FINANCE FINANCE FIN2004 FIN2004 Lesson 12 Options RWJLT Chapter 24
Dec 31, 2015
FINANCEFINANCE
FIN2004FIN2004Lesson 12
Options
RWJLT Chapter 24
In the Headlines“The 10 Largest Trading Losses In History” http://newsfeed.time.com/2012/05/11/top-10-biggest-trading-
losses-in-history/slide/all/ March 11, 2012 (and Wikipedia). Excludes Hedge Funds
Trader Name Loss in
$Billions
Institution Market Year
Howie Hubler $9.0 Morgan
Stanley
Credit Default Swaps 2008
Jerome Kerviel $7.2 Societe
Generale
European Index
Futures
2008
Generale Futures
Brian Hunter $6.5 Amaranth
Advisors
Gas Futures 2006
Bruno Iksil $5.8 JP Morgan
Chase
Credit Default Swaps 2012
John Meriwether $4.6 Long Term
Capital
Management
Interest Rate &
Equity Derivatives
1998
12-1
Trader Name Loss in
$Billions
Institution Market Year
Yasuo Hamanaka $2.6 Sumitomo
Corporation
Copper Futures 1996
Isac Zagury, Rafael
Sotero
$2.5 Aracruz Foreign Exchange
Options
2008
In the Headlines (cont’d)
Sotero Options
Kweku Adoboli $2.0 UBS Equities ETF and
Delta 1
2011
Robert Citron $1.7 Orange County Interest Rate
Derivatives
1994
Heinz
Schimmelbusch
$1.3 Metallgesell-
schaft
Oil Futures 1993
12-2
Lecture Outline
1. Derivative Securities – Overview
2. Options Basics
3. Options Payoffs
4. Put-Call Parity
5. Determinants of Option Values
6. Not Examinable:
Options Valuation: The Binomial Model
Options Valuation: The Black-Scholes Model
Options and Corporate Finance12-3
Derivative Securities – Overview
� A derivative security is one for which the ultimate payoff (or gain)
to the investor depends directly on the value of another security
(the “underlying asset”) or commodity.
� Types of derivatives:
• Options: Call Options & Put Options
Forwards Futures• Forwards & Futures
• Extended Derivatives: Swaps / Convertible Securities / Other
Embedded Derivatives (bonds with Call feature)
� Derivatives are useful for risk-management (e.g. an airline can
use an energy derivative to hedge the risk of rising fuel prices), but
they can also be use for speculation (by taking advantage of their
large leverage effect).
12-4
Derivative Securities – Overview (cont’d)
� The underlying assets of derivatives include:
• Agricultural commodities (corn, soybeans, wheat, (live) cattle,
pork, lumber, dairy, even orange juice, etc).
• Energy products (crude oil, refined oil, natural gas, electricity,
etc.)
• Metals (steel, copper, silver, gold, platinum, etc.)
• Currencies (Euro, Chinese Yuan, Japan Yen, S$, etc.)
• Stock, bonds, and indices (S&P 500, Dow Jones, Nasdaq-100,
Global indices etc.)
• Options (Stock Options, Index Options, Futures Options,
Foreign Currency Options, Interest Rate Options, etc.)
12-5
Global Derivatives Markets:
Exchange-Traded vs. Over-The-Counter
� Exchange-Traded Derivatives are standardized contracts (e.g.
exchange-traded options are trade in multiples of 100 options)
traded on regulated exchanges that provide clearing and regulatory
safeguards to investors.
Visit http://www.bis.org/statistics/derstats.htm for derivative statistics.
• Main Options Exchanges in the U.S. – International Securities
Exchange and Chicago Board Options Exchange (makes
trading easy, creates liquid secondary market).
� OTC (Over-The-Counter) derivatives are customized contracts
provided directly by dealers to end-users or other dealers.
12-6
Options Basics
� A Call Option is a security that gives its owner (or the holder of the
option)
• the right (but not the obligation)
• to purchase
• a given asset (usually a stock)• a given asset (usually a stock)
• on a given date (or anytime before a given date)
• at a predetermined price (referred to as the Exercise Price)
� European Options - can be exercised only on the expiration date.
American Options - can be exercised at any time before expiration.
� A Put Option, in contrast to a Call Option, gives its owner the right
to sell an asset on (or before) a given date at a predetermined price.
12-7
Options Basics (cont’d)
� Options are “side bets” between investors – e.g. when
investors trade options on common stock among themselves,
these option trades do not involve the firms who issued the
shares (the underlying asset) on which the options are based.
� If an investor sells a Call Option (or “writes a Call”), he
allows the buyer of the Call Option to purchase the shares allows the buyer of the Call Option to purchase the shares
from him at the Exercise Price, if the Call Option buyer
chooses to do so on the expiration date.
� If an investor sells a Put Option (or “writes a Put”), he
allows the buyer of the Put Option to sell the shares to him at
the Exercise Price, if the Put Option buyer chooses to do so
on the expiration date.12-8
� Option Terminology:
• Call – Call Option
• Put – Put Option
• Buy (or Long) – e.g. “Long a Put” means “Buy a Put”
• Sell (or Short, or Write) – e.g. “Short a Call” means “Sell a Call”
• Alternative terminologies:
Options Basics (cont’d)
• Alternative terminologies:
– Exercise Price also called Strike Price
– Price/Value/Cost of the Option also called Premium of the
Option
– Maturity also referred to as Expiration of the Option
� There are four possible positions for option investors:
(i) Buy a Call Option, (ii) Sell a Call Option
(iii) Buy a Put Option, (iv) Sell a Put Option 12-9
Notation used for Options discussion:
S : Market price of underlying asset (at any time).
S0 : Market price of underlying asset today.
ST : Market price of underlying asset at maturity (option’s
Options Basics (cont’d)
T
expiration date).
X : Exercise Price or Strike Price of the option (also denoted as E).
r : Risk-free interest rate.
C0 : The price of a call option today.
CT : The price of a call option at the option’s expiry date.
12-10
� Since the owner of a Call Option has the right but not the obligation
to buy the share for X dollars (Exercise Price) at maturity, he will do
so only if the market price of the share at maturity exceeds X dollars.
� When ST > X at maturity, the owner of the Call Option would
exercise the option to buy the share at X and then sell it at ST in the
Payoffs (at Maturity) – Call Options
exercise the option to buy the share at X and then sell it at ST in the
market, hence profiting from the difference. In this case, the value
(“Payoff”) of the Call Option is (ST – X).
� However, if ST < X at maturity, the owner of the Call Option can buy
the share at the lower market price ST. Thus, he would not exercise
the Call Option, and will let the Call Option expire. The value
(“Payoff”) of the Call Option is then ZERO.
12-11
At Maturity – Call Option Payoff & Profit vs.
Market Price of Stock (for BUYER)
$
Payoff: CT = Max{ST – X, 0}
If ST > X, Payoff = (ST – X)
If ST ≤ X, Payoff = 0
STX
450
12-12
option’s Premium
(cost of option)
Profit = Payoff – Premium
At Maturity – Call Option Payoff & Profit vs.
Market Price of Stock (for WRITER)
$ If ST > X, Payoff = -(ST – X)
If ST ≤ X, Payoff = 0
STX 450
12-13
option’s Premium
Profit = Payoff + Premium
� Since the owner of a Put Option has the right but not the obligation to
sell the share for X dollars (Exercise Price) at maturity, he will do so
only if the market price of the share at maturity is below X dollars.
� When ST < X at maturity, the owner of the Put Option would buy the
share from the market at ST dollars, and then exercise the option to
Payoffs (at Maturity) – Put Options
share from the market at ST dollars, and then exercise the option to
sell the share at X, hence profiting from the difference. In this case,
the value (“Payoff”) of the Put Option is (X – ST).
� However, if ST > X at maturity, the owner of the Put Option can sell
the share at the higher market price ST. Thus, he would not exercise
the Put Option, and will let the Put Option expire. The value
(“Payoff”) of the Put Option is then ZERO.
12-14
At Maturity – Put Option Payoff & Profit vs.
Market Price of Stock (for BUYER)
$If ST < X, Payoff = (X – ST)
If ST > X, Payoff = 0
STX
450
12-15
option’s Premium
(cost of option)
Profit = Payoff – Premium
At Maturity – Put Option Payoff & Profit vs.
Market Price of Stock (for WRITER)
$If ST < X, Payoff = -(X – ST)
If ST > X, Payoff = 0
STX450
12-16
option’s Premium
Profit = Payoff + Premium
� In-the-Money (holder of option will gain if option is exercised now)
• A Call Option is in-the-money when the current market price of the stock is
higher than the exercise price (i.e. S > X).
• A Put Option is in-the-money when the market price of the stock is lower
than the exercise price (i.e. S < X).
� At-the-Money (holder of option will neither gain nor lose if option is exercised now)
Payoff Descriptions
� At-the-Money (holder of option will neither gain nor lose if option is exercised now)
• A Call Option or a Put Option is at-the-money if the market price of the
stock is equal to the exercise price of the options (i.e. S = X).
� Out-of-the-Money (holder of option will lose if option is exercised now)
• A Call Option is out-of-the-money when the market price of the stock is
lower than the exercise price (i.e. S < X).
• A Put Option is out-of-the-money when the market price of the stock is
higher than the exercise price (i.e. S > X).12-17
Investment Strategy Investment
Example – 3 Different Investment Strategies:
Stock, Call Options, Call Options + T-Bills
You have $10,000 to invest. You can invest in three different ways.
The stock is selling for $100/share. Each Call Option (with a Strike
Price of $100) is selling for $10. The risk-free rate is 3%.
All Stocks Buy stock @ $100 100 shares $10,000
All Options Buy calls @ $10 1,000 options $10,000
Calls+T-Bills Buy calls @ $10 100 options $1,000
& T-bills with 3% T-bills $9,000
yield
12-18
Investment Value Under 3 Scenarios of Stock Price
$95 $105 $115
All Stocks $9,500 $10,500 $11,500
Example – 3 Different Investment Strategies Stock:
Investment Values
All Stocks $9,500 $10,500 $11,500
All Options $0 $5,000 $15,000
Calls+T-Bills $9,270 $9,770 $10,770
12-19
Calls $0
T-Bills $9,270
Calls $500
T-Bills $9,270
Calls $1,500
T-Bills $9,270
Example – 3 Different Investment Strategies:
Investment Returns
Investment Return Under 3 Scenarios of IBM Stock Price
$95 $105 $115
All Stocks -5% 5% 15%
12-20
All Options -100% -50% 50%
Calls+T-Bills -7.3% -2.3% 7.7%
Observation: For the same fluctuation in price of the underlying
stock, the “All Options” strategy provides the highest returns
volatility – while it has the potential to achieve substantial gains
(50%), it may also suffer a complete loss!
“All Options” strategy is
essentially a leveraged
investment, as there is a
disproportionately higher
increase in return for a
smaller increase in price
Example – 3 Different Investment Strategies:
Investment Returns (cont’d)
smaller increase in price
in the underlying asset.
12-21
Creating a payoff position using a mix of
the underlying asset and its options
Any set of payoffs (that depends on the value of some
underlying asset), can be constructed with a mix of simple
options on that asset � By adding and subtracting various
combinations of Calls and Puts (at various Exercise Prices), combinations of Calls and Puts (at various Exercise Prices),
we can create a variety of financial instruments with an
endless range of payoff positions.
12-22
Creating a Protective Put Position: Stock + Put
Buy a Stock
&
Buy a Put Option on the Stock
Protective Put allows the
Stock
Put
12-23
Protective Put allows the
investor to limit the value
of his stock to a
minimum of $X, while
allow him to enjoy
unlimited upside.
Put
Stock+Put
Profits: Protective Put vs. Stock Investment
Protective Put
limits investor’s
Price paid to buy
the Put Option
Assuming S0 = X
12-24
limits investor’s
loss to $P.
Put-Call Parity
� Consider the following two investments:
• Investment 1 – Protective Put
Buy one stock and one Put Option on of the stock with
Exercise Price of $50.
• Investment 2 – Call Option + Risk-free securities
Buy a Call Option on the same stock with Exercise
Price of $50 and T-bills with face value (maturity
value) of $50.
� If we analyze the payoffs of the two investments…
12-25
Investment 1 – Payoff
(i) + (ii): Stock + Put Option
$
S < $50 Payoff = $50
S ≥ $50 Payoff = S
(i) Stock
(ii) Put Option with
Exercise Price of $50
$50
$0
$50
ST
12-26
Investment 2 - Payoff
(i) + (ii): Call Option + T-bills
$50
$
S < $50 Payoff = $50
S ≥ $50 Payoff = S
12-27
(ii) T-bills with maturity value
of $50
(i) Call Option with
Exercise Price of $50
$50
$0
$50
ST
Note: T-bills and Call Option to have the same maturity date.
Put-Call Parity
� Payoffs of Investment 1 and Investment 2 are identical.
� Value principle: When two investments have identical payoffs,
they must be worth the same value (same PV).
� Hence: PV(Stock + Put) = PV(Call + Risk-free Security)
S0 + P = C + X / (1 + rf)T
12-28
� The above equation is known as the Put-Call Parity. It relates the
price of a Call to the price of the corresponding Put on the same
stock.
� If the Put-Call Parity is violated, arbitrage opportunity would arise
(i.e. one can buy the cheaper investment and sell the more
expensive one simultaneously and make a riskless profit).
PV of T-bills with maturity value of $X in time T
(alternatively, zero-coupon bond with par value of $X)
Put-Call Parity
Price of
Underlying
Stock
Price of
Put=
Price of
Call
PV of
Exercise Price+ +
S + P = C + PV(X)S + P = C + PV(X)
���� P = C + PV(X) – S
e.g. zero-coupon
bond with par
value = X
12-29
When the price of a Call Option on a stock is found, the price of the
Put Option on the same stock (having the same Exercise Price and
maturity date) can be computed using the above relationship.
Call Option Value Bounds
� Upper bound
Call price must be less than or equal to the stock price.
� Lower bound
Call price must be greater than or equal to the stock
price minus the exercise price or zero, whichever is price minus the exercise price or zero, whichever is
greater.
� That is, the value of a call option C0 must fall within
max (S0 – X, 0) < C0 < S0
If either of these bounds are violated, there is an
arbitrage opportunity.12-30
Option Values
� Intrinsic Value – refers to the payoff that could be made if the
option was immediately exercised.
• Call Options: Intrinsic value = Stock Price – Exercise Price
• Put Options: Intrinsic value = Exercise Price – Stock Price
But in each of the above cases the Intrinsic Value cannot be But in each of the above cases the Intrinsic Value cannot be
negative (i.e. it is either ZERO or positive value).
� Time Value of an Option (not the same as time value of money) –
the Option Price (value of the option) is usually above its Intrinsic
Value, the difference reflects the option’s time value.
• Most of the Time Value reflects the “volatility value” – the
volatility of the stock increases the chance of the options
(whether Put or Call) getting into-the-money.12-31
Call Option Value before Expiration is
highlighted in pink (Intrinsic Value in black)
12-32
Determinants of Options Value
� Stock Price
Call: The value of a Call Option will increase if the stock price
increases, because its payoff will be higher.
Put: The value of a Put Option will decline if the stock price
increases, because its payoff will be lower.increases, because its payoff will be lower.
� Exercise Price
Call: The value of a Call Option will decline if it has a higher
Exercise Price, because its payoff will be lower.
Put: The value of a Put Option will increase if it has a higher
Exercise Price, because its payoff will be higher.
12-33
� Time to Expiration
Call and Put: Both the Call Option value and the Put Option value
will increase if they have longer maturity, since the underlying
stock will have more “time opportunity” to move in favour of the
option holder.
� Risk-Free Rate
Determinants of Options Value (cont’d)
Call: The value of a Call Option will increase if the risk-free rate
increases, since the present value of the Exercise Price will be
lower (Note: The Exercise Price is paid only in the future, at the
time when the Call Option is exercised).
Put: The value of Put Option will decline if the risk-free rate
increases, since the present value of the Exercise Price will be
lower (Note: The exercise proceeds is received only in the future,
at the time when the Put Option is exercised).12-34
� Volatility in Stock Price
Call and Put: Both Call Option value and the Put Option value will
increase if there is higher volatility in the underlying stock, since
higher volatility would increase the probability of the options
moving into-the-money.
Determinants of Options Value (cont’d)
moving into-the-money.
12-35
Determinants of Options Value (cont’d)
Call Put
1. Stock Price + –
2. Exercise Price – +
3. Time to Expiration + +
4. Risk-Free Rate + –
5. Volatility in Stock Price + +
12-36
Options Quotes: Example
• Example of a call option quote: Below are quotes for options
on biotech firm Amgen’s stock, as of November 2003, when
Amgen’s closing stock price was $60:
• Thus the call option which expired in April 2004 and allowed
its owner to purchase a share of Amgen stock for $65, was sold
for $1.95. 12-37
Options Valuation:
The Binomial Model
Non-Examinable
12-38
Options Valuation
� We cannot use the traditional discounted cash flow
method (DCF) to value options. This is because DCF
requires us to:
(i) estimate expected future cash flows, and
(ii) discount those cash flows at the opportunity cost of
capital.
� An option’s expected cash flows and relevant risk impact
change every time the underlying stock’s price changes.
Moreover, the underlying stock price changes constantly.
12-39
� We can value an option by setting up an option equivalent – by
combining common stock investment and borrowing.
� How do we do this? First of all, note that the value of an option
prior to expiration inherits the properties of its payoff upon
expiration.
� Thus to price the option we:
Valuing an Option via an Option Equivalent
� Thus to price the option we:
1. First, calculate the option’s payoff upon expiration.
2. Second, we find a portfolio (via investment in common stock
and borrowing) that replicates the option payoff and that can be
priced.
3. Third, in arbitrage-free equilibrium, the value of this portfolio
will also be the value of the option.12-40
$65
Example: Valuing an Option via an Option
Equivalent
• Let’s illustrate option pricing using a simple binomial
example: A firm’s stock is presently selling for $50. At the
exercise date, one year from now, the price of the stock may
either increase to $65 or may drop to $45. The one-year risk-
free rate is 12.5%.
• Consider a call option with exercise price of $57. The call option
payoff one year later is either CH or CL:
CH = max{65 – 57, 0} = $8
CL = max{45 – 57, 0} = $0
$50
$45
12-41
One year later
• Is there a portfolio invested in the stock and the risk-free asset that replicates
the same payoff pattern?
• Δ = number of shares in the original stock that we need to purchase (to
replicate the portfolio). Also called the hedge ratio or option delta.
• B = the amount that is borrowed at the risk-free rate (to replicate the portfolio).
Example: Valuing an Option via an Option
Equivalent (cont’d)
• B = the amount that is borrowed at the risk-free rate (to replicate the portfolio).
• Equate the combinations of Δ and B to the call option payoff (recall that the
risk-free rate is 12.5% and the exercise date is one year from now):
Δ($65) + B(1 + 12.5%) = $8
Δ($45) + B(1 + 12.5%) = $0
• Solving for Δ and B give:
Δ = 0.4
B = -$1612-42
• Note that we could equivalently find the hedge ratio as follows:
Δ = Delta = spread of possible option prices = $8 – $0 = 0.4
spread of possible stock prices $65 – $45
• Thus, to replicate the call option’s payoff, we need to:
Buy 0.4 shares by paying 0.4($50) = $20.
Example: Valuing an Option via an Option
Equivalent (cont’d)
Buy 0.4 shares by paying 0.4($50) = $20.
Borrow $16 to partially finance the purchase.
• The net cost of the portfolio that replicates the option’s payoff is $4.
• In an (arbitrage-free) equilibrium, this $4 must be the value of the call
option.
• Implication: A call option is like a leveraged portfolio in which the
purchase of a stock is partially financed with a risk-free loan.12-43
Delta and the Hedge Ratio
• The above practice of the construction of a riskless hedge is
called delta hedging.
• The delta of a call option is between 0 and 1.
Recall from the example:
$0$8call of valuein Swing=
−==
A call option that is deep in-the-money will have a delta of 1. The
value of a call that is assumed to end in-the-money will move dollar
for dollar in the same direction as the price of the underlying asset.
• The delta of a put option is between -1 and 0.
12-44
0.4$45$65
$0$8
stock underlying of valueof Swing
call of valuein SwingΔ =
−
−==
Delt and Hedge Ratio (cont’d)
• Amount of borrowing
= (PV of the lower possible stock price at maturity)(Delta)
From previous example: ($45/1.125)(0.4) = $16
• Value of call option
= (Stock Price)(Delta) – Amount borrowed
From previous example: ($50)(0.4) – $16 = $4
12-45
Options Valuation:
The Black-Scholes Model
Non-Examinable
12-46
� The B&S model is based on the replication method previously discussed.
Value of Call Option = Function of (S, X, σσσσ, r, T)
� It is founded on the following main assumptions:
• Can buy or sell the stock at all times (no restriction on short sales).
• No transaction costs.
The Black –Scholes Model
• No transaction costs.
• Unlimited borrowing and lending at the risk-free rate.
• Prices evolve smoothly.
• Constant risk-free rate and volatility.
• Stock price is log-normally distributed (follows a log-normal random
walk).
• Stocks do not pay dividends.
12-47
C = S0N(d1) – Xe-rTN(d2)
Tdd σ−= 12
The Black–Scholes Formula
PV(Exercise Price)
T
TX
S0
dσσσσ
σσσσ2
1
21)(ln ++++
====
( r++++ )
12-48
Where:
– ln ( ) is the natural logarithm function.
– N (d) denotes the standard normal distribution function. probability that a random draw from a normal dist. will be less than d.
– T is the number of periods to exercise date.
– σ is the standard deviation per period of the stock’s logarithmic return (continuously compounded).
– r the risk-free interest rate (continuously compounded).
Tσσσσ
Simplified Analogy to the Simple Binomial Model
)N(dXe))N(dS(C 2
rT
10
−−=
= × DeltaValue of a
call Stock
price–
Amount
borrowed
12-49
• A number of ready made tools are available to enable you to
compute option prices.
• One option price tool available on the web is at:
http://www.option-price.com/index.php
Inputs: Current Stock Price S (in $); Option Exercise Price X
Black-Scholes Formula – Online
Inputs: Current Stock Price S (in $); Option Exercise Price X
(in $); r is the annual risk-free interest rate to maturity
of the option (in %); Annual Standard Deviation σ (in
%); Time to Option Expiration T (note here the input is
in days). [Includes input for dividend yield (in %) if
dividends issued].
Output: Call Price C.
12-50
Standard Normal Curve
12-51
Call Option Example: Computing d1 and d2
S0 = $100 X = $95
r = 10% T = 0.25 year (one quarter)
σ = 0.50
d1 = ln(S0/X) + T(r + (σ2/2)1 0
σT1/2
d1 = ln(100/95) + 0.25(0.10 + 0.52/2)
0.5(0.251/2)
= 0.43
d2 = d1 – σT1/2 = 0.43 – 0.5(0.251/2) = 0.18
12-52
Probabilities from Normal Distribution
From Cumulative Normal Distribution Tables
d N(d)
0.42 0.6628
0.43 0.6664
0.44 0.6700
N (0.43) = 0.6664
Note: Interpolation may be used
to obtain values that fall N (0.43) = 0.6664
d N(d)
0.16 0.5636
0.18 0.5714
0.20 0.5793
N (0.18) = 0.571412-53
to obtain values that fall
between two figures
given in the table.
Call Option Value
C = S0N(d1) – Xe-rT N(d2)
= (100)(0.6664) – 95e-(0.10)(0 .25)(0.5714)
= $13.70
Implied Volatility
Using Black-Scholes and the actual price of the option, one
can solve for implied volatility.
12-54
Value of Put Option using Black-Scholes
P = Xe-rT[1 – N(d2)] – S0[1 – N(d1)]
Using the previous data:
S0 = $100, r = 10%, X = $95, T = 0.25
P = 95e-(0.10)(0.25)(1 – 0.5714) – 100(1 – 0.6664)
= $6.35
12-55
Alternative way to compute value of Put Option:
Using Put-Call Parity
P = C + PV(X) – S0
= C + Xe-rT – S0
Using the example data:Using the example data:
C = $13.70, X = $95, S0 = $100, r = 10%, T = 0.25
P = 13.70 + 95e –(0.10)(0.25) – 100 = $6.35
12-56
Employee Stock Options (ESOs)
� Employee Stock Options (ESOs) allow employees to purchase
company stock at a fixed price.
� They are granted primarily for two basic reasons:
• Align employee interests with owner interests.
• Feasible form of compensation for cash-strapped companies.
� ESO Features differ from company to company, but some
common ones are:
• Typical expiration of 10 years.
• Cannot be sold or transferred unless the employee dies, then options
transfer to the estate.
• Vesting (waiting) period during which they cannot be exercised.
• Employee loses the options if he leaves the company.12-57
Options
and
Corporate Finance
Non-Examinable
12-58
Options and Corporate Finance
� Common Stock (Equity) is a Call Option
• The stockholders have a call option on the firm’s
assets with the strike price equal to the face value of
the firm’s debt.
• If the firm’s assets are worth more than the debt, the • If the firm’s assets are worth more than the debt, the
option is in-the-money.
– Stockholders will exercise the option by paying off
the debt.
• If the firm’s assets are worth less than the debt, the
option expires unexercised.
– The company will default on its debt.12-59
Common Stock (Equity) as a Call Option
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Similar to a call option, common stock has limited downside
(the worst is zero value) but can enjoy unlimited upside.
Options and Capital Budgeting
� The Investment Timing Decision
• The option to wait is valuable when the
economy or market is expected to be better in
the future.the future.
• The option to wait may actually turn a bad
project into a good project.
• Waiting a year or two may allow the firm to
capture higher cash flows.
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� Managerial Options – whether to modify a
project after implementation.
• Option to expand: make project bigger if
successful.
Options and Capital Budgeting (cont’d)
successful.
• Option to abandon: shut down project if things
don’t go as planned.
• Option to suspend or contract: downsize when
market is weaker than expected.
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Options and Corporate Securities
� Warrants
• Issued by the firm: gives the holder the right,
but not the obligation, to purchase the
common stock directly from the company at a
fixed price before an expiry date.fixed price before an expiry date.
• Used as “sweeteners” or “equity kickers”:
warrants are sometimes issued together with
privately placed bonds, public issues of
bonds, and new stock issues to make the
issue more attractive.12-63
� Convertible Bonds
• Bonds that may be converted into a fixed
number of shares on or before the maturity
date.
Options and Corporate Securities (cont’d)
date.
• The conversion option is essentially a call
option on the company’s stock with the strike
price equal to the bond price.
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� Callable Bonds
Similar to options, Callable Bonds grant the firm
the option to retire the bonds early at a specified
call price.
Options and Corporate Securities (cont’d)
call price.
� Put Bonds
Similar to options, Put Bonds grant the
bondholder the option to demand repayment from
the firm at specified intervals before maturity.
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� Insurance and loan guarantees
These can be viewed as combination of the
underlying asset plus a put option. If the asset
declines in value, the owner of the put option
Options and Corporate Securities (cont’d)
declines in value, the owner of the put option
(i.e. insured) exercises the option and “sells” the
underlying asset to the seller of the put option
(i.e. insurer).
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