Principles of Finance with Excel (Основы финансов c Excel)

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PFE, Chapter 23: Introduction to options page 15

ABCD E

August 7, 2001, CSCO closing price

19.26

Expiration date

Exercise

price, X

Call price

In or out

of the money?

Oct01 12.50 6.90 in the money <-- =IF($B$2>B20,"in the money","out of the money")

Oct01 15.00 5.00 in the money <-- =IF($B$2>B21,"in the money","out of the money")

Oct01 17.50 3.20 in the money <-- =IF($B$2>B22,"in the money","out of the money")

Oct01 20.00 1.80 out of the money <-- =IF($B$2>B23,"in the money","out of the money")

Oct01 22.50 0.95 out of the money <-- =IF($B$2>B24,"in the money","out of the money")

Oct01 25.00 0.45 out of the money

Oct01 27.50 0.20 out of the money

Oct01 30.00 0.15 out of the money

Oct01 35.00 0.05 out of the money

Oct01 40.00 0.05 out of the money

Oct01 45.00 0.05 out of the money

Oct01 50.00 0.05 out of the money

Oct01 55.00 0.10 out of the money

Oct01 60.00 0.05 out of the money

CISCO OCTOBER OPTIONS

In or out of the money?

The call with exercise price $50 (selling for $0.05) is out of the money—its exercise price

is more than Cisco’s current share price.

If the call’s exercise price is equal to the current stock price, it is termed an at-the-money

call. The call with an exercise price of $20 is almost at the money, and option traders would

refer to it loosely as the at-the-money call.

A put is said to be in the money if the put’s exercise price is greater than the current stock

price. In the table below, showing Cisco’s October put options, the $50 call (currently selling for

$29.50) is in the money and the $12.50 put (selling for $0.10) is out of the money. There is no

actual at-the-money put, but traders would refer to the $20 exercise put (selling for $1.40) as the

at-the-money put.

PFE, Chapter 23: Introduction to options page 16

ABCD E

Exercise

price, X

Put price

In or out

of the money?

Oct01 12.50 0.10 out of the money <-- =IF(B36>$B$2,"in the money","out of the money")

Oct01 15.00 0.25 out of the money <-- =IF(B37>$B$2,"in the money","out of the money")

Oct01 17.50 0.65 out of the money <-- =IF(B38>$B$2,"in the money","out of the money")

Oct01 20.00 1.40 in the money <-- =IF(B39>$B$2,"in the money","out of the money")

Oct01 22.50 2.55 in the money <-- =IF(B40>$B$2,"in the money","out of the money")

Oct01 25.00 4.10 in the money

Oct01 27.50 6.00 in the money

Oct01 30.00 7.50 in the money

Oct01 35.00 10.70 in the money

Oct01 40.00 16.30 in the money

Oct01 45.00 21.50 in the money

Oct01 50.00 29.50 in the money

Oct01 55.00 31.12 in the money

Oct01 60.00 37.50 in the money

MORE OPTION TERMINOLOGY

Terminology Definition

European option The option is exercisable only on the exercise date T.

American option The option is exercisable on or before the exercise date

T. Most options traded on exchanges are American

options. Although in principle an American option

should be worth more than a European option, in many

cases this is not true (see Chapter 24).

At-the-money option An option whose exercise price X is equal to the

underlying stock’s current stock price S

. “In-the-

money” is often loosely used to describe an option

whose exercise price X is approximately equal to the

current stock price S

In-the-money option An option from which money can be made by

immediate exercise. A call option is in the money if

the current stock price S

is greater than the option’s

exercise price X. A put option is in the money if the

current stock price S

is less than the option’s exercise

price X.

Out-of-the-money

option

An option from which no money can be made by

immediate exercise. A call option is out of the money

if X > S

. A put option is out of the money if S

> X.

Figure 23.8: Option pricing involves a lot of terminology. Here are some very basic terms.

PFE, Chapter 23: Introduction to options page 17

23.2. Why buy a call option?

Here are two simple reasons why you might want to buy a call option.

Reason 1: A call option allows you to delay the purchase of a stock: It’s 7 August

2001, and you’re thinking about buying a share of Cisco for its current market price of $19.26.

As an alternative, you can buy a September call option with X = $20. This option will cost you

$1.35. Here’s your thinking:

• If, on 21 September 2001, Cisco’s stock price is > $20.00, you’ll exercise the option

and purchase the share for $20. If you’re careful, you’ll realize that there are several

“sub-possibilities”:

o Cisco’s 21 Sept. stock price = $35. Now you’ve made out like a bandit: You

spent $1.35 for the option, but you bought the stock for $20, saving $15.00. Your

net profit is $13.35 ($15.00 - $1.35 cost of the option).

o If Cisco’s 21 Sept. stock price = $21.00, you’ll still exercise the option and

purchase the stock for $20.00. You’ve saved $1.00 on the purchase price of the

stock, but this time you will have lost a bit of money, since the option cost you

$1.35. Your net profit will be -$0.65.

• If on 21 September Cisco’s stock is selling for less than $20, you will not exercise

your call option. If you still want to purchase the stock, you’ll buy it on the open

market. In all cases, you will be out only the $1.35 cost of the option.

PFE, Chapter 23: Introduction to options page 18

Reason 2: A call option allows you to make a bet on the stock price going up. This

bet is: a) low cost, b) high upside potential, and c) one-sided

Suppose you buy the Cisco call option above: You spend $1.35 on 7 August 2001 to

purchase an option which—on 21 September—gives you the right to purchase Cisco stock for

$20. Your purpose is to bet on the price of Cisco stock in September. As you can see in the

Figure 23.8:

• This bet has a low cost: You’ve put up only $1.35 to make it.

• You will never lose more than the $1.35. This is what we mean when we say that the

bet is “one-sided”: You can only lose a limited amount of money.

• The bet has very high upside potential: The profits, both in dollars and as a

percentage of the money you put up, rise very rapidly when the stock price in

September increases over $20.

PFE, Chapter 23: Introduction to options page 19

ANALYZING THE PROFIT FROM A CALL OPTION

Price of

Cisco on

September

Exercise the option? Your profit or loss In percentage

$15 No—the option gives you the right to buy

Cisco for $20, but the market price is less,

so you would not exercise the option

-$1.35

/1.35

100%

1.35

Profit loss

Option cost

−

==−

$20 Yes/No—doesn’t matter (you’re buying

the stock at its market price)

-$1.35

/1.35

100%

1.35

Profit loss

Option cost

−

==−

$21 Yes—the option lets you buy the stock for

$20, but the market price is $21. So you

should exercise (even though you’ve lost

money—see next column)

()

21 20 1.35 0.35

Profit on exercise option cost−

=−− =−

(21 20) 1.35 0.35

26%

1.35 1.35

Profit on exercise option cost

option cost

−

−− −

==−

$25 Yes

()

25 20 1.35 3.65

Profit on exercise option cost−

=−− =

(25 20) 1.35 3.65

270%

1.35 1.35

Profit on exercise option cost

option cost

−

−−

$30 Yes

()

30 20 1.35 8.65

Profit on exercise option cost−

=−− =

(30 20) 1.35 8.65

641%

1.35 1.35

Profit on exercise option cost

option cost

−

−−

Figure 23.8: Analyzing the profit from a call option. If the stock price is down on September 21, your loss is limited to $1.35.

However, if the price goes above $20, your percentage gains from the option are very large. The call option is a “one-sided” bet on

the stock price going up—if the stock price goes up, you make money; if the stock price goes down, you lose a limited amount of

money.

PFE, Chapter 23: Introduction to options page 20

You can summarize all of this in a spreadsheet:

ABCDEFGHIJKL

Call purchase price, 7 August 2001 1.35

Call exercise price, X 20

Market price of Cisco.

21 September 2001

Exercise

the call?

Dollar

profit/loss

Percentage

profit/loss

0 no -1.35 -100.00%

5 no -1.35 -100.00%

10 no -1.35 -100.00%

16 no -1.35 -100.00%

18 no -1.35 -100.00%

20 no -1.35 -100.00%

21 yes -0.35 -25.93%

22 yes 0.65 48.15%

25 yes 3.65 270.37%

28 yes 6.65 492.59%

30 yes 8.65 640.74%

32 yes 10.65 788.89%

34 yes 12.65 937.04%

Technical note: The data series graphed above

are non-contiguous in the spreadsheet (they're

column A and column C). For how to do this: see

Chapter 26.

PROFIT FROM BUYING A CISCO CALL

Bought for $1.35 on 7Aug01; Exercise price: X=$20

Exercise date: 21Sep01

Dollar Profit/Loss on Cisco Call Option

-2

0 5 10 15 20 25 30 35

Cisco stock price on 21Sep01

=IF(A18>$B$3,"yes","no")

=C18/$B$2

=IF(A18>$B$3,A18-$B$3,0)-$B$2

23.3. Why buy a put option?

As in the case of the call, there are two simple reasons to buy a put:

Reason 1: The put option allows you to delay the decision to sell the stock.

It’s 7 August 2001, and you own a share of Cisco stock. You’re considering selling the

stock; its current market price is $19.26. As an alternative, you can buy a September put option

with X = $20. This put option will cost you $2.00. Here’s your thinking:

•

If, on 21 September 2001, Cisco’s stock price is < $20.00, you’ll exercise the option

and sell the share for $20. As in the case of the call option discussed above, there are

several “sub-possibilities”:

PFE, Chapter 23: Introduction to options page 21

o Cisco’s 21 Sept. stock price = $5. Now you’ve made a lot of money: You spent

$2 for the option, but you sold the stock for $20, which is $15.00 more than its

market price. Your net profit is $13.00 ($15.00 - $2.00 cost of the option).

o If Cisco’s 21 Sept. stock price = $19.00, you’ll still exercise the option and sell

the stock for $20.00. Compared to the market price, you’ve made $1.00 on the

sale of the stock, but this time you will have lost a bit of money, since the option

cost you $2.00. Your net profit will be -$1.00.

•

If on 21 September Cisco’s stock is selling for more than $20, you will not exercise

your put option. If you still want to sell the stock, you’ll sell it on the open market.

In all cases, you will be out only the $2.00 cost of the option.

Reason 2: A put option allows you to make a bet on the stock price going down

If you buy a put for $2.00 and wait until 21 September to exercise, here are your profits:

, , 21 01 20

20.00 2.00 In this case you exercise the put and

make 20 minus the cost of the put

, , 21 01 20

2.00 In this case you don't exercise the

Cisco stock price S on Sep

Put profits

Cisco stock price S on Sep

≤

−−

−

− put;

your loss is the cost of the put

⎧

⎪

⎨

⎪

⎩

In a spreadsheet:

PFE, Chapter 23: Introduction to options page 22

ABCDEFGHIJKL

Call purchase price, 7 August 2001 2

Call exercise price, X 20

Market price of Cisco.

21 September 2001

Exercise

the put

Dolla

profit/loss

Percentage

profit/loss

0 yes 18 900.00%

5 yes 13 650.00%

10 yes 8 400.00%

16 yes 2 100.00%

18 yes 0 0.00%

20 no -2 -100.00%

21 no -2 -100.00%

22 no -2 -100.00%

25 no -2 -100.00%

28 no -2 -100.00%

30 no -2 -100.00%

32 no -2 -100.00%

34 no -2 -100.00%

Technical note: The data series graphed above

are non-contiguous in the spreadsheet (they're

column A and column C). For how to do this: see

Chapter 26.

PROFIT FROM BUYING A CISCO PUT

Bought for $2.00 on 7Aug01; Exercise price: X=$20

Exercise date: 21Sep01

Dollar Profit/Loss on Cisco Put

Option

-2

0 5 10 15 20 25 30 35

Cisco stock price on 21Sep01

=IF(A18<$B$3,"yes","no")

=C18/$B$2

=IF(A18<$B$3,$B$3-A18,0)-$B$2

23.4. General properties of option prices

In this section we review three general properties of option prices. We look at the effects

of option time to maturity, exercise price, the stock price, interest rates, and risk on option prices.

Our discussion is informal and intuitive.

Property 1: Options with more time to maturity are worth more

The longer you have to exercise an option, the more it should be worth. The intuition

here is clear: Suppose you have a September call option to buy Cisco stock for $20 and also an

October call option to buy Cisco for $20. Since Cisco options are American options, anything

PFE, Chapter 23: Introduction to options page 23

the October call gives you all the opportunities associated with the September call—and then

some. Thus the October call should be worth more than the September call.

Here’s some data for the Cisco options. Notice that the prices of the options increase

with maturity:

ABCD

Stated expiration date

Exercise

price, X

Call price Put price

Aug01 20.00 0.65 1.45

Sep01 20.00 1.35 2.00

Oct01 20.00 1.80 2.55

Jan02 20.00 2.90 3.40

Jan03 20.00 5.40 5.20

Jan04 20.00 6.80 5.80

CISCO OPTIONS:

THE EFFECT OF EXPIRATION DATE

ON OPTION PRICE

Cisco Options: The effect of option maturity on the

option price

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

Aug01 Sep01 Oct01 Jan02 Jan03 Jan04

Call price

Put price

The argument in this paragraph seems to depend critically on the calls being American and not European. It holds,

however, for European call also—see Chapter 21, Section ???.

PFE, Chapter 23: Introduction to options page 24

Property 2: Calls with higher exercise prices are worth less; puts with higher

exercise prices are worth more

Suppose you had two October calls on Cisco: One call has an exercise price of $20 and

the second call has an exercise price of $30. The second call is worth less than the first. Why?

Think about calls as bets on the stock price: The first call is a bet that the stock price will go

over $20, whereas the second call is a bet that the stock price will go over $30. You’re always

more likely to win the first bet (Cisco will go over $20) than the second bet.

From the table below you can see that Cisco’s option prices conform to this property:

ABCDEF G H IJ

Stated

expiration

date

Exercise

price, X

Call price Put price

Oct01 10.00 10.00 0.10

Oct01 12.50 6.90 0.25

Oct01 15.00 5.00 0.65

Oct01 17.50 3.20 1.40

Oct01 20.00 1.80 2.55

Oct01 22.50 0.95 4.10

Oct01 25.00 0.45 6.00

Oct01 27.50 0.20 7.50

Oct01 30.00 0.15 10.70

Oct01 35.00 0.05 16.30

Oct01 40.00 0.05 21.50

Oct01 45.00 0.05 29.50

Oct01 50.00 0.05 31.12

Oct01 55.00 0.10 37.50

Oct01 60.00 0.05 36.75

Oct01 65.00 0.05

CISCO OCTOBER OPTIONS:

THE EFFECT OF THE EXERCISE PRICE

ON THE OPTION PRICE

Cisco October 01 options

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Exercise price

Option price

Call price

Put price

Here we’ve looked at all the options which expire on the same date (October 2001). As

you can see: The higher the option exercise price, the lower the call price and the higher the put

price. (There are a few exceptions; see paragraph below.)

The logic of this is clear:

•

If an October 2001 Cisco call option with exercise price $10 (the right to buy a share

of Cisco for $10) is worth $10, then an October 2001 call with exercise price $12.50

(the right to buy a share of Cisco for $12.50—more than $10) is worth less.