Chapter
Twenty-Five
Options and
Corporate Securities
© 2003 The McGraw-Hill Companies, Inc. All rights reserved.
25.1
Option Terminology 25.1
•
•
•
•
•
•
•
•
Call
Put
Strike or Exercise price
Expiration date
Option premium
Option writer
American Option
European Option
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.2
Options: The Basics
• An option gives the owner of the option the right, but not the
obligation, to buy or sell a certain asset at a fixed price (the
strike price or exercise price) during a specified period of
time.
• Options on stock and other assets are examples of derivative
securities. The value of an option is derived from the price and
other features of the underlying assets.
• The act of purchasing or selling the underlying asset, as
specified in the option contract, is referred to as exercising the
option.
• The maturity date of the option is called the expiration date;
the owner of the option cannot exercise the option after the
expiration date.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.3
Options: The Basics (cont.)
• An American option can be exercised anytime up to the
expiration date.
• A European option can be exercised only on the expiration
date.
• Options on stocks and bonds are traded on several exchanges,
the largest of which is the Chicago Board Options Exchange
(CBOE).
• Option trading in Canada began in 1975 on the Montreal
Exchange.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.4
Stock Option Quotations
• Things to notice
– Prices are higher for options with the same strike price but
longer expirations (why?)
– Call options with strikes less than the current price are
worth more than the corresponding puts
– Call options with strikes greater than the current price are
worth less than the corresponding puts
– C = Max(0, S - E), P = Max (0, E – S)
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.5
Variable Explanation
• S1 = Stock price at expiration (in one period)
• S0 = Stock price today
• C1 = Value of the call option on the expiration date (in one
period)
• C0 = Value of the call option today
• P1 = Value of the put option on the expiration date (in one
period)
• P0 = Value of the put option today
• E = Exercise price on the option
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
Option Payoffs – Calls 25.2
• The value of the call at
expiration is the
intrinsic value
– C1 = Max(0, S1 - E)
– If S1<E, then the payoff
is 0
– If S1>E, then the payoff
is S1 – E
• Assume that the
exercise price is $35
Call Option Payoff
Diagram
20
Call Value
25.6
15
10
5
0
0 10 20 30 40 50 60
Stock Price
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.7
Example 1
• Suppose that on October 1, an investor purchases a
call option to buy 100 shares of The Bank of
Montreal (BOM) common stock: the expiration date
is the third Friday in December; the exercise price is
$30; the price of the option is quoted as $1½; the
current market price of BOM stock is $27½.
• How much does the investor pay for the option?
• What is the investor’s gain (or loss) if the price of
BOM stock declines to $25 between October 1 and
the third Friday in December?
• What is the investor’s gain (or loss) if the price of
BOM stock increases to $32.75?
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.8
Example 1 (cont.)
• The price of the option is $1½ per share, or a total cost of
$150 (i.e., the option contract costs $1½ x 100 = $150).
• If the price of BOM stock declines to $25, the investor would
not exercise the option (i.e., he would not choose to purchase
100 shares of stock at $30 per share at a time when the market
price of the stock is less than $30 per share).
• When the market price of the stock is less than the exercise
price of the call option, the option is said to be “out of the
money.”
• If on the expiration date, the market price of the stock is less
than the exercise price of the option, then the option is
worthless; the investor has lost $150 on the transaction, the
purchase price of the option, because the option expired out of
the money.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.9
Example 1 (cont.)
• If the price of the stock exceeds the exercise price, then the
option is “in the money.”
• When the price of the stock is $32.75 on the expiration date;
the owner of the option could exercise the option for a profit.
• The investor can exercise the option and purchase 100 shares
of stock for ($30x100) $3,000, and then immediately sell the
shares for ($32.75x100) $3,275.
• The investor’s profit is ($3,275 - $3,000) $275, less the $150
purchase price of the option, for a net profit of ($275 - $150)
$125.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
Option Payoffs - Puts
• The value of a put at
expiration is the
intrinsic value
Payoff Diagram for Put
Options
– P1 = Max (0, E – S1)
– If S1<E, then the payoff
is E-S1
– If S1>E, then the payoff
is 0
• Assume that the
exercise price is $35
40
Option Value
25.10
30
20
10
0
0 10 20 30 40 50 60
Stock Price
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.11
Example 2
• On October 1, an investor purchases a Times Mirror
December 30 put, currently quoted at $3. The market price of
Times Mirror stock is $27½.
• What is the investor’s gain (or loss) if the price of Times
Mirror stock declines to $25 between October 1 and the third
Friday in December?
• What is the investor’s gain (or loss) if the price of Times
Mirror stock increases $32?
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.12
Example 2 (cont.)
• A put is “in the money” if the market price is less than the
exercise price and is “out of the money” if the market price
exceeds the exercise price.
• If the market price of Times Mirror stock is $25 on the
expiration date, the investor will exercise the option
• That is to say, he will buy 100 shares in the market for
($25x100) $2,500, and then sell the 100 shares for the writer
of the call option for ($30x100) $3,000).
• The profit from this transaction is ($3,000 - $2,500) $500.
• Since the purchase price of the option is ($3x100) $300, the
investor’s net profit is ($500 - $300) $200.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.13
Example 2 (cont.)
• The writer of the option incurs a loss of $500 when the put is
exercised; he is obligated to purchase, for $3,000, stock with a
market value of only $2,500.
• This loss is partially offset by the $300 he received when he
sold the option, so that his net profit is ($300 - $500) -$200, or
a $200 loss.
• If the market price exceeds the exercise price, the put owner
will not exercise the option.
• If the market price is $32 on the expiration date, the owner of
the option would not choose to exercise an option to sell, at
$30 per share, stock which can be sold in the market for $32
per share.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.14
Example 2 (cont.)
• Consequently, the option expires out of the money; the buyer
of the option loses the $300 he paid to acquire the option.,
while the option writer has a net profit of $300.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.15
Call Option Bounds
• Upper bound
– Since a call option is simply the right to buy the
stock, the option cannot be worth more than the
stock.
– Call price must be less than or equal to the stock
price
– C0 ≤ S0
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.16
Call Option Bounds (cont.)
• Lower bound
– The lower bound on the value of a call option depends on
whether the option is in or out of the money.
– The value of the call option at expiration is equal to zero if
the option is out of the money.
– A call that is in the money prior to expiration is worth at
least the difference between the value of the stock and the
exercise price of the call.
– Call price must be greater than or equal to the stock price
minus the exercise price or zero, whichever is greater
• If either of these bounds are violated, there is an arbitrage
opportunity
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.17
Figure 25.3 – Value of a call option before
expiration
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.18
A Simple Model
• An option is “in-the-money” if the payoff is
greater than zero
• If a call option is sure to finish in-the-money,
the option value would be
C0 = S0 – PV(E) = S0 – [E / (1+Rf)]
If the option expires in t time periods
C0 = S0 – [E / (1+Rf)]^t
• If the call is worth something other than this,
then there is an arbitrage opportunity
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.19
Example 3
• Suppose a share of stock is currently selling for $100, and the
risk-free rate (Rf) is 10%.
• Also assume that, one year from now, the stock price will be
either $105 or $120.
• A call option with expiration in one year has an exercise price
of $100.
• Suppose that in addition to buying the option today, you also
lend an amount equal to the present value of the exercise
price.
• How much is the call worth today?
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.20
Example 3 (cont.)
• One year from now, the stock will be worth either $105 or
$120. If you buy the option today, you will have either ($105 $100) $5 or ($120 - $100) $20 one year from now.
• Since you also lend an amount equal to the present value of
the exercise price: ($100 / 1.10) = $90.91.
• At the end of the year, you have $100 from the repayment of
the loan and either $5 or $20 from the exercise of the option.
• The total return is either ($100+$5) $105 or ($100+$20) $120.
• The strategy of buying and lending $90.91 has the same
possible future returns as does the strategy of simply buying
the stock.
• Since the two strategies have the same future returns, they
must have the same value today.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.21
Example 3 (cont.)
• Therefore, the value of the call option plus the present value of
the exercise price must be the same as the price of the stock:
C0 + $90.91 = $100
C0 = $9.09
Therefore, the value of the call option is $9.09
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.22
What Determines Option Values?
• Stock price
– As the stock price (S0) increases, the call price
increases and the put price decreases
• Exercise price
– As the exercise price (E) increases, the call price
decreases and the put price increases
• Time to expiration (t)
– Generally, as the time to expiration increases both
the call and the put prices increase since this
provides the holder of the option a longer period
of time during which to exercise it.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.23
What Determines Option Values? (cont.)
• Risk-free rate
– As the risk-free rate (Rf) increases, the call price
increases and the put price decreases
– The purchase of a call option will pay the exercise
price at some future date
– The higher the interest rate, the lower the present
value of this future amount
– Thus, the higher the interest rate, the more the call
option is worth
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.24
What about Variance? 25.3
• When an option may finish out-of-the-money (expire
without being exercised), there is another factor that
helps determine price
• The variance in underlying asset returns is a less
obvious, but important, determinant of option values
• The greater the variance, the more the call and the put
are worth
– If an option finishes out-of-the-money, the most you can
lose is your premium, no matter how far out it is
– The more an option is in-the-money, the greater the gain
– You gain from volatility on the upside, but don’t lose
anymore from volatility on the downside
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.25
Table 25.1 – Five factors that determine option
values
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.26
Employee Stock Options 25.4
• An Employee Stock Option (ESO) gives an
employee the right to purchase shares of a stock at a
fixed price for a fixed period.
• ESOs are quite common; one study found that at the
end of 1994, 90% of firms listed on the Toronto
Stock Exchange used stock options.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.27
Employee Stock Options Features
• ESOs are call options, but include several unique
features.
• ESOs tend to have longer lives than regular options,
typically 10 years.
• For a period of time known as the “vesting” period
the ESO cannot be exercised.
• Holders of ESOs may be forced to exercise following
resignation from the company.
• Firms grant ESOs to align shareholder and
management interests and to motivate employees.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.28
Employee Stock Options Features (cont.)
• Executives granted many ESOs can become very
wealthy if the firm does well.
• Firms grant ESOs when they do not have enough
cash to pay ordinary wages. Since ESOs do not
require any cash outlay upfront, they provide a
tempting alternative form of compensation.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.29
Employee Stock Options Repricing
• When issued, the strike price associated with the
ESO is equal to the stock price.
• The ESO is “underwater” in situations where the
stock price falls significantly.
• ESO repricing may occur in such situations, through
designating a new strike price. Repricing occurs to
maintain the incentive associated with the ESOs.
• Some critics argue that repricing represents an award
for failing, effectively undercutting the motivational
benefits associated with ESOs.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.30
Figure 25.4 – Executive stock options in Canada
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.31
Equity: A Call Option
• The financial decision-making process can often be
reformulated in terms of options.
• Corporate securities can be viewed as options on the
value of the firm.
• Suppose a firm has a single debt issue coming due in
one year. At that time, the shareholders will have a
choice.
• If the value of the firm (V1) exceeds the face value of
the debt (D1), then the shareholders will payoff the
debt and the stock will be worth S1 = (V1 - D1). By
paying off the debt, the shareholders own the assets
of the firm.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.32
Equity: A Call Option (cont.)
• If V1 is less than D1, then the shareholders will not
exercise their option to acquire the firm’s assets, and
the bondholders will own the firm. The stock (equity)
is worth zero in this case.
• Consequently, the equity in a firm with debt can be
viewed as a call option on the assets of the firm.
• The bondholder’s own the firm and they have written
a call option against the value of the firm, with an
exercise price equal to the value of the debt.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.33
Example
• A firm has a $500 debt issue due in one year.
The risk-free rate is 10%, and the current
market-value of the firm’s assets is $475.
What is the value today of the equity in the
firm?
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.34
Example (cont.)
• The firm’s shareholders own a call option on the
firm’s assets.
• The exercise price of the option is $500.
C0 = S0 – [E / (1+Rf)]^t
= $475 - $500 / (1.10) = $20.45
Therefore, the firm’s equity is worth $20.45
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.35
Warrants
• A warrant gives the holder the right to buy common
stock directly from the company at a fixed price
during a specified time period.
• To the holder, a warrant is essentially a call option,
although warrants usually have longer maturities.
• Typically, warrants are attached to the bond with
which they are issued; however, some warrants are
detachable, which means the warrants can be sold
separately from the bond.
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.36
Difference between Warrants and Call Options
• To a firm, a warrant is substantially different from a
call option.
- A call option sold on the firm’s stock is a private transaction
between investors, in which the firm is not directly involved.
- When a call option is exercised, existing stock merely changes
hands, but when a warrant is exercised, the firm must issue
new stock (i.e., exercise results in additional shares
outstanding so the earnings per share will be diluted)
- In case of warrants, the exercise price is paid to the company
and generates cash for the firm
- Warrants are generally very long term.
- Warrants can be detached from the original securities and sold
separately
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.37
Convertibles 25.7
• Convertible bonds (or preferred stock) may be
converted into a specified number of common shares
at the option of the security holder
• The conversion price is the effective price paid for
the stock
• The conversion ratio is the number of shares received
when the bond is converted
• Convertible bonds will be worth at least as much as
the straight bond value or the conversion value,
whichever is greater
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.38
Figure 25.5 – Minimum value of a convertible bond
versus the value of the stock for a given interest rate
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.39
Figure 25.6 – Value of a convertible bond versus
value of the stock for a given interest rate
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.40
Valuing Convertibles
• Suppose you have a 10% bond that pays semi-annual
coupons and will mature in 15 years. The face value
is $1,000 and the yield to maturity on similar bonds
is 9%. The bond is also convertible with a conversion
price of $100. The stock is currently selling for $110.
What is the minimum price of the bond?
–
–
–
–
Straight bond value = 1081.44
Conversion ratio = 1000/100 = 10
Conversion value = 10*110 = 1100
Minimum price = $1100
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.41
Reasons for Issuing Warrants and Convertibles
25.8
• They allow companies to issue cheap bonds by
attaching sweeteners to the new bond issue.
Coupon rates can then be set at below market
rate for straight bonds
• They give companies the chance to issue
common stock in the future at a premium over
current prices
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.42
Table 25.3 – The case for and against convertibles
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.43
Other Options 25.9
• Call provision on a bond
– Allows the company to repurchase the bond prior to maturity at a
specified price that is generally higher than the face value
– Increases the required yield on the bond – this is effectively how the
company pays for the option
• Put bond
– Gives the bondholder the right to require the company to repurchase
the bond prior to maturity at a fixed price
• Overallotment option
– Underwriters have the right to purchase additional shares from a firm
in an IPO (chapter 15)
• Insurance and Loan Guarantees
– These are essentially put options
• Managerial options
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.
25.44
Summary 25.10
• The most familiar options are puts and calls. The
holder has the right, but not the obligation, to sell
(buy) the underlying asset at a given price on or
before a given date
• There are five factors that impact an options value:
price of underlying, exercise price, expiration date,
risk-free interest rate, and volatility
• Warrants given the holder the right to buy shares
directly from the company at a fixed price for a
specified period of time
• Convertible bonds are a combination of a straight
bond and a call option, both of which will affect the
minimum value of the bond
Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved.