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prepared by:Carol EdwardsBA, MBA, CFA
Instructor, FinanceBritish Columbia Institute of Technology
Fundamentals
of Corporate
Finance
Second Canadian Edition
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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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Financial Alchemy with Options• Protective Put
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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Financial Alchemy with Options• Protective Put
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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What Determines Option Values?• Upper and Lower Limits of Option Value
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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What Determines Option Values?• Upper and Lower Limits of Option Value
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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What Determines Option Values?• Upper and Lower Limits of Option Value
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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What Determines Option Values?• Upper and Lower Limits of Option Value
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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What Determines Option Values?• Upper and Lower Limits of Option Value
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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What Determines Option Values?• Upper and Lower Limits of Option Value
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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What Determines Option Values?• Upper and Lower Limits of Option Value
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.