FINANCIAL MANAGEMENT
THEORY & PRACTICE
ADAPTED FOR THE SECOND CANADIAN
EDITION BY:
JIMMY WANG
LAURENTIAN
UNIVERSITY
CHAPTER 19
FINANCIAL OPTIONS AND
APPLICATIONS IN CORPORATE
FINANCE
CHAPTER 19 OUTLINE
• Financial Options
• Introduction to Option Pricing Models: The
Binomial Approach
• The Valuation of Put Options
• Applications of Option Pricing in Corporate
Finance
Copyright © 2014 by Nelson Education Ltd.
19-3
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19-4
Financial Options
• An option is a contract that gives its holder
the right, but not the obligation, to buy (or
sell) an asset at some predetermined price
within a specified period of time
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What is the Single Most Important
Characteristic of an Option?
• It does not obligate its owner to take any
action. It merely gives the owner the right to
buy or sell an asset.
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Option Terminology
• Call option: An option to buy a specified
number of shares of a security within some
future period
• Put option: An option to sell a specified
number of shares of a security within some
future period
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19-7
Option Terminology (cont’d)
• Strike (or exercise) price: The price stated in
the option contract at which the security can
be bought or sold
• Option price: The market price of the option
contract
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19-8
Option Terminology (cont’d)
• American option: An option can be exercised
any time before it expires.
• European option: An option can only be
exercised on its expiration date
• Writer: The seller of an option
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19-9
Option Terminology (cont’d)
Call Option
Put Option
Buyer
Right to buy asset
Right to sell asset
Seller
Obligation to sell asset
Obligation to buy asset
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19-10
Option Terminology (cont’d)
• Expiration date: The last day that the option
contract can be exercised
• Exercise value: The value of an option if it were
exercised today (for a call = current stock price –
strike price; for a put = strike price – current stock
price)
• Note: The exercise value is zero if the stock price
is less than the strike price for a call. Exercise
value = max [current price of stock – strike price,
0] for a call.
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19-11
Option Terminology (cont’d)
• In-the-money call: A call whose strike price is
less than the current price of the underlying
stock
• Out-of-the-money call: A call option whose
strike price exceeds the current stock price
• At-the-money call: A call option whose strike
price is equal to the current stock price
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19-12
Option Terminology (cont’d)
• In-the-money put: A put whose strike price
exceeds the current price of the underlying
stock
• Out-of-the-money put: A put option whose
strike price is less than the current stock price
• At-the-money put: A put option whose strike
price is equal to the current stock price
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19-13
Option Terminology (cont’d)
• Covered option: A call option written against a
stock held in an investor’s portfolio
• Naked (uncovered) option: An option sold
without the stock to back it up
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19-14
Option Terminology (cont’d)
• LEAPS: Long-Term Equity AnticiPation
Securities, which are similar to conventional
options except that they are long-term
options with maturities of up to 2 1/2 years
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19-15
Consider the Following Data:
Strike price = $25
Stock Price
$25
30
35
40
45
50
Call Option Price
$3.00
7.50
12.00
16.50
21.00
25.50
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19-16
Exercise Value of Option
Price of
stock (a)
$25.00
30.00
35.00
40.00
45.00
50.00
Strike
price (b)
$25.00
25.00
25.00
25.00
25.00
25.00
Exercise value
of option (a)–(b)
$0.00
5.00
10.00
15.00
20.00
25.00
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Market Price of Option
Price of
Strike
Exer.
stock (a) price (b) val. (c)
$25.00 $25.00
$0.00
30.00
25.00
5.00
35.00
25.00
10.00
40.00
25.00
15.00
45.00
25.00
20.00
50.00
25.00
25.00
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Mkt. Price
of opt. (d)
$3.00
7.50
12.00
16.50
21.00
25.50
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Time Value of Option
Price of
stock (a)
Strike
price (b)
Exer.
Val. (c)
Mkt. P of
opt. (d)
Time value
(d) – (c)
$25.00
$25.00
$0.00
$3.00
$3.00
30.00
25.00
5.00
7.50
2.50
35.00
25.00
10.00
12.00
2.00
40.00
25.00
15.00
16.50
1.50
45.00
25.00
20.00
21.00
1.00
50.00
25.00
25.00
25.50
0.50
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19-19
Call Time Value Diagram
Option
value
30
25
20
15
Market price
10
5
Exercise value
5
10
15
20
25
30
35
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40
Stock price
19-20
Option Time Value vs. Exercise Value
• The time value, which is the option price less
its exercise value, declines as the stock price
increases.
• This is due to the declining degree of leverage
provided by options as the underlying stock
price increases and the greater loss potential
of options at higher option prices.
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19-21
Determinants of the Price of an Option
As this variable increases
The price of CALL option
The price of PUT
option
Market price versus strike price
Increases
Decreases
Level of strike price
Decreases
Increases
Length of option
Increases
Increases
Volatility of stock price
Increases
Increases
Level of interest rates
Increases
Decreases
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19-22
Introduction to Option Pricing Models:
The Binomial Approach
• All option pricing models are based on the concept of a
riskless hedge.
• Portfolio replication is the technique often used to
evaluate the option price.
• Option contracts can be valued by valuing portfolios of
primitive securities when those portfolios have the
same payoffs as these options.
• The binomial approach assumes that stock prices can
move to only two values over any short time period.
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Binomial Option Pricing
Five steps involved in the process:
1.Define the possible ending prices of the stock.
2.Find the range of option values at expiration.
3.Buy exactly enough stock to equalize the
range of payoffs for the stock and the option.
• N = (Cu – Cd) / (Pu – Pd)
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Binomial Option Pricing (cont’d)
4. Create a riskless hedged investment. The
value of the portfolio stays regardless of
whether stock goes up or down, so the
portfolio is riskless.
5. Find the call option’s price.
– PV of portfolio = current value of stock in portfolio
– current option price
– Current option price = current value of stock in
portfolio – PV of portfolio
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19-25
The Black-Scholes
Option Pricing Model (OPM)
OPM assumptions:
• The stock underlying the call option provides
no dividends during the call option’s life.
• There are no transactions costs for the
sale/purchase of either the stock or the
option.
• RRF is known and constant during the option’s
life.
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19-26
Assumptions (cont’d)
• Security buyers may borrow any fraction
of the purchase price at the short-term
risk-free rate.
• No penalty for short selling, and sellers receive
immediately the full cash proceeds
at today’s price.
• The call option can be exercised only on its
expiration date.
• Security trading takes place in continuous time,
and stock prices move randomly in continuous
time.
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19-27
OPM Equations
V = P[N(d1)] – Xe -r t[N(d2)]
RF
d1 =
ln(P/X) + [rRF + (2/2)]t
 t 0.5
d2 = d1 –  t 0.5
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19-28
OPM Illustration
What is the value of the following call
option according to the OPM?
Assume:
P = $20
X = $20
rRF = 6.4%
t = 0.25 year or 3 months
σ2 = 0.16 (that is, σ = 0.4)
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First: Find D1 and D2
d1 = {ln($20/$20) + [(0.064 +
0.16/2)](0.25)} ÷ {(0.4)(0.25)0.5}
d1 = (0 + 0.036)/0.2 = 0.180
d2 = d1 – (0.4)(0.25)0.5
d2 = 0.180 – 0.20 =–0.020
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Second: Find N(D1) and N(D2)
• N(d1) = N(0.180) = 0.5000 + 0.0714 = 0.5714
• N(d2) = N(–0.020) = 0.5000 – 0.0080 = 0.4920
• Note: Values obtained from Excel using
NORMSDIST function. For example:
N(d1) = NORMSDIST(0.180) = 0.5714
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Third: Find Value of Option
V = $20 × N(d1) – $20 × e–(0.064)(0.25) ×
N(d2)
= $20(0.5714) – $20e–(0.064)(0.25)(0.4920)
= $11.43 – $20(0.9851)(0.4920)
= $11.43 – $9.69 = $1.74
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Impacts of OPM Parameters
• How do the following factors affect a call
option’s value?
• Current stock price: A call option value
increases as the current stock price increases.
• Strike price: As the exercise price increases, a
call option’s value decreases.
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Impact on Call Value (cont’d)
• Option period: As the expiration date is
lengthened, a call option’s value increases (more
chance of becoming in the money.)
• Risk-free rate: Call option’s value tends to
increase as rRF increases (reduces the PV of the
exercise price).
• Stock return variance: Option value increases
with variance of the underlying stock (more
chance of becoming in the money).
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Effects of OPM Factors
Case
P
X
T
rRF
σ2
Vcall
Base case
$20
$20
0.25
6.4%
0.16
$1.74
↑P by $5
25
20
0.25
6.4%
0.16
$5.57
↑x by $5
20
25
0.25
6.4%
0.16
$0.34
↑t to 6 months
20
20
0.5
6.4%
0.16
$2.54
↑rRF to 9%
20
20
0.25
9.0%
0.16
$1.81
↑σ2 to 0.25
20
20
0.25
6.4%
0.25
$2.13
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19-35
The Valuation of Put Options
• A put option gives its holder the right to sell a
share of stock at a specified stock on or before
a particular date.
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19-36
Put-Call Parity
• Portfolio 1:
– Put option
– Share of stock, P
• Portfolio 2:
– Call option, V
– PV of exercise price, X
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Portfolio Payoffs at Expiry Date T for
PT<X and PT≥X
PT≥X
PT<X
Port. 1 Port. 2
Stock
Put
Port. 1
PT
PT
X – PT
0
Port. 2
Call
0
PT – X
Cash
X
X
Total
X
X
PT
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PT
19-38
Put-Call Parity Relationship
• Portfolio payoffs are equal, so portfolio values
also must be equal.
• Put + Stock = Call + PV of Exercise Price
-rRFt
Put + P = V + Xe
-rRFt
Put = V – P + Xe
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19-39
Illustration: Put-Call Parity
• Given: Vcall = $1.74, P = $20, X = $20,
rRF = 6.4%, t = 0.25 year
• Apply the put-call parity relationship
– Vput = Vcall – P + Xe–rRFt
=$1.74 – $20 + $20e–(0.064)(0.25)
= $1.74 – $20 + $19.68 = $1.42
• Note: This put must have the same exercise price
and expiration date as the call.
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19-40
Applications of Option Pricing in
Corporate Finance
• Option pricing is used in four major areas in
corporate finance:
1. Real options analysis for project (real asset)
evaluation and strategic decisions
2. Risk management (options serve as insurance)
3. Capital structure decisions (equity seen as a call
and option-like securities)
4. Compensation plans (stock option)
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19-41