lesson 12 - options

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:


• 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


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


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


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.


moving into-the-money.

12-35


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).


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.


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

12-60

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.


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


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).

12-66

lesson 12 - options

Documents

options stock options

futures options

rate options

index options

exchangetraded options

options basics3

options payoffs4

foreign currency options