14

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Chapter 14
Options
•
Options on common stocks
•
Why options
•
Option “
Moneyness
”
•
Option payoffs and profits
•
Option strategies
•
Option prices, intrinsic values and
arbitrage
•
Put

call parity
•
Stock index options
•
Foreign currency options
•
Warrants
•
The Canadian Derivatives Clearing
Corporation
Ayşe
Yüce
Copyright © 2012 McGraw

Hill Ryerson
© 2009 McGraw

Hill Ryerson
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Stock Options
In this chapter, we will discuss general features
of options, but will focus on options on
individual common stocks.
We will see the tremendous flexibility that
options offer investors in designing investment
strategies.
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Option Basics
A stock option is a
derivative security
,
because
the value of the option is “derived” from the
value of the underlying common stock.
There are two basic option types.
Call options
are options to
buy
the underlying asset.
Put options
are options to
sell
an underlying asset.
Listed Option contracts are standardized to
facilitate trading and price reporting.
Listed stock options give the option holder the right
to buy or sell 100 shares of stock.
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Option Basics
Option contracts are legal agreements between two parties
—
the buyer of the option, and the seller of the option.
The minimum terms stipulated by stock option contracts are:
The identity of the underlying stock.
The strike price, or exercise price.
The option contract size.
The option expiration date, or option maturity.
The option exercise style (
American
or
European
).
The delivery, or settlement, procedure.
Stock options trade at organized options exchanges, such as
the CBOE, as well as over

the

counter (OTC) options
markets.
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Option Price Quotes
A list of available option contracts and their prices for a
particular security is known as an
option chain
.
Option chains are available online through many sources,
including the Montreal exchange (
http://www.m

x.ca
), CBOE
(
http://quote.cboe.com
) and Yahoo!
(
http://finance.yahoo.com
).
Stock option ticker symbols include:
Letters to identify the underlying stock.
A Letter to identify the expiration month as well as whether the option
is a call or a put.
A Letter to identify the strike price (a bit more complicated
—
see
Yahoo or Stock

Trak
for tables to explain this letter.)
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Listed Option Quotes on the Web
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The Canadian Derivatives Clearing Corporation
The Canadian Derivatives Clearing Corporation is the
clearing agency for all derivatives exchanges in
Canada (Montreal and Winnipeg).
All option contracts traded in Canada are originally
issued, guaranteed, and cleared by the CDCC.
Brokerage firms merely act as intermediaries between
investors and the CDCC.
Visit the CDCC at:
www.cdcc.com
.
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Why Options?
A basic question asked by investors is: “Why
buy stock options instead of shares in the
underlying stock?”
To answer this question, we compare the
possible outcomes from these two investment
strategies:
Buy the underlying stock
Buy options on the underlying stock
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Buying the Stock versus Buying a Call Option
IBM is selling for $90 per share and call
options with a strike price of $90 are $5 per
share.
Investment for 100 shares:
IBM Shares: $9,000
One listed call option contract: ($500)
Suppose further that the option expires in three
months.Finally, let’s say that in three months,
the price of IBM shares will either be: $100,
$90, or $80.
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Buying the Underlying Stock versus
Buying a Call Option
Let’s calculate the dollar and percentage return given
each of the prices for IBM stock:
Buy 100 IBM Shares
($9000 Investment):
Buy One Call Option
($500 Investment):
Dollar
Profit:
Percentage
Return:
Dollar
Profit:
Percentage
Return:
Case I: $100
$1,000
11.11%
$500
100%
Case II: $90
$0
0%

$500

100%
Case III: $80

$1,000

11.11%

$500

100%
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Why Options? Conclusion
Whether one strategy is preferred over another is a matter
for each individual investor to decide.
That is, in some instances investing in the underlying stock will be
better. In other instances, investing in the option will be better.
Each investor must weight the risk and return trade

off offered by
the strategies.
It is important to see that call options offer an alternative
means of formulating investment strategies.
For 100 shares, the
dollar
gain and loss potential with call options
is
lower.
The positive and negative
percentage return
with call options is
higher
.
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Stock Index Options
A stock index option is an option on a stock
market index.
Because the actual delivery of all stocks
comprising a stock index is impractical, stock
index options have a
cash settlement procedure.
That is, if the option expires in the money, the option
writer simply pays the option holder the intrinsic value
of the option.
The cash settlement procedure is the same for calls
and puts.
14

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Index Option Trading
Ayşe
Yüce
Copyright © 2012
McGraw

Hill Ryerson
The
intrinsic value
of an option is the payoff that an option holder
receives if the underlying stock price does not change from its current
value.
That is, if S is the current stock price, and K is the strike price of the
option:
Call option intrinsic value = MAX[0, S
–
K
]
In words: The call option intrinsic value is the
maximum
of zero
or
the stock price minus the strike price.
Put option intrinsic value = MAX[0, K
–
S
]
In words: The put option intrinsic value is the
maximum
of zero
or
the strike price minus the stock price.
14
Option intrinsic Values
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Intrinsic Values and Arbitrage, Calls
Call options with American

style exercise
must sell for at least their intrinsic value.
(Otherwise, there is
arbitrage
)
Suppose: S = $60; C = $5; K = $50.
Instant Arbitrage. How?
Buy the call for $5.
Immediately exercise the call, and buy the stock
for $50.In the next instant, sell the stock at the
market price of $60.
You made a profit with zero cash outlay.
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Intrinsic Values and Arbitrage, Puts
Put options with American

style exercise must sell
for at least their intrinsic value. (Otherwise, there
is
arbitrage
)
Suppose: S = $40; P = $5; K = $50.
Instant Arbitrage. How?
Buy
the put for $5.
Buy
the stock for $40.
Immediately
exercise
the put, and sell the stock for $50
You made a profit with zero cash outlay.
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Option “
Moneyness
”
“In

the

money” option: An option that would yield a positive
payoff if exercised
“Out

of

the

money” option: An option that would NOT yield
a positive payoff if exercised
Use the relationship between S (the stock price) and K (the
strike price):
Note for a given strike price, only the call or the put can be “in

the

money.”
In

the

Money
Out

of

the

Money
Call Option
S > K
S
≤ K
Put Option
S < K
S
≥ K
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“In the Money”
options have a
positive
intrinsic value.
For calls, the strike price is
less
than the stock price.
For puts, the strike price is
greater
than the stock price.
“Out of the Money”
options have a
zero
intrinsic value.
For calls, the strike price is
greater
than the stock price.
For puts, the strike price is
less
than the stock price.
“At the Money”
options is a term used for options when the
stock price and the strike price are about the same.
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Option “Moneyness”
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Option Writing
The act of selling an option is referred to as
option writing
.
The seller of an option contract is called
the
writer
.
The Writer
of a call option contract
is obligated
to sell the
underlying asset to the call option holder.
The call option
holder
has
the
right
to exercise the call option
(i.e., buy the underlying asset at the strike price).
The Writer
of a put option contract
is obligated
to buy the
underlying asset from the put option holder.
The put option
holder has
the
right
to exercise
the put option (i.e.,
sell the underlying asset at the strike price).
Because option writing
obligates
the option writer, the
writer receives the price of the option today from the buyer.
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Option Exercise
Option holders have the
right to exercise
their option.
If this right is only available at the option expiration date,
the option is said to have
European

style
exercise.
If this right is available at any time up to and including the
option expiration date, the option is said to have
American

Style
exercise.
Exercise style is not linked to where the option trades.
European

style
and
American

Style
options trade in
the U.S., as well as on other option exchanges
throughout the world.
Very Important: Option holders also have the
right to sell
their option at any time. That is, they do not have to exercise
the option if they no longer want it.
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Option Payoffs versus Option Profits
It is useful to think about option investment strategies in
terms of their initial cash flows and terminal cash flows.
The initial cash flow of an option is the price of the option
which is often called the option premium.
The terminal cash flow of an option is the value of an option at
expiration. (The terminal cash flow can be realized by the
option holder by exercising the option.)
The terminal cash flow is often called the option payoff.
Option Profits are calculated by subtracting the initial
cash flow (option premium) from the terminal cash flow
(option payoff).
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Call Option Payoffs
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Put Option Payoffs
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Call Option Profits
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Put Option Profits
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Option Strategies
Protective put

Strategy of buying a put option on a
stock already owned. This protects against a decline in
value (i.e., it is "insurance")
Covered call

Strategy of selling a call option on stock
already owned. This exchanges “upside” potential for
current income.
Straddle

Buying or selling a call and a put with the
same
exercise price. Buying is a
long
straddle; selling is
a
short
straddle.
There are many option trading strategies available to option
traders. For ideas on option trading strategies, see:
www.commodityworld.com
www.writecall.com
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Arbitrage
Arbitrage
:
No possibility of a loss
A potential for a gain
No cash outlay
In finance, arbitrage is not allowed to persist.
“Absence of Arbitrage” = “No Free Lunch”
The “Absence of Arbitrage” rule is often used in finance to
figure out prices of derivative securities.
Think about what would happen if arbitrage were
allowed to persist. (Easy money for everybody)
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The Upper Bound for a Call Option Price
Call option price must be less than the stock price.
Otherwise,
arbitrage
will be possible.
Suppose you see a call option selling for $65, and the
underlying stock is selling for $60.
The arbitrage:
sell
the call, and
buy
the stock.
Worst case? The option is exercised and you pocket $5.
Best case? The stock sells for less than $65 at option expiration,
and you keep all of the $65.
There was zero cash outlay today, there was no possibility
of loss, and there was a potential for gain.
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The Upper Bound for a European Put Option Prices
European Put option price must be less than the strike price.
Otherwise,
arbitrage
will be possible.
Suppose there is a put option with a strike price of $50 and this put
is selling for $60.
The
Arbitrage
:
Sell
the put, and
invest
the $60 in the bank. (Note
you have zero cash outlay).
Worse case? Stock price goes to zero.
You must pay $50 for the stock (because you were the put writer).
But, you have $60 from the sale of the put (plus interest).
Best case? Stock price is at least $50 at expiration.
The put expires with zero value (and you are off the hook).
You keep the entire $60, plus interest.
The Upper Bound for European Put Option Prices
There will be an arbitrage if price of the put, plus the interest you could earn over the
life of the option, is greater than the stock price.
For example, suppose the risk

free rate is 3 percent per quarter.
We have a put option with an exercise price of $50 and 90 days to maturity.
What is the maximum put value that does not result in an arbitrage?
Notice that the answer, $48.54, is the present value of the strike price computed at
the risk

free rate.
Therefore:
The maximum price for a European put option is the present value
of the strike price computed at the risk

free rate.
30
Option prices must be at least zero.
An option holder can simply discard the option.
This means that no one would pay someone to take an option off their hands.
Therefore, the price of the option cannot be negative.
American Calls.
Can an American call sell for less than its intrinsic value? No.
Suppose
S =
$60, and a call option has a strike price of K
=
$50 and a price
of $5.
The $5 call price is less than the intrinsic value of S

K
=
$10.
The Arbitrage Strategy:
Buy the call option at its price of C
=
$5.
Immediately exercise the call option and buy the stock at K =
$50.
Then, sell the stock at the current market price of S = $60.
Obtain $5 profit.
Therefore, an American call option price is never less than its intrinsic value.
Minimum American call option price = MAX[S

K, 0]
31
The Lower Bound on Option Prices
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Can an American put sell for less than its intrinsic value? No.
Suppose
S =
$40, and a put option has a strike price of K
=
$50 and a price of
$5.
The $5 put price is less than the intrinsic value of K

S
=
$10.
The Arbitrage Strategy:
Buy the put option at its price of P
=
$5.
Buy the stock at its price of S = $40.
Immediately exercise the put option and sell the stock at K =
$50.
Obtain $5 profit.
Therefore, an American put option price is never less than its intrinsic value.
Minimum American put option price = MAX[K

S, 0]
32
The Lower Bound on American Puts
The Lower Bounds for European
Options
European Calls.
European options cannot be exercised before expiration.
Therefore, we cannot use the arbitrage strategies to set lower bounds for
American options.
We must use a different approach (which can easily be found).
The lower bound for a European call option is
greater than
its intrinsic value.
European call option price
≥
MAX[
S

K
/(1 +
r
)
T
, 0]
European Puts.
The lower bound for a European put option price is
less
than
its
intrinsic value.
In fact, in

the

money European puts will frequently sell for less than their
intrinsic value. How much less?
Using an arbitrage strategy that accounts for the fact that European put options
cannot be exercised before expiration:
European put option price
≥
MAX[
K
/(1 +
r
)
T
–
S
, 0]
33
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Put

Call Parity
Put

Call Parity is perhaps the most
fundamental relationship in option pricing.
Put

Call Parity is generally used for options
with European

style exercise.
Put

Call Parity states: the difference between
the call price and the put price equals the
difference between the stock price and the
discounted strike price.
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The Put

Call Parity Formula
In the formula:
C is the call option price today
S is the stock price today
r is the risk

free interest rate
P is the put option price today
K is the strike price of the put and the call
T is the time remaining until option expiration
Note: this formula can be rearranged:
e

rT
is a discount factor,
so Ke

rT
is simply the
discounted strike price.
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Why Put

Call Parity Works
If two securities have the same risk

less pay

off
in the future, they must sell for the same price
today.
Today, suppose an investor forms the following
portfolio:
Buys 100 shares of Microsoft stock
Writes one Microsoft call option contract
Buys one Microsoft put option contract.
At option expiration, this portfolio will be worth: $K
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Why Put

Call Parity Works
At option expiration, this portfolio will be worth:
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Put

Call Parity Notes
Notice that the portfolio is
always
worth $K at
expiration. That is, it is riskless.
Therefore, the value of this portfolio today is $K/(1+r)
T
That is, to prevent arbitrage: today’s cost of buying 100
shares and buying one put (net of the proceeds of writing
one call), should equal the price of a risk

less security
with a face value of $K, and a maturity of T.
Fun fact: If S = K (and if
rT
> 0), then C > P.
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Useful Websites
•
For information on options ticker symbols, see:
www.cboe.com
www.m

x.ca
•
To learn more about options, see:
www.e

analytics.com
www.tradingmarkets.com
www.investorlinks.com
•
Exchanges that trade index options include:
www.cboe.com
www.cbot.com
www.cme.com
www.m

x.ca
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