option strategies

OPTION STRATEGIES

ALAN ANDERSON, Ph.D. ECI RISK TRAINING

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

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SPREADS

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

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EXAMPLES

 bull spread  bear spread  butterfly spread

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BULL SPREAD

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

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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

EXAMPLE

Assume that:

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

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A European call option on IBM stock with a strike of 53 matures on September 1 and sells for $2

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This information is summarized as follows:

c1 = $3 X1 = $50

c2 = $2 X2 = $53

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where:

c1 = the price paid for the call with strike X1

c2 = the price paid for the call with strike X2

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The investor buys the first call and sells the second call

The payoffs are given in the following table:

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S MAX (S - X1, 0)

-MAX (S - X2, 0)

TOTAL 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

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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)

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where:

S = underlying asset price

X = strike price

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The payoff to the bull spread is illustrated as follows:

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The profits are given in the following table:

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S MAX (S - X1,0)-c1

-MAX (S - X2,0)+c2

TOTAL 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

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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

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where:

C = call price

P = put price

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The profits to the bull spread are illustrated as follows:

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BEAR SPREAD

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

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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

EXAMPLE

Using the same two call options from the previous example:

c1 = $3 X1 = $50

c2 = $2 X2 = $53

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The investor buys the first call and sells the second call

The payoffs are given in the following table and graph:

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S -MAX (S - X1, 0)

MAX (S - X2, 0)

TOTAL 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

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The profits are given in the following table and graph:

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S -MAX (S -X1,0)+c1

MAX (S -X2,0)-c2

TOTAL 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

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BUTTERFLY SPREAD

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

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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

EXAMPLE

Assume that:

A European call option on IBM stock with a strike of 47 matures on September 1 and sells for $5

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

A European call option on IBM stock with a strike of 53 matures on September 1 and sells for $2

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This is summarized as follows:

c1 = $5 X1 = $47

c2 = $3 X2 = $50

c3 = $2 X3 = $53

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

The payoffs are given in the following table and graph:

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S MAX (S - X1, 0)

-2*MAX (S - X2, 0)

MAX (S - X3, 0)

TOTAL 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

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Payoff to Butterfly Spread

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

45.00 46.00 47.00 48.00 49.00 50.00 51.00 52.00 53.00 54.00 55.00

Stock Price ($)

Payo

ff (

$)

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The profits are given in the following table and graph:

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S MAX (S - X1, 0)

-2*MAX (S - X2, 0)

MAX (S - X3, 0)

TOTAL 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

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Profit/Loss to Butterfly Spread

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

45.00 46.00 47.00 48.00 49.00 50.00 51.00 52.00 53.00 54.00 55.00

Stock Price ($)

Pro

fit/

Lo

ss (

$)

COMBINATIONS

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

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EXAMPLE

Assume that:

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

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

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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:

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S MAX (S - X, 0)

MAX (X - S , 0)

TOTAL 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

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Payoff to Straddle

0

1

2

3

4

5

6

7

8

9

10

40 42 44 46 48 50 52 54 56 58 60

Stock Price ($)

Pa

yo

ff (

$)

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The profits are given in the following table and graph:

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S MAX (S - X,0) - c

MAX (X - S ,0) - p

TOTAL 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

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Profit/Loss to Straddle

-6

-4

-2

0

2

4

6

40 42 44 46 48 50 52 54 56 58 60

Stock Price ($)

Pro

fit/

Lo

ss (

$)

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

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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

STRANGLE

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

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EXAMPLE

Assume that:

A European call on IBM stock with a strike of 53 matures on September 1 and sells for $2

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

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c = $2 p = $2

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

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

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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

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

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S MAX (S - X, 0)

MAX (X - S , 0)

TOTAL 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 0 3

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Payoff to Strangle

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

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 ($)

Payo

ff (

$)

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S MAX (S - X,0) - c

MAX (X - S ,0) - p

TOTAL 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 -2 -1

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Profit/Loss to Strangle

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

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 ($)

Pro

fit/

Lo

ss (

$)

STRIPS

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

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EXAMPLE

Assume that:

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

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

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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:

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S MAX (S - X, 0)

MAX (X - S , 0)

TOTAL 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

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Payoff to Strip

0.00

5.00

10.00

15.00

20.00

25.00

40.00 42.00 44.00 46.00 48.00 50.00 52.00 54.00 56.00 58.00 60.00

Stock Price ($)

Payo

ff (

$)

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S MAX (S - X, 0)

MAX (X - S , 0)

TOTAL 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

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Profit/Loss to Strip

-10.00

-5.00

0.00

5.00

10.00

15.00

40.00 42.00 44.00 46.00 48.00 50.00 52.00 54.00 56.00 58.00 60.00

Stock Price ($)

Pro

fit/

Lo

ss (

$)

STRAPS

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

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EXAMPLE

Assume that:

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

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

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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:

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S MAX (S - X, 0)

MAX (X - S , 0)

TOTAL 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

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Payoff to Strap

0.00

5.00

10.00

15.00

20.00

25.00

40.00 42.00 44.00 46.00 48.00 50.00 52.00 54.00 56.00 58.00 60.00

Stock Price ($)

Payo

ff (

$)

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S MAX (S - X, 0)

MAX (X - S , 0)

TOTAL 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

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Profit/Loss to Strap

-10.00

-5.00

0.00

5.00

10.00

15.00

40.00 42.00 44.00 46.00 48.00 50.00 52.00 54.00 56.00 58.00 60.00

Stock Price ($)

Pro

fit/

Lo

ss (

$)

OTHER OPTIONS STRATEGIES

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

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Two of these strategies are known as:

 covered call  protective put

COVERED CALL

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

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

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

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c = $3 X = $50

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

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S -MAX (S - X, 0)

TOTAL 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

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COVERED CALL

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

46 47 48 49 50 51 52 53 54 55

Stock Price ($)

Payo

ff (

$)

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S -MAX (S - X, 0)+c

TOTAL 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

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COVERED CALL

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

46 47 48 49 50 51 52 53 54 55

Stock Price ($)

Pro

fit/

Lo

ss (

$)

PROTECTIVE PUT

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

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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

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

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p = $2 X = $50

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

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S MAX (X - S, 0)

TOTAL 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

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PROTECTIVE PUT

0

1

2

3

4

5

6

46 47 48 49 50 51 52 53 54 55

Stock Price ($)

Payo

ff (

$)

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S MAX (X - S , 0) - p

TOTAL 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

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PROTECTIVE PUT

-3

-2

-1

0

1

2

3

4

46 47 48 49 50 51 52 53 54 55

Stock Price ($)

Pro

fit/

Lo

ss (

$)