip = C(S,X,t) + 2P(S,X,t)
$
0
-(2P+C)
X-P-.5C
X
S
X+2P+C
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Ratio Spreads
• Delta Neutral
• Delta & Gamma Neutral
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Synthetic Call
• Basic Premise
– We know that
C(S,X,t) = S – B(X,t) + P(S,X,t)
– We assume that for a very short time
C(S,X,t) = ∂ 1S – ∂ 2B(X,t)
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Here’s a Picture of ∂ 1
Call
Call
∆C/∆S
C2
C1
B(X,t)
B
(X,t)
Stock
S1
Stock
S2
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Here’s a Picture of ∂ 2
Call
Call
∆C/∆X
C1
C2
BB(X,t)
(X1,t)
B (X2,t) Stock
Stock
S
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Important Relationships
• ∂ 1 and ∂ 2 are always less than 1
• ∂ 2 is always less than ∂ 1
• Exact values can be estimated using the
Black-Scholes OPM
• Proportions must be continuously
adjusted
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Example
• Suppose
∂ 1 = 0.7
∂ 2 = 0.6
S = $50
B(X,t) = $46
• Then C(S,X,t) =
(.7*50) – (.6*46) =
$7.40
• Then, sell 100-option contract
(receive $740)
– Sell 60 bonds (receive
another $2760, making total
$3500)
– Buy 70 shares stock (pay
$3500)
– Zero net investment
• After a moment
– S = $50.125
– B(X,t) = $46.10
– C(S,X,t)=7.4275
• Close position, net zero
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Example
• Now, suppose calls selling on CBOE for
$7.75 per share
– Sell 100-share call contract for $775
– Create synthetic for $740
– Pocket profit of $35
• How will adjustment process work?
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Synthetic Put
• Basic Premise
– We know that
P(S,X,t) = C(S,X,t) + B(X,t) – S
– We assume that for a very short time
C(S,X,t) = ∂ 1S – ∂ 2B(X,t)
So for a very short time
P(S,X,t) = ∂ 1S – ∂ 2B(X,t) + B(X,t) – S
P(S,X,t) = (∂ 1 – 1) S + (1 – ∂ 2 ) B(X,t)
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