Chapter 8
Financial Options and
Applications in Corporate
Finance
1

Topics in Chapter





Financial Options Terminology
Option Price Relationships
Black-Scholes Option Pricing Model
Put-Call Parity

2

The Big Picture:
The Value of a Stock Option
Cost of equity (rs)

D1
Stock Price =
(1 + rs )1

Risk-free bond

Dividends
(Dt)

D2
+
(1 + rs)2

Portfolio of stock and risk-free bond that replicates cash flows of the option

... +

D∞
+
(1 + rs)∞

Value of option must be the same as the replicating portfolio

3

What is a financial option?


An option is a contract which 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.

4

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.

5

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. 6

Option Terminology




Strike (or exercise) price: The price stated in the option contract at which the security can be bought or sold.
Expiration date: The last date the option can be exercised.

7

Option Terminology
(Continued)


Exercise value: The value of a call option if it were exercised today =






Max[0, Current stock price - Strike price] Note: The exercise value is zero if the stock price is less than the strike price. Option price: The market price of the option contract.
8

Option Terminology
(Continued)


Time value: Option price minus the exercise value. It is the additional value because the option has remaining time until it expires.

9

Option Terminology
(Continued)


Writing a call option: For every new option, there is an investor who
“writes” the option.




A writer creates the contract, sells it to another investor, and must fullfill the option contract if it is exercised.
For example, the writer of a call must be prepared to sell a share of stock to the investor who owns the call.
10

Option Terminology
(Continued)




Covered option: A call option written against stock held in an investor’s portfolio.
Naked (uncovered) option: An option written without the stock to back it up.

11

Option Terminology
(Continued)




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.

12

Option Terminology
(Continued)


LEAPS: Long-term Equity
AnticiPation Securities that are similar to conventional options except that they are long-term options with maturities of up to 2
½ years.

13

Consider the following data: Strike price = $25.
Stock Price
Call Option Price
$25
$3.00
30
7.50
35
12.00
40
16.50
45
21.00
50
25.50
14

Exercise Value of Option
Price of stock (a)

Strike price (b)

Exercise value of option (a)–(b)

$25.00
30.00
35.00
40.00
45.00
50.00

$25.00
25.00
25.00
25.00
25.00
25.00

$0.00
5.00
10.00
15.00
20.00
25.00
15

Market Price of Option
Price of Strike
Exer. Mkt. Price stock price val. (c) of opt. (d)
(a)
(b)
$25.00 $25.00 $0.00
$3.00
30.00
25.00
5.00
7.50
35.00
25.00 10.00
12.00
40.00
25.00 15.00
16.50
45.00
25.00 20.00
21.00
50.00
25.00 25.00
25.50
16

Time Value of Option
Price of Strike
Exer.
Mkt. P of stock price Val. (c)
(a)
(b) opt. (d)
$25.00 $25.00 $0.00
$3.00
30.00
25.00
5.00
7.50
35.00
25.00 10.00 12.00
40.00
25.00 15.00 16.50
45.00
25.00 20.00 21.00
50.00
25.00 25.00 25.50

Time value (d) – (c)
$3.00
2.50
2.00
1.50
1.00
0.50
17

Call Time Value Diagram
Option value

30
25
20
Market price

15
Exercise value

10
5

5

10

15

20

25

30

35

40

18

Stock Price

Option Time Value Versus
Exercise Value




The time value, which is the option price less its exercise value, declines as the stock price