Principles of Finance with Excel (Основы финансов c Excel)
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PFE, Chapter 23: Introduction to options page 5
you $3 to buy this option. Having bought, you then have the right for the next three months to
buy a share of Peacemount stock for $36.
Why buy this option? By spending $3 now, you lock in $36 as the maximum price
Peacemount stock will cost you in the next three months. If the price of the stock goes up in the
next three months, this will save you a lot of money. If, for example, Peacemount stock is
selling on 26 February 2004 for $50, then by using your call option, you can buy the stock for
$36. You will have a profit of $11 (buying the stock for $36 instead of $50 saves you $14; from
this amount you have to deduct the $3 cost of the option). If, on the other hand, Peacemount
stock declines below $36, then you will not exercise the option but you will only lose your $3
investment. In option market jargon: The call option offers upside gains but only limited
downside losses.
There’s another reason to buy the option: You might be able to sell it at some time
during the next three months and make a profit. Suppose that in one week the price of
Peacemount stock is $45. Then the price of the call option should be at least $9, since the owner
of the option could immediately make a profit of $9 by exercising it.
2
Notice that in this example
the price of the stock increases by 25% (from $36 to $45), whereas the price of the option
increases by at least 300%. This makes the option a very interesting speculation. In option
market jargon: The call option’s market price is very sensitive to the price of the underlying
asset (in our case: the price of Peacemount stock).
In addition to call options, this chapter also discusses put options. Whereas a call option
is the right to buy a share of stock in the future, a put option is the right to sell a share of stock.
2
Whoever holds the option can purchase a share of Peacemount for $36. The stock price is now $45, so the
immediate realizable profit is $9.
PFE, Chapter 23: Introduction to options page 6
An example is given in Figure 23.3: For $2.50 you could, on 26 November 2003, buy the right
to sell one share of Peacemount stock for $36 during the next three months.
Why might you be interested in buying this put option? One reason is that, for holders of
Peacemount stock, the put option places a floor on your losses. Suppose you own a share of
Peacemount stock. On 26 November 2003 shares of Peacemount are selling for $35.50. If you
buy the put option today for $2.50, you guarantee yourself that at any point during the next three
months you will realize at least $33.50 from your stock.
To see this, suppose that on 26 February 2004 the price of Peacemount is $20. Instead of
selling your share on the open market, you will use (“exercise”) the put option to sell the share
for $36. Accounting for the cost of the option, your net receipts will be $33.50 ($36 for the share
minus the $2.50 cost of the put option).
PFE, Chapter 23: Introduction to options page 7
CALL OPTION ON PEACEMOUNT STOCK
Price on 26 November 2003: $3
If presented at the Asheville Stock Exchange on or before 26 February
2004, this piece of paper gives you the right to buy one share of Peacemount stock
for $36. After 26 February 2004 this piece of paper is worthless.
The holder of this piece of paper can sell it to someone else at any time.
Some additional information:
• On 26 November 2003, shares of Peacemount stock sold for $35.50.
• Peacemount’s stock price has experienced considerable variations during the past three
months:
PEACEMOUNT STOCK PRICE
32.50
33.00
33.50
34.00
34.50
35.00
35.50
36.00
17-Jun-03
5-Jul-03
23-Jul-03
10-Aug-03
28-Aug-03
15-Sep-03
3-Oct-03
21-Oct-03
8-Nov-03
26-Nov-03
Figure 23.2. A call option on Peacemount stock. The option gives the holder the right to buy a
share of Peacemount on or before 26 February 2004 for $36. The market price of the option on
26 November 2003 is $3.
PFE, Chapter 23: Introduction to options page 8
PUT OPTION ON PEACEMOUNT STOCK
Price on 26 November 2003: $2.50
If presented at the Asheville Stock Exchange on or before 26 February
2004, this piece of paper gives you the right to sell one share of Peacemount stock
for $36. After 26 February 2004 this piece of paper is worthless.
The holder of this piece of paper can sell it to someone else at any time.
Figure 23.3. A (hypothetical) put option on Peacemount stock. The option gives the holder the
right to sell a share of Peacemount on or before 26 February 2004 for $36. The market price of
the option on 26 November 2003 is $2.50.
What’s next?
In this chapter shows you basic option definitions and introduces you to option cash
flows. In addition we show you how option strategies—the ability to combine options and
stocks in portfolios—can change the payoff patterns available to investors. When you finish this
chapter, you will understand why stock options are really interesting securities, and why you
might want to invest in them.
Finance concepts discussed
• Call and put options
• Option strategies: protective puts, spreads, butterflies
PFE, Chapter 23: Introduction to options page 9
Excel functions used
• Max
• Min
BASIC OPTION TERMINOLOGY AND SYMBOLS
Name Definition Symbol
Call option The right to buy a stock or other asset at
a pre-determined price on or before
some future date.
C
Put option The right to sell a stock or other asset at
a pre-determined price on or before
some future date.
P
Exercise price The pre-determined price of the
option—the price at which the
stock/asset can be purchased in the
future. Also called the strike price.
X
Exercise date The last date on which the option can be
exercised. Past this date the option is
worthless.
T
Underlying asset The stock or other asset which can be
purchased with an option (in our
previous examples: Gold or one share
of Peacemount stock).
S
S
0
: stock price today
S
T
: the stock price
on the exercise date
T
Figure 23.4: Option pricing involves a lot of terminology. Here are some very basic terms.
23.1. What’s an option?
A call option on a stock is the right to buy a stock on or before a given date at a pre-
determined price. Figure 23.6 gives options prices for options on Cisco stock on August 7, 2002;
we will use these prices in the examples which follow.
PFE, Chapter 23: Introduction to options page 10
Cisco call options
For example, row 21 of the Cisco spreadsheet tells you that on 7 August 2001, a call
option on Cisco stock with an exercise price of $20.00 and an exercise date of 21 September
2001 was selling for $1.35:
4
20
21
22
ABCDEF
Stated expiration date
Exercise
price, X
Call price Put price
Actual
expiration
date
Days to
maturity
Sep01 17.50 2.75 0.90 21 Sep01 45
Sep01 20.00 1.35 2.00 21 Sep01 45
Sep01 22.50 0.55 3.80 21 Sep01 45
Suppose you purchased this call option on 7 August. Figure 23.5 shows the option’s cash
flow pattern:
CALL OPTION CASH FLOW PATTERN
7-Aug-01 21-Sep-01
Pay: $1.35 If Cisco's stock price > $20,
you'll exercise your call
to buy the stock for $20.
Your gain on 21 Sept:
Actual stock price - $20
If Cisco's stock price <
$20,
you will
not
exercise you
r
call option.
Your gain on 21 Sept: 0.
In principle, you have the right to
buy Cisco stock for $20 on any
date before 21 September. In
actual fact, you'll only want to
exercise the call
option at its terminal date (see
next chapter).
Figure 23.5: The cash flows from buying a Cisco call option on 7 August 2001 for $1.35 and
possibly exercising it on 21 September 2001. The option has exercise price X = $20.
PFE, Chapter 23: Introduction to options page 11
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ABCDEF
August 7, 2001, CSCO closing price
19.26
Stated expiration date
Exercise
price, X
Call price Put price
A
ctual
expiration
date
Days to
maturity
Aug01 7.50 11.90 0.05 17 Aug01 10
Aug01 10.00 9.60 0.20 17 Aug01 10
Aug01 12.50 6.50 0.10 17 Aug01 10
Aug01 15.00 4.20 0.10 17 Aug01 10
Aug01 17.50 2.10 0.40 17 Aug01 10
Aug01 20.00 0.65 1.45 17 Aug01 10
Aug01 22.50 0.15 3.40 17 Aug01 10
Aug01 25.00 0.05 5.00 17 Aug01 10
Aug01 27.50 0.10 7.50 17 Aug01 10
Aug01 30.00 0.10 11.90 17 Aug01 10
Aug01 32.50 0.05 17 Aug01 10
Aug01 35.00 0.05 16.20 17 Aug01 10
Sep01 10.00 9.50 21 Sep01 45
Sep01 12.50 6.30 0.15 21 Sep01 45
Sep01 15.00 4.50 0.40 21 Sep01 45
Sep01 17.50 2.75 0.90 21 Sep01 45
Sep01 20.00 1.35 2.00 21 Sep01 45
Sep01 22.50 0.55 3.80 21 Sep01 45
Sep01 25.00 0.20 5.50 21 Sep01 45
Sep01 27.50 0.10 21 Sep01 45
Sep01 30.00 0.05 21 Sep01 45
Oct01 10.00 10.00 0.10 19 Oct01 73
Oct01 12.50 6.90 0.25 19 Oct01 73
Oct01 15.00 5.00 0.65 19 Oct01 73
Oct01 17.50 3.20 1.40 19 Oct01 73
Oct01 20.00 1.80 2.55 19 Oct01 73
Oct01 22.50 0.95 4.10 19 Oct01 73
Oct01 25.00 0.45 6.00 19 Oct01 73
Oct01 27.50 0.20 7.50 19 Oct01 73
Oct01 30.00 0.15 10.70 19 Oct01 73
Oct01 35.00 0.05 16.30 19 Oct01 73
Oct01 40.00 0.05 21.50 19 Oct01 73
Oct01 45.00 0.05 29.50 19 Oct01 73
Oct01 50.00 0.05 31.12 19 Oct01 73
Oct01 55.00 0.10 37.50 19 Oct01 73
Oct01 60.00 0.05 36.75 19 Oct01 73
Oct01 65.00 0.05 19 Oct01 73
Jan02 10.00 9.50 0.30 18 Jan02 164
Jan02 12.50 8.20 0.60 18 Jan02 164
Jan02 15.00 5.70 1.20 18 Jan02 164
Jan02 17.50 4.10 2.00 18 Jan02 164
Jan02 20.00 2.90 3.40 18 Jan02 164
Jan02 22.50 1.85 4.90 18 Jan02 164
Jan02 25.00 1.20 7.00 18 Jan02 164
Jan02 26.25 0.95 7.50 18 Jan02 164
Jan02 27.50 0.80 9.80 18 Jan02 164
Jan02 30.00 0.45 11.30 18 Jan02 164
Jan02 32.50 0.45 13.10 18 Jan02 164
Jan02 35.00 0.15 15.00 18 Jan02 164
Jan02 37.50 0.20 20.10 18 Jan02 164
CISCO OPTIONS, August 7, 2001
CLOSING PRICE ON CHICAGO
BOARD OF OPTIONS EXCHANGE
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ABCDEF
Stated expiration date
Exercise
price, X
Call price Put price
A
ctual
expiration
date
Days to
maturity
Jan02 40.00 0.10 19.30 18 Jan02 164
Jan02 42.50 0.10 25.90 18 Jan02 164
Jan02 45.00 0.10 27.00 18 Jan02 164
Jan02 47.50 0.15 34.12 18 Jan02 164
Jan02 50.00 0.05 30.10 18 Jan02 164
Jan02 52.50 0.10 34.50 18 Jan02 164
Jan02 55.00 0.05 37.00 18 Jan02 164
Jan02 57.50 0.05 39.70 18 Jan02 164
Jan02 60.00 0.10 40.10 18 Jan02 164
Jan02 62.50 0.05 43.00 18 Jan02 164
Jan02 65.00 0.05 45.80 18 Jan02 164
Jan02 67.50 0.05 31.37 18 Jan02 164
Jan02 70.00 0.05 50.80 18 Jan02 164
Jan02 72.50 0.05 53.50 18 Jan02 164
Jan02 75.00 0.05 58.50 18 Jan02 164
Jan02 77.50 0.05 59.70 18 Jan02 164
Jan02 80.00 0.05 62.20 18 Jan02 164
Jan02 82.50 0.19 30.00 18 Jan02 164
Jan02 85.00 0.05 46.00 18 Jan02 164
Jan02 87.50 0.06 52.50 18 Jan02 164
Jan02 90.00 0.05 56.50 18 Jan02 164
Jan02 95.00 0.12 65.37 18 Jan02 164
Jan02 100.00 0.05 70.87 18 Jan02 164
Jan02 105.00 0.05 48.00 18 Jan02 164
Jan02 110.00 0.06 84.12 18 Jan02 164
Jan02 115.00 0.31 63.00 18 Jan02 164
Jan02 120.00 0.05 97.90 18 Jan02 164
Jan03 10.00 10.60 0.95 17 Jan03 528
Jan03 12.50 9.50 1.60 17 Jan03 528
Jan03 15.00 7.70 2.60 17 Jan03 528
Jan03 17.50 6.50 3.80 17 Jan03 528
Jan03 20.00 5.40 5.20 17 Jan03 528
Jan03 25.00 3.70 7.80 17 Jan03 528
Jan03 30.00 2.30 11.60 17 Jan03 528
Jan03 35.00 1.75 15.90 17 Jan03 528
Jan03 40.00 1.10 20.90 17 Jan03 528
Jan03 45.00 0.95 25.50 17 Jan03 528
Jan03 50.00 0.65 32.20 17 Jan03 528
Jan03 55.00 0.50 37.20 17 Jan03 528
Jan03 60.00 0.40 40.20 17 Jan03 528
Jan03 65.00 0.30 48.40 17 Jan03 528
Jan03 70.00 0.25 49.00 17 Jan03 528
Jan03 75.00 0.15 48.62 17 Jan03 528
Jan03 80.00 0.15 42.87 17 Jan03 528
Jan03 85.00 0.20 29.75 17 Jan03 528
Jan03 90.00 0.40 56.50 17 Jan03 528
Jan03 95.00 0.25 56.75 17 Jan03 528
Jan03 100.00 0.10 83.10 17 Jan03 528
Jan04 10.00 11.90 1.30 16 Jan04 892
Jan04 15.00 9.00 3.20 16 Jan04 892
Jan04 20.00 6.80 5.80 16 Jan04 892
Jan04 25.00 5.50 8.50 16 Jan04 892
Jan04 30.00 4.00 11.90 16 Jan04 892
Figure 23.6: Cisco stock option prices on 7 August 2001. A blank in the price (for example the Oct01 puts with exercise price 65) indicates
that no options were traded. On 7 August 2001 Cisco option with maturities as far out as January 2004 were traded.
PFE, Chapter 23: Introduction to options page 12
Now let’s see what happens on September 21:
• Suppose the Cisco stock price on September 21 is $35. In this case you get to buy one
share of Cisco for $20. Your gain is $35 - $20 = $15.
• If the Cisco stock price on September 21 is $18, you would not exercise your call option
to buy a share of Cisco for $20 (why should you? you could buy it on the open market
for less). The option expires unexercised, and your gain is $0.
Cisco put options
What about the Cisco put option with an exercise price of $20? It was selling, on 7
August 2001, for $2.00. The put option gives you the right to sell a share of Cisco on or before
the terminal date for its exercise price. The put option’s cash flow pattern is shown in Figure
23.7.
PUT OPTION CASH FLOW PATTERN
7-Aug-01 21-Sep-01
Pay: $2.00 If Cisco's stock price < $20,
you'll exercise your put
to sell the stock for $20.
Your gain on 21 Sept:
$20 - Actual stock price
If Cisco's stock price >
$20,
you will
not
exercise you
r
put option.
Your gain on 21 Sept: 0.
In principle, you have the right to
sell Cisco stock for $20 on any
date before 21 September. In
actual fact, you will only rarely
want to exercise the put option
before its terminal date (see next
chapter).
Figure 23.7: The cash flows from buying a Cisco put option on 7 August 2001 for $2 and
possibly exercising it on 21 September 2001. The option has exercise price X = $20.
PFE, Chapter 23: Introduction to options page 13
If Cisco’s stock price on September 21 is $15, you will exercise your put option and sell a
share of Cisco for $20, thus gaining $5.
3
On the other hand if Cisco’s share price on September
21 is $30, you will not exercise the put option (why sell a share using the option for $20 when
you can sell it on the open market for $30?).
Option websites
All the data in this chapter was gathered from public sources on the Web. Many of these
websites have superb data and also educational features. Here are some websites we especially
enjoy.
• The website of the Chicago Board of Options Exchange (CBOE): http://www.cboe.com
• Option metrics: http://www.impliedvol.com/
• Equity analytics: http://www.e-analytics.com/optaaa.htm
European versus American options
Cisco’s stock options are American stock options—they can be exercised on or before the
option maturity date T. A European stock option can be exercised only on its maturity date T.
Clearly an American stock option is worth at least as much as a European stock option.
Two notes about American versus European stock options:
3
What if you don’t own a share of Cisco on 21 September? No problem: You buy a share on the open market for
$15 and use your option to sell it for $20.
PFE, Chapter 23: Introduction to options page 14
• The terminology has nothing to do with geography. Most traded options, whether in the
U.S., Europe, or Asia, are American and not European.
• A remarkable fact about American call options is the following: In many cases an
American call option is worth exactly the same as an equivalent European call option.
This happens if the stock on which the option is written does not pay a dividend before
the option expiration date T . Since Cisco stock does not pay dividends, the “American”
feature of Cisco stock call options is worthless, and the call options on Cisco stock are
worth the same as if they are European options. We discuss the reasons for this in
Chapter 24.
In the money, out of the money, at the money
A call option is said to be “in the money” if the current stock price is larger than the
option’s exercise price. Look at the Cisco October calls in the spreadsheet below. The call with
the exercise price of $12.50 (currently selling for $6.90) has an exercise price less than Cisco’s
current stock price of $19.26. Thus this call is in the money—the stock price is greater than the
call’s exercise price.