copyright © 2003 mcgraw hill ryerson limited 25-1 prepared by: carol edwards ba, mba, cfa...

copyright © 2003 McGraw Hill Ryerson Limited

25-125-1

prepared by:Carol EdwardsBA, MBA, CFA

Instructor, FinanceBritish Columbia Institute of Technology

Fundamentals

of Corporate

Finance

Second Canadian Edition


25-225-2

Chapter 25Options

Chapter Outline Calls and Puts What Determines Option Values Spotting the Option


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Calls and Puts•What is an Option?

An option gives the holder (purchaser) of that option the right, but not the obligation, to do something at a future date.

In finance, there are two types of options you will have to deal with:Call OptionsPut Options


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Calls and Puts•What is an Option?

Call OptionsA call option is the right to buy an asset at a specified exercise price on or before the exercise date.

Put OptionsA put option is the right to sell an asset at a specified exercise price on or before the exercise date.


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Calls and Puts• Call Options

You buy a call option on ABC shares, which gives you the right to buy an ABC share for $30 (the exercise price) on or before December 31st of the current year.

If you have the right to buy an ABC share, then someone must have the obligation to sell it to you if you want to buy it.The person who is obligated to sell the asset to

you is known as the seller or writer of the call option.


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Calls and Puts• Put Options

You buy a put option on ABC shares, which gives you the right to sell an ABC share for $30 (the exercise price) on or before December 31st of the current year.

If you have the right to sell an ABC share, then someone must have the obligation to buy it from you if you want to sell.The person who is obligated to buy the asset

from you is known as the seller or writer of the put option.


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Calls and Puts

Buyer Seller

Call Option Right to buy asset Obligation to sell asset

Put Option Right to sell asset Obligation to buy asset

The seller of the option must be compensated for taking on the obligation.

Thus, the buyer of the option must pay a price for the option.

The price of an option is called its premium.

• Calls and Puts To summarize:


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Calls and Puts

Stock Price $20 $25 $30 $35 $40 $45

Call Value $0 $0 $0 $5 $10 $15

Put Value $10 $5 $0 $0 $0 $0

• Calls and Puts The value of an option at expiration is a

function of the asset’s price and the exercise price.

Assuming the exercise price is $30 and ABC shares have the following values, then at expiry, the following would occur:


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Calls and Puts

Stock Price Value of Option at Expiration at Expiration

Call Option

Greater than Stock Price – Exercise Priceexercise price

Less thanexercise price Zero

Put OptionGreater than Zeroexercise price

Less thanexercise price Exercise Price – Stock

Price

Summary: Valuing Calls and Puts


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Calls and Puts• Value Diagrams

Sometimes it is easier to draw a diagram of an option to understand the pay-offs to the buyer and the seller of the option.

In each of the diagrams which follows, the option has an exercise price of $30 and allows the holder to buy or sell one ABC share.

Note: For simplicity, the premium is assumed to be zero in each of the diagrams.


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Option ValueCall option value to buyer given

a $30 exercise price.

Share Price

Cal

l o

pti

on

val

ue

20 30 40

?$10


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Option ValuePut option value to a buyer given a $30

exercise price.

?

Share Price

Pu

t o

pti

on

val

ue

20 30 40

$30

$10


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Option Value

Share Price

Cal

l o

pti

on

$ p

ayo

ff

30 40

Call option pay-off to seller (writer)given a $30 exercise price.

?-$10


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Option ValuePut option pay-off to seller (writer)

given a $30 exercise price.

Share Price

Pu

t o

pti

on

$ p

ayo

ff

20 30 -$30

?-$10


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Financial Alchemy with Options• Protective Put

Now we will look at how options can be used to modify the risk characteristics of a portfolio.

Suppose you are generally optimistic about ABC’s prospects, but that you don’t like high levels of risk.

You buy the stock and you also buy a put option with a $30 exercise price. If the stock price rises, your option will be

worthless. If the stock price falls, however, your losses are

limited to $30 since the put option gives you the right to sell the stock for $30.


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Because you hold the stock and the put, your losses are limited to $30.

The value of each component will be as follows:

Stock Price < $30 Stock Price $30

Value of Stock Stock price Stock price+ Value of Put $30 - stock price 0

Total Value $30 Stock Price


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This strategy is called a protective put because the put option protects you from losses.

In effect, you have purchased stock price insurance.

Note that such protection is not free:You will have to pay a premium to purchase the

put. If the premium for this option is $2.15, then your

insurance against the stock falling below $30 a share will have cost you $2.15.


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Financial Alchemy with Options

Share Price

Po

siti

on

Val

ue

Protective Put

Long the Stock

Protective Put – Long Stock and Long Put

Long Put


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Financial Alchemy with Options• Straddle

Suppose you think that ABC will be subject to considerable volatility over the next couple of months. How can you bet on the expected volatility of the

stock? A straddle is a strategy for profiting from high

volatility. A straddle involves purchasing a put and a call.

If the stock price falls, the put will be profitable. If the stock price rises, the call will be profitable.


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Financial Alchemy with Options• Straddle

There is a cost to your strategy: you will have to pay a premium for the call and for the put.Unless the stock price moves far enough that

the profit on either the put or call covers the initial cost of the two options, you will lose money.

The net position of the strategy is shown by the dashed V-shaped line on the next slide,

The profit, taking into account the premiums on the this strategy, is shown by the solid V-shaped line on the next slide.


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Share Price

Po

siti

on

Val

ue

Financial Alchemy with Options

Straddle

Straddle – Long Call and Long Put

Long Call

Long Put


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Financial Alchemy with Options•Other Strategies

There are many other option strategies which can be pursued.

Combining options with various assets, gives you considerable leeway to tailor the risk features of a portfolio.

For practice, try Check Point 25.3 on page 745 of your text.


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What Determines Option Values?• Upper and Lower Limits of Option Value

The upper limit on the value of a call option is the stock price itself.Thus, the option cannot be worth more than the

asset it entitles you to buy. The lower limit on the value of a call option is

the value of the call at expiry.After expiry, any option is valueless.At expiry the option has its lowest value. Thus, before expiry, the value of an option

cannot be less than its value at expiry. These limits can be seen on the next slide.


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Option ValueUpper and Lower Limits on Option Values

Share Price

Cal

l o

pti

on

val

ue

20 30 40

Value of the Stock

Value of Option at Expiry

Value of Option before expiry


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Figure 25.7 on page 746 of your text is a copy of the previous slide.

If you look at Figure 25.7, you should notice the following:Point A: When the stock is worthless, the option

is worthless.Point B: When the stock price becomes very

high, the option price approaches the stock price less the present value of the exercise price.

Point C: The option price before expiry exceeds its value at expiry.


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How high point C is on the graph will be determined by a number of factors:How High Interest Rates Are

Having a call option is the same as buying the stock on credit.

You pay the purchase price of the option, but you do not have to pay the exercise price for the stock until you exercise the option.

The higher interest rates are, the more valuable this option to delay will be.


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How high point C is on the graph will be determined by a number of factors:The Length of Time Until Expiry

The longer the life of the asset, the greater the chance that you will find an opportunity to exercise it.

Thus, options with a long life are more valuable than those with a short life.


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How high point C is on the graph will be determined by a number of factors:The Standard Deviation of the Price of the

Stock. Substantial movement in the price of the stock

is very valuable in an option. A stock whose price moves by 1% or 2% is

not worth much. A stock whose price halves or doubles is very

valuable.


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To see how this works, imagine that ABC has an equal chance of being worth $25 or $35 at expiry.

The expected value of the option will be:

Stock Price at Expiry $25 $35 Avg Value

$ 0 $ 5 $2.50 Now imagine that ABC has an equal chance of being

worth $20 or $40 at expiry. The expected value of the option will be:

Stock Price at Expiry $20 $40 Avg Value$ 0 $10 $5.00


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These two cases highlight a valuable asymmetry in options: If the stock price is below the exercise price at

expiry, the option is valueless. This is true regardless of whether the stock

price is one cent below the exercise price, or many dollars below it.

However, if the stock price is above the exercise price, the holder reaps all the benefits of stock price advances.


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Thus, in our example, if the stock price is $35, the option is worth $5.

But if the stock price jumps to $40, the value of the option doubles to $10.

Therefore, volatility helps an option owner.


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What Determines Option Values?• What Affects the Price of a Call Option?

If the following increase: The value of the call will:

STOCK PRICE

DECREASE

INTEREST RATE

TIME TO EXPIRY

VOLATILITY OF THESTOCK PRICE

INCREASE

EXERCISE PRICE

INCREASE

INCREASE

INCREASE


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What Determines Option Values?•Valuing Options

Calculating the value of an option is a difficult undertaking.

You can see two methods which are used by reading:The Finance in Action Box on page 750 of

your book.Appendix 25A, in which the Black-Scholes

Option Pricing Model is described.


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Spotting the Option• Options on Real Assets

Real options are options embedded in real assets.

You learned in Chapter 8, that capital investment projects are more valuable if they have the flexibility provided by options.

The most common real options are:The option to expand the project at a later date.The option to abandon the project.The option to change how the project will

operate and/or what it will produce.The option to delay implementation.


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Spotting the Option•Options on Financial Assets

When companies issue securities, they often include an option in the package.Warrants

The right to buy shares from a company at a stipulated price before a specified date.

Convertible SecurityThe right to exchange the security for

another security, usually common shares.Callable Bond

The right of the issuer to repurchase the bond before maturity.


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Summary of Chapter 25 There are two types of options:

Call options confer the right to buy an asset for a specific exercise price on or before a specified date.

Put options confer the right to sell an asset for a specific exercise price on or before a specified date.

The payoff to buying a call is the maximum of the stock price minus the exercise price or zero.

The payoff to buying a put is the maximum of the exercise price minus the stock price or zero.

The payoff to the seller of an option is the mirror image of the the payoff to the option buyer.


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Summary of Chapter 25If the following increase: The value of a call will:

STOCK PRICE

DECREASE

INTEREST RATE

TIME TO EXPIRY

VOLATILITY OF THESTOCK PRICE

INCREASE

EXERCISE PRICE

INCREASE

INCREASE

INCREASE


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Summary of Chapter 25 Options may be present in capital investment

projects. Such options add value to the project and

include the right to expand, abandon or delay implementation of the project.

Options may also be present in security issue. Such options include warrants, convertible

securities and the right of the issuer to call a security.

copyright © 2003 mcgraw hill ryerson limited 25-1 prepared by: carol edwards ba, mba, cfa...

Documents

option valuesspotting

specified exercise price

exercise date

assets price

abc shares

seller writer

putsthe value

future date