Principles of Finance with Excel (Основы финансов c Excel)

Подождите немного. Документ загружается.

PFE, Chapter 22: Introduction to options page 10

You can summarize all of this in a spreadsheet:

ABCDEFGHIJKL

Call purchase price, 7 Aug

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 ???.

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 40

Cisco stock price on 21Sep01

=IF(A21>$B$6,"yes","no")

=C21/$B$5

=IF(A21>$B$6,A21-$B$6,0)-$B$5

22.3. Why buy a put option?

As in the case of the call, there are two primary types of 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 22: Introduction to options page 11

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 purchase the stock, you’ll buy it on the open

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

Reason 2: A call 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

≤

−−

−

ut;

your loss is the cost of the put











In a spreadsheet:

PFE, Chapter 22: Introduction to options page 12

ABCDEFGHIJKL

Call purchase price, 7 Aug

Call exercise price, X 20

Market price of Cisco.

21 September 2001

Exercise

the put

Dollar

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 ???.

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 40

Cisco stock price on 21Sep01

=IF(A21<$B$6,"yes","no")

=C21/$B$5

=IF(A21<$B$6,$B$6-A21,0)-$B$5

22.4. General properties of option prices

In this section we review some 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 22: Introduction to options page 13

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:

108

ABCDEF

Stated expiration date

Exercise

price, X

Call price Put price

Actual

expiration

date

Days to

maturity

Aug01 20.00 0.65 1.45 17 Aug01 10

Sep01 20.00 1.35 2.00 21 Sep01 45

Oct01 20.00 1.80 2.55 19 Oct01 73

Jan02 20.00 2.90 3.40 18 Jan02 164

Jan03 20.00 5.40 5.20 17 Jan03 528

Jan04 20.00 6.80 5.80 16 Jan04 892

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:

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 22, Section ???.

PFE, Chapter 22: Introduction to options page 14

MNOPQRSTUVWX

Stated expiration date

Exercise

price, X

Call price Put price

Lookup

Oct01 10.00 10.00 0.10 Sunday 1 20

Oct01 12.50 6.90 0.25 Monday 2 19

Oct01 15.00 5.00 0.65 Tuesday 3 18

Oct01 17.50 3.20 1.40 Wednesda 4 17

Oct01 20.00 1.80 2.55 Thursday 5 16

Oct01 22.50 0.95 4.10 Friday 6 22

Oct01 25.00 0.45 6.00 Saturday 7 21

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 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.

•

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

of Cisco in October for $10) is worth $0.10, then the right to sell a share of Cisco for

$12.50 should be worth more. And so it is.

The graph and the table show what appear to be a few exceptions to this rule. For

example, the Cisco put with X = $65 traded for less than the put with X = $60. If you see this

kind of behavior it almost always has to do with the fact that the options in question are

infrequently traded. In the example given here, the $65 and $60 calls only traded several times

during the day in question. The result is that the option prices given in the table refer to options

traded on Cisco stock at different times and with different prices. (Notice that one of the

options—the October put with exercise price $65—didn’t trade at all.)

PFE, Chapter 22: Introduction to options page 15

When the stock price goes up, call option prices go up and put option prices go

down

You can’t see this in the original data, but here’s an example:

[Example forthcoming?]

The reason for this behavior is obvious, if you think of an option as a bet: Suppose you

buy a Cisco X=20 October 2001 call option. We can view this option as a bet that Cisco’s stock

price in October will be above $20. The probability of your winning this bet is higher if Cisco’s

current stock price is higher, and hence so is the call option’s price. Thus, for example, if you’re

willing to pay $1.80 for the X=20 October call when Cisco’s current stock price is $19.26, you

would be willing to pay more for the same call when Cisco’s stock price is $22.

The logic for puts is the same, though the result is opposite: The higher the stock price,

the lower the put option price.

When the interest rate goes up, call prices go up and put prices tend to go down

When

[Example forthcoming?]

When the risk of the underlying asset goes up, option prices tend to increase

[Example forthcoming?]

Summary table

Here’s a summary table of the effects of basic parameters on option prices:

PFE, Chapter 22: Introduction to options page 16

Variable Call price? Put price?

Stock price ↑

↑ ↓

Exercise price X ↑ Call price ↓ Put price ↑

Time to maturity ↑ Call price ↑ Put price ↑

Interest rate ↑ Call price ↑ Put price ↓ (usually?)

Stock price volatility ↑ Call price ↑ Put price ↑

22.5. Writing options, shorting stock

Our whole discussion thus far has been from the point of view of the option purchaser.

For example in Section 2 we derived the profit pattern from buying a Cisco 20 call for $1.35 on 7

August 2001 and waiting until the call maturity on 21 September 2001. Similarly in Section 3

we looked at the profit from buying a Cisco 20 put.

There’s another side to this story: When you buy a call, someone else sells the call. In

the jargon of options markets, the call seller is writing a call.

Call buyer: On 7 August 2001 buys, for $1.35, the right to buy one share of Cisco stock

for $20 on or before 21 September 2001.

Call writer: On 7 August 2001 sells, for $1.35, the obligation to sell one share of Cisco

stock for $20—as per demand of the call option buyer—on or before 21 September.

Here’s the way the call writer’s profit pattern looks:

PFE, Chapter 22: Introduction to options page 17

CALL OPTION CASH FLOW PATTERN--the call writer

7-Aug-01 21-Sep-01

Receives: $1.35 If Cisco's stock price > $20

( denote this by S

> 20 ),

the call will be exercised.

The call writer has to sell

one share of Cisco stock

for $20.

Call writer's loss: S

- $20

If Cisco's stock price <

$20,

( denote this by S

< 20 ),

the call will not be exercised.

Call writer's loss: 0

In principle, the call buyer has the

right to buy Cisco stock for $20 on

any date before 21 September. In

actual fact, the call buyer will only

want to exercise the call

option at its terminal date (see next

chapter).

Here’s the profit graph from writing a call option:

ABCDEFGHIJK

Call price, 7 August 2001 1.35

Call exercise price, X 20

: Market price

of Cisco,

21 September 2001

Will call

buyer exercise

the call?

Dollar

profit/loss

0no1.35

5no1.35

10 no 1.35

16 no 1.35

18 no 1.35

20 no 1.35

21 yes 0.35

22 yes -0.65

25 yes -3.65

28 yes -6.65

30 yes -8.65

32 yes -10.65

34 yes -12.65

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 ???.

PROFIT FROM WRITING A CISCO CALL

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

Exercise date: 21Sep01

Dollar Profit/Loss on Cisco Call Option

-15

-13

-11

-9

-7

-5

-3

-1

0 5 10 15 20 25 30 35

: Cisco stock price on 21Sep01

Profit = Call price - max(S

-20,0)

=IF(A21>$B$6,"yes","no")

=$B$5-IF(A21>$B$6,A21-$B$6,0)

Writing puts

PFE, Chapter 22: Introduction to options page 18

There’s a similar story for puts:

Put buyer: On 7 August 2001 buys, for $2.00, the right to sell one share of Cisco stock

for $20 on or before 21 September 2001.

Put writer: On 7 August 2001 sells, for $2.00, the obligation to buy one share of Cisco

stock for $20—as per demand of the put option buyer—on or before 21 September.

Here’s the way the call writer’s profit pattern looks:

PUT OPTION CASH FLOW PATTERN--the put writer

7-Aug-01 21-Sep-01

Receives: $2.00 If Cisco's stock price < $20

( denote this by S

< 20 ),

the put will be exercised.

The put writer has to buy

one share of Cisco stock

for $20.

Put writer's loss: $20 - S

If Cisco's stock price > $20,

( denote this by S

> 20 ),

the put will not be exercised.

Put writer's loss: 0

In principle, the put buyer has the

right to sell Cisco stock for $20 on

any date before 21 September. In

actual fact, she will only rarely want

to exercise the put option before its

terminal date (see Section ?? of

this chapter).

Here’s a graph of the profit pattern from writing a put:

PFE, Chapter 22: Introduction to options page 19

ABCDEFGHIJK

Put price, 7 August 2001 2

Put exercise price, X 20

: Market price

of Cisco,

21 September 2001

Will put

buyer exercise

the put?

Dollar

profit/loss

to put writer

0yes-18

5yes-13

10 yes -8

16 yes -2

18 yes 0

20 no 2

21 no 2

22 no 2

25 no 2

28 no 2

30 no 2

32 no 2

34 no 2

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 ???.

PROFIT FROM WRITING A CISCO PUT

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

Exercise date: 21Sep01

Put Writer: Dollar Profit/Loss on Cisco Put

Option

-18

-13

-8

-3

0 5 10 15 20 25 30 35

: Cisco stock price on 21Sep01

=IF(A21<$B$6,"yes","no")

=$B$5-IF(A21<$B$6,$B$6-A21,0)

Profit = Put price - max(20-S

,0)

Short-selling a stock

Short-selling a stock (“shorting”) is the stock equivalent of writing an option. Here’s

how shorting a stock compares to buying a stock:

Stock buyer: On 7 August 2001 buys one share of Cisco stock, for $19.26. When you

sell the stock—call the date T—you’ll get the stock price S

. Of course you will have

also earned any dividends that Cisco will have paid up to and including date T.

Ignoring

the time value of money, your profit from buying the stock is:

19.26

S Cisco dividends

−

Stock shorter: On 7 August 2001 contacts his broker and borrows one share of Cisco

stock, which he then sells, thus receiving $19.26. At some future date T, the short-seller

of the stock will purchase a share of Cisco on the open market, paying the then-current

Not something you’re like to have to worry about: Cisco has never paid a dividend!