Option Strategies

OPTION STRATEGIES

ALAN ANDERSON, Ph.D.
ECI RISK TRAINING
www.ecirisktraining.com

(c) ECI Risk Training 2009
1

Due to their unique payoff profiles, options
may be used to create investment strategies that
would be impossible with other financial assets

2

3

SPREADS

A spread is created from two calls or
two puts on the same underlying asset

4

EXAMPLES

  bull spread
  bear spread
  butterfly spread

5

BULL SPREAD

A bull spread gains when the price
of the underlying asset rises, but the
potential profit is limited

6

A bull spread is created by:

  buying an option with a LOW strike price
  selling an option with a HIGH strike price

with the same asset and maturity
7

EXAMPLE

Assume that:

A European call option on IBM
stock with a strike of 50 matures
on September 1 and sells for $3

8


9

This information is summarized as follows:

c1 = $3 X1 = $50
c2 = $2 X2 = $53

10

where:

c1 = the price paid for the call with strike X1
c2 = the price paid for the call with strike X2

11

The investor buys the first call
and sells the second call

The payoffs are given in the
following table:

12

S MAX -MAX TOTAL
(S - X1, 0) (S - X2, 0) PAYOFF
49.00 0.00 0.00 0.00
49.50 0.00 0.00 0.00
50.00 0.00 0.00 0.00
50.50 0.50 0.00 0.50
51.00 1.00 0.00 1.00
51.50 1.50 0.00 1.50
52.00 2.00 0.00 2.00
52.50 2.50 0.00 2.50
53.00 3.00 0.00 3.00
53.50 3.50 -0.50 3.00
54.00 4.00 -1.00 3.00
13

The payoff to a call buyer is MAX (S – X, 0)
The payoff to a call seller is -MAX (S – X, 0)
The payoff to a put buyer is MAX (X – S, 0)
The payoff to a put seller is -MAX (X – S, 0)

14

where:

S = underlying asset price
X = strike price

15

The payoff to the bull spread
is illustrated as follows:

16

17

The profits are given in
the following table:

18

S MAX -MAX TOTAL
(S - X1,0)-c1 (S - X2,0)+c2 PROFIT
49.00 -3.00 2.00 -1.00
49.50 -3.00 2.00 -1.00
50.00 -3.00 2.00 -1.00
50.50 -2.50 2.00 -0.50
51.00 -2.00 2.00 0.00
51.50 -1.50 2.00 0.50
52.00 -1.00 2.00 1.00
52.50 -0.50 2.00 1.50
53.00 0.00 2.00 2.00
53.50 0.50 1.50 2.00
54.00 1.00 1.00 2.00
19

The profit to a call buyer is MAX (S – X, 0) - C
The profit to a call seller is -MAX (S – X, 0) + C
The profit to a put buyer is MAX (X – S, 0) - P
The profit to a put seller is -MAX (X – S, 0) + P

20

where:

C = call price
P = put price

21

The profits to the bull spread
are illustrated as follows:

22

23

BEAR SPREAD

A bear spread gains when the price
of the underlying asset falls, but the
potential profit is limited

24

A bear spread is created by:

  buying an option with a HIGH strike price
  selling an option with a LOW strike price

with the same asset and maturity
25

EXAMPLE

Using the same two call options
from the previous example:

c1 = $3 X1 = $50
c2 = $2 X2 = $53

26

The investor buys the first call
and sells the second call

following table and graph:

27

S -MAX MAX TOTAL
(S - X1, 0) (S - X2, 0) PAYOFF
49.00 0.00 0.00 0.00
49.50 0.00 0.00 0.00
50.00 0.00 0.00 0.00
50.50 -0.50 0.00 -0.50
51.00 -1.00 0.00 -1.00
51.50 -1.50 0.00 -1.50
52.00 -2.00 0.00 -2.00
52.50 -2.50 0.00 -2.50
53.00 -3.00 0.00 -3.00
53.50 -3.50 0.50 -3.00
54.00 -4.00 1.00 -3.00
28

29

The profits are given in the

30

S -MAX MAX TOTAL
(S -X1,0)+c1 (S -X2,0)-c2 PROFIT
49.00 3.00 -2.00 1.00
49.50 3.00 -2.00 1.00
50.00 3.00 -2.00 1.00
50.50 2.50 -2.00 0.50
51.00 2.00 -2.00 0.00
51.50 1.50 -2.00 -0.50
52.00 1.00 -2.00 -1.00
52.50 0.50 -2.00 -1.50
53.00 0.00 -2.00 -2.00
53.50 -0.50 -1.50 -2.00
54.00 -1.00 -1.00 -2.00
31

32

BUTTERFLY SPREAD

A butterfly spread gains when the
price of the underlying asset stays
within a specific range of prices

33

A butterfly spread is created by:
  buying an option with a LOW strike price
  buying an option with a HIGH strike price
  selling two options with an INTERMEDIATE
strike price

all with the same asset and maturity
34

EXAMPLE

Assume that:


35



36

This is summarized as follows:

c1 = $5 X1 = $47
c2 = $3 X2 = $50
c3 = $2 X3 = $53

37

The investor buys the first and
third calls, and sells two of the
second call


38

S MAX -2*MAX MAX TOTAL
(S - X1, 0) (S - X2, 0) (S - X3, 0) PAYOFF

45 0.00 0.00 0.00 0.00
46 0.00 0.00 0.00 0.00
47 0.00 0.00 0.00 0.00
48 1.00 0.00 0.00 1.00
49 2.00 0.00 0.00 2.00
50 3.00 0.00 0.00 3.00
51 4.00 -2.00 0.00 2.00
52 5.00 -4.00 0.00 1.00
53 6.00 -6.00 0.00 0.00
54 7.00 -8.00 1.00 0.00
55 8.00 -10.00 2.00 0.00
39

Payoff to Butterfly Spread

3.50

3.00

2.50

2.00
Payoff ($)

1.50

1.00

0.50

0.00
45.00 46.00 47.00 48.00 49.00 50.00 51.00 52.00 53.00 54.00 55.00
Stock Price ($)

40


41

S MAX -2*MAX MAX TOTAL
(S - X1, 0) (S - X2, 0) (S - X3, 0) PROFIT

45 0.00 0.00 0.00 -1.00
46 0.00 0.00 0.00 -1.00
47 0.00 0.00 0.00 -1.00
48 1.00 0.00 0.00 0.00
49 2.00 0.00 0.00 1.00
50 3.00 0.00 0.00 2.00
51 4.00 -2.00 0.00 1.00
52 5.00 -4.00 0.00 0.00
53 6.00 -6.00 0.00 -1.00
54 7.00 -8.00 1.00 -1.00
55 8.00 -10.00 2.00 -1.00
42

Profit/Loss to Butterfly Spread

2.50

2.00

1.50

1.00
Profit/Loss ($)

0.50

0.00
45.00 46.00 47.00 48.00 49.00 50.00 51.00 52.00 53.00 54.00 55.00

-0.50

-1.00

-1.50
Stock Price ($)

43

COMBINATIONS

A combination consists of one call and
one put with the same underlying asset

44

EXAMPLE

Assume that:

A European call on IBM stock with a strike
of 50 matures on September 1 and sells for $3

45

A European put on IBM stock
with a strike of 50 matures on
September 1 and sells for $2

46

c = $3 p = $2 X = $50

An investor buys the call and the put; this
position is known as a straddle

The payoffs are given in the following table
and graph:
47

S MAX MAX TOTAL
(S - X, 0) (X - S , 0) PAYOFF
40 0 10 10
42 0 8 8
44 0 6 6
46 0 4 4
48 0 2 2
50 0 0 0
52 2 0 2
54 4 0 4
56 6 0 6
58 8 0 8
60 10 0 10
48

Payoff to Straddle

10

9

8

7

6
Payoff ($)

5

4

3

2

1

0
40 42 44 46 48 50 52 54 56 58 60
Stock Price ($)

49


50

S MAX MAX TOTAL
(S - X,0) - c (X - S ,0) - p PROFIT

40 -3 8 5
42 -3 6 3
44 -3 4 1
46 -3 2 -1
48 -3 0 -3
50 -3 -2 -5
52 -1 -2 -3
54 1 -2 -1
56 3 -2 1
58 5 -2 3
60 7 -2 5
51

Profit/Loss to Straddle

6

4
Profit/Loss ($)

2

0
40 42 44 46 48 50 52 54 56 58 60

-2

-4

-6
Stock Price ($)

52

An investor who buys a straddle will
profit if the underlying asset is highly
volatile

53

An investor who expects the underlying
asset to be highly stable can sell a call and a
put; this position is known as a short straddle

54

STRANGLE

With a strangle, a call with a high strike
and a put with a low strike are purchased

55

EXAMPLE

Assume that:

A European call on IBM stock

56


57

c = $2 p = $2

An investor buys the call with strike
of 53 and the put with strike of 50

58

The payoff and profit diagrams show
that the position resembles a straddle,
but with a “flat bottom”

59

This position requires a larger movement
in the stock price to produce a profit, but
produces smaller losses if the stock price
remains within the two strike prices

60

The payoffs and profits to the strangle
are shown in the following tables and
graphs:

61

S MAX MAX TOTAL
(S - X, 0) (X - S , 0) PAYOFF
45 0 5 5
46 0 4 4
47 0 3 3
48 0 2 2
49 0 1 1
50 0 0 0
51 0 0 0
52 0 0 0
53 0 0 0
54 1 0 1
55 2 0 2
56 3 62
0 3

Payoff to Strangle

7.00

6.00

5.00

4.00
Payoff ($)

3.00

2.00

1.00

0.00
44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00 52.00 53.00 54.00 55.00 56.00 57.00 58.00 59.00
Stock Price ($)

63

S MAX MAX TOTAL
(S - X,0) - c (X - S ,0) - p PROFIT

45 -2 3 1
46 -2 2 0
47 -2 1 -1
48 -2 0 -2
49 -2 -1 -3
50 -2 -2 -4
51 -2 -2 -4
52 -2 -2 -4
53 -2 -2 -4
54 -1 -2 -3
55 0 -2 -2
56 1 64
-2 -1

Profit/Loss to Strangle

3.00

2.00

1.00

0.00
Profit/Loss ($)

44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00 52.00 53.00 54.00 55.00 56.00 57.00 58.00 59.00

-1.00

-2.00

-3.00

-4.00

-5.00
Stock Price ($)

65

STRIPS

A strip is similar to a straddle except that
one call and two puts are purchased with
the same strike price

66

EXAMPLE

Assume that:


67


68

c = $3 p = $2 X = $50

An investor buys the call and two puts; this
position is known as a strip

The payoffs and profits are given in the
following tables and graphs:
69

S MAX MAX TOTAL
(S - X, 0) (X - S , 0) PAYOFF
40 0 20 20
42 0 16 16
44 0 12 12
46 0 8 8
48 0 4 4
50 0 0 0
52 2 0 2
54 4 0 4
56 6 0 6
58 8 0 8
60 10 0 10
70

Payoff to Strip

25.00

20.00

15.00
Payoff ($)

10.00

5.00

0.00
40.00 42.00 44.00 46.00 48.00 50.00 52.00 54.00 56.00 58.00 60.00
Stock Price ($)

71

S MAX MAX TOTAL
(S - X, 0) (X - S , 0) PROFIT

40 0 20 13
42 0 16 9
44 0 12 5
46 0 8 1
48 0 4 -3
50 0 0 -7
52 2 0 -5
54 4 0 -3
56 6 0 -1
58 8 0 1
60 10 0 3
72

Profit/Loss to Strip

15.00

10.00

5.00
Profit/Loss ($)

0.00
40.00 42.00 44.00 46.00 48.00 50.00 52.00 54.00 56.00 58.00 60.00

-5.00

-10.00
Stock Price ($)

73

STRAPS

A strap is similar to a straddle except that
two calls and one put are purchased with the
same strike price

74

EXAMPLE

Assume that:


75


76

c = $3 p = $2 X = $50

An investor buys two calls and one put;
this position is known as a strap

The payoffs and profits are given in the
following tables and graphs:
77

S MAX MAX TOTAL
(S - X, 0) (X - S , 0) PAYOFF
40 0 10 10
42 0 8 8
44 0 6 6
46 0 4 4
48 0 2 2
50 0 0 0
52 4 0 4
54 8 0 8
56 12 0 12
58 16 0 16
60 20 0 20
78

Payoff to Strap

25.00

20.00

15.00
Payoff ($)

10.00

5.00

0.00
40.00 42.00 44.00 46.00 48.00 50.00 52.00 54.00 56.00 58.00 60.00
Stock Price ($)

79

S MAX MAX TOTAL
(S - X, 0) (X - S , 0) PROFIT

40 0 10 2
42 0 8 0
44 0 6 -2
46 0 4 -4
48 0 2 -6
50 0 0 -8
52 4 0 -4
54 8 0 0
56 12 0 4
58 16 0 8
60 20 0 12
80

Profit/Loss to Strap

15.00

10.00

5.00
Profit/Loss ($)

0.00
40.00 42.00 44.00 46.00 48.00 50.00 52.00 54.00 56.00 58.00 60.00

-5.00

-10.00
Stock Price ($)

81

OTHER OPTIONS
STRATEGIES

Options can also be combined with the
underlying asset to create more patterns
of payoffs and profits

82

Two of these strategies are known as:

  covered call
  protective put

83

COVERED CALL

A covered call is created by buying the
underlying asset and selling a call on the
asset

84

In this case, the owner of the underlying
asset collects the option price while placing
a limit on the position’s potential profits

85

EXAMPLE
Assume that:

A European call on IBM stock with a strike of
50 matures on September 1 and sells for $3

An investor buys one share of the IBM stock at
$50 and sells this call
86

c = $3 X = $50

The payoffs and profits are
given in the following tables
and graphs:

87

S -MAX TOTAL
(S - X, 0) PAYOFF
46 0 -4
47 0 -3
48 0 -2
49 0 -1
50 0 0
51 -1 0
52 -2 0
53 -3 0
54 -4 0
55 -5 0
88

COVERED CALL

0
46 47 48 49 50 51 52 53 54 55

-0.5

-1

-1.5
Payoff ($)

-2

-2.5

-3

-3.5

-4

-4.5
Stock Price ($)

89

S -MAX TOTAL
(S - X, 0)+c PROFIT
46 3 -1
47 3 0
48 3 1
49 3 2
50 3 3
51 2 3
52 1 3
53 0 3
54 -1 3
55 -2 3
90

COVERED CALL

3.5

3

2.5

2

1.5
Profit/Loss ($)

1

0.5

0
46 47 48 49 50 51 52 53 54 55

-0.5

-1

-1.5
Stock Price ($)

91

PROTECTIVE PUT

A protective put is created by buying the
underlying asset and buying a put on the asset

92

In this case, the owner of the asset:

  earns a smaller profit if the asset price
rises above the strike price

  does not suffer any further losses if the
asset price falls below the strike price
93

EXAMPLE
Assume that:

A European put on IBM stock with a strike of
50 matures on September 1 and sells for $2

An investor buys one share of the IBM stock
and buys this put
94

p = $2 X = $50

The payoffs and profits are
given in the following tables
and graphs:

95

S MAX TOTAL
(X - S, 0) PAYOFF
46 4 0
47 3 0
48 2 0
49 1 0
50 0 0
51 0 1
52 0 2
53 0 3
54 0 4
55 0 5
96

PROTECTIVE PUT

6

5

4
Payoff ($)

3

2

1

0
46 47 48 49 50 51 52 53 54 55
Stock Price ($)

97

S MAX TOTAL
(X - S , 0) - p PROFIT
46 2 -2
47 1 -2
48 0 -2
49 -1 -2
50 -2 -2
51 -2 -1
52 -2 0
53 -2 1
54 -2 2
55 -2 3
98

PROTECTIVE PUT

4

3

2
Profit/Loss ($)

1

0
46 47 48 49 50 51 52 53 54 55

-1

-2

-3
Stock Price ($)

99

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