A new strain of avian (bird) virus has popped up in China and has health officials at the World Health Organization are worried.  They fear it may jump across species and infect humans, causing a pandemic. The virus is 100% lethal in birds, killing them within 24 to 48 hours. A human vaccine against the avian virus has been successfully manufactured in the U.S. and there is enough to inoculate the entire U.S. population. You are a scientist at the Center for Disease Control and have been called before Congress where they are debating whether to make immunizations against this avian flu legally mandatory for all US citizens. Ignoring the constitutionality of such a law, in writing, present a scientifically persuasive case for why Congress should adopt your position. In addition to making a persuasive argument for why this is the case, please state what the alternative strategy should be. Position on Vaccination: One can protect the entire U.S. population against an epidemic without having to vaccinate everyone.  I chose position 2, and the idea no traveler can enter/leave China without the vaccination. Alternatively, all travelers having been to/from China must have the vaccination to enter the US. 1 Chapter 8 Financial Options and Applications in Corporate Finance 2 Topics in Chapter Financial Options Terminology Option Price Relationships Black-Scholes Option Pricing Model Put-Call Parity 3 Stock Price = + + + D1 D2 D∞ (1 + rs )1 (1 + rs)∞ (1 + rs)2 Dividends (Dt) Risk-free bond Portfolio of stock and risk-free bond that replicates cash flows of the option Value of option must be the same as the replicating portfolio Cost of equity (rs) The Big Picture: The Value of a Stock Option ... For value box in Ch 4 time value FM13. ‹#› 4 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. 5 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. 6 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. 7 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. 8 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. 9 Option Ter.

1. A new strain of avian (bird) virus has popped up in China and
has health officials at the World Health Organization are
worried. They fear it may jump across species and infect
humans, causing a pandemic. The virus is 100% lethal in birds,
killing them within 24 to 48 hours. A human vaccine against the
avian virus has been successfully manufactured in the U.S. and
there is enough to inoculate the entire U.S. population. You are
a scientist at the Center for Disease Control and have been
called before Congress where they are debating whether to make
immunizations against this avian flu legally mandatory for all
US citizens.
Ignoring the constitutionality of such a law, in writing, present
a scientifically persuasive case for why Congress should adopt
your position.
In addition to making a persuasive argument for why this is the
case, please state what the alternative strategy should be.
Position on Vaccination: One can protect the entire U.S.
population against an epidemic without having to vaccinate
everyone.
I chose position 2, and the idea no traveler can enter/leave
China without the vaccination.
Alternatively, all travelers having been to/from China must
have the vaccination to enter the US.
1
Chapter 8
Financial Options and
Applications in Corporate Finance

2. 2
Topics in Chapter
Financial Options Terminology
Option Price Relationships
Black-Scholes Option Pricing Model
Put-Call Parity
3
Stock Price = + + +
D1
D2
D∞

3. (1 + rs )1
(1 + rs)∞
(1 + rs)2
Dividends (Dt)
Risk-free bond
Portfolio of stock and
risk-free bond that
replicates cash flows
of the option
Value of option must
be the same as the
replicating portfolio
Cost of
equity (rs)
The Big Picture:
The Value of a Stock Option
...
For value box in Ch 4 time value FM13.
‹#›
4
What is a financial option?

4. 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.
5
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.
6
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.

5. 7
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.
8
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.

6. 9
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.
10
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.
11
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

7. to back it up.
12
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.
13
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.

8. 14
Consider the following data:Strike price = $25.Stock PriceCall
Option Price$25$3.00 30 7.50 3512.00 4016.50 4521.00
5025.50
15
Exercise Value of OptionPrice of
stock (a)Strike
price (b)Exercise value
of option (a)–(b)$25.00$25.00$0.0030.0025.00
5.0035.0025.0010.0040.0025.0015.0045.0025.0020.0050.0025.0
025.00
16
Market Price of OptionPrice of
stock (a)Strike
price (b)Exer.

9. val. (c)Mkt. Price
of opt. (d)$25.00$25.00$0.00 $3.0030.0025.00 5.00
7.5035.0025.0010.0012.0040.0025.0015.0016.5045.0025.0020.0
021.0050.0025.0025.0025.50
17
Time Value of OptionPrice 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$3.0030.0025.00 5.00 7.50
2.5035.0025.0010.0012.00 2.0040.0025.0015.0016.50
1.5045.0025.0020.0021.00 1.0050.0025.0025.0025.50 0.50
18
5 10 15 20 25 30 35 40
Stock Price

10. Option value
30
25
20
15
10
5
Market price
Exercise value
Call Time Value Diagram
19
Option Time Value Versus Exercise Value
The time value, which is the option price less its exercise value,

11. 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.
20
The Binomial Model
Stock assumptions:
Current price: P = $27
In next 6 months, stock can either
Go up by factor of 1.41
Go down by factor of 0.71
Call option assumptions
Expires in t = 6 months = 0.5 years
Exercise price: X = $25
Risk-free rate: rRF = 6%
21
Binomial Payoffs at Call’s Expiration
Current

12. stock price
P = $27
Ending "up" stock price = P(u) = $38.07
Option payoff: Cu = MAX[0,P(u)−X] = $13.07
Ending “down" stock price = P(d) = $19.17
Option payoff: Cd = MAX[0,P(d)−X] = $0.00
u = 1.41
d = 0.71
X = $25
22
Create portfolio by writing 1 option and buying Ns shares of
stock.
Portfolio payoffs:
Stock is up: Ns(P)(u) − Cu
Stock is down: Ns(P)(d) − Cd
23

13. The Hedge Portfolio with a Riskless Payoff
Set payoffs for up and down equal, solve for number of shares:
Ns= (Cu − Cd) / P(u − d)
In our example:
Ns= ($13.07 − $0) / $27(1.41 − 0.71)
Ns=0.6915
24
Riskless Portfolio’s Payoffs at Call’s Expiration: $13.26
Current
stock price
P = $27
Ending "up" stock price = P(u) = $38.07
Ending "up" stock value = NsP(u) = $26.33
Option payoff: Cu = MAX[0,P(u)−X] = $13.07
Portfolio's net payoff = P(u)Ns - Cu = $13.26
Ending “down" stock price = P(d) = $19.17
Ending “down" stock value = NsP(d) = $13.26
Option payoff: Cd = MAX[0,P(d)−X] = $0.00
Portfolio's net payoff = P(d)Ns - Cd = $13.26
u = 1.41
d = 0.71
X = $25
Ns = 0.6915

14. 25
Riskless payoffs earn the risk-free rate of return.
Discount at risk-free rate compounded daily.
VPortfolio = PV of riskless payoff
VPortfolio = Payoff / (1 + rRF/365)365*t
VPortfolio = $13.26 / (1 + 0.06/365)365*0.5
VPortfolio = $12.87
26
The Value of the Call Option
Because the portfolio is riskless:
VPortfolio = PV of riskless payoff
By definition, the value of the portfolio is:
VPortfolio = Ns(P) − VC
Equating these and rearranging, we get the value of the call:
VC = Ns(P) − PV of riskless payoff

15. 27
Value of Call
VC = Ns(P) − Payoff / (1 + rRF/365)365*t
VC = 0.6915($27)
− $13.26 / (1 + 0.06/365)365*0.5
= $18.67 − $12.87
= $5.80
(VC = $5.81 if no rounding in any intermediate steps.)
28
Multi-Period Binomial Pricing
If you divided time into smaller periods and allowed the stock
price to go up or down each period, you would have a more
reasonable outcome of possible stock prices when the option
expires.
This type of problem can be solved with a binomial lattice.
As time periods get smaller, the binomial option price
converges to the Black-Scholes price, which we discuss in later
slides.

16. 29
Replicating Portfolio
From the previous slide we have:
VC = Ns(P) − Payoff / (1 + rRF/365)365*t
The right side of the equation is the same as creating a portfolio
by buying Ns shares of stock and borrowing an amount equal to
the present value of the hedge portfolio’s riskless payoff (which
must be repaid).
The payoffs of the replicating portfolio are the same as the
option’s payoffs.
30
Replicating Portfolio Payoffs: Amount Borrowed and Repaid
Amount borrowed:
PV of payoff = $12.87
Repayment due to borrowing this amount:
Repayment = $12.87 (1 + rRF/365)365*t
Repayment = $13.26
Notice that this is the same as the payoff of the hedge portfolio.

17. 31
Replicating Portfolio Net Payoffs
Stock up:
Value of stock = 0.6915($38.07) =$26.33
Repayment of borrowing = $13.26
Net portfolio payoff = $13.07
Stock down:
Value of stock = 0.6915($19.17) =$13.26
Repayment of borrowing = $13.26
Net portfolio payoff = $0
Notice that the replicating portfolio’s payoffs exactly equal
those of the option.
32
Replicating Portfolios and Arbitrage
The payoff’s of the replicating portfolio exactly equal those of
the call option.
Cost of replicating portfolio
= Ns(P) − Amount borrowed
= 0.6915($27) − $12.87
= $18.67 − $12.87
= $5.80

18. If the call option’s price is not the same as the cost of the
replicating portfolio, then there will be an opportunity for
arbitrage.
33
Arbitrage Example
Suppose the option sells for $6.
You can write option, receiving $6.
Create replicating portfolio for $5.80, netting $6.00 −$5.80 =
$0.20.
Arbitrage:
You invested none of your own money.
You have no risk (the replicating portfolio’s payoffs exactly
equal the payoffs you will owe because you wrote the option.
You have cash ($0.20) in your pocket.
34
Arbitrage and Equilibrium Prices
If you could make a sure arbitrage profit, you would want to
repeat it (and so would other investors).

19. With so many trying to write (sell) options, the extra “supply”
would drive the option’s price down until it reached $5.80 and
there were no more arbitrage profits available.
The opposite would occur if the option sold for less than $5.80.
35
Assumptions of the
Black-Scholes Option Pricing Model
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.
Risk-free rate, rRF, is known and constant during the option’s
life.
(More...)
36
Assumptions (Continued)
Security buyers may borrow any fraction of the purchase price
at the short-term risk-free rate.

20. No penalty for short selling and sellers receive immediately full
cash proceeds at today’s price.
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.
37
VC = P[N(d1)] - Xe -rRFt[N(d2)]
d1 =
d2 = d1 -
What are the three equations that make up the OPM?
38
What is the value of the following call option according to the
OPM?

21. Assume:
P = $27
X = $25
rRF = 6%
t = 0.5 years
σ = 0.49
39
d1 = {ln($27/$25) + [(0.06 + 0.492/2)](0.5)}
÷ {(0.49)(0.7071)}
d1 = 0.4819
d2 = 0.4819 - (0.49)(0.7071)
d2 = 0.1355
First, find d1 and d2.
40
Second, find N(d1) and N(d2)

22. N(d1) = N(0.4819) = 0.6851
N(d2) = N(0.1355) = 0.5539
Note: Values obtained from Excel using NORMSDIST function.
For example:
N(d1) = NORMSDIST(0.4819)
16
‹#›
41
Third, find value of option.
VC = $27(0.6851) - $25e-(0.06)(0.5)(0.5539)
= $19.3536 - $25(0.97045)(0.6327)
= $5.06

23. 42
What impact do the following parameters have on a call
option’s value?
Current stock price: Call option value increases as the current
stock price increases.
Strike price: As the exercise price increases, a call option’s
value decreases.
43
Impact on Call Value (Continued)
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).
44

24. 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.
45
Put-Call Parity
Portfolio 1:
Put option,
Share of stock, P
Portfolio 2:
Call option, VC
PV of exercise price, X
46
Portfolio Payoffs at Expiration Date T for PT<X and
PT≥XPT<XPT≥XPort. 1Port. 2Port. 1Port. 2Stock PTPTPutX-
PT0Call0PT-XCashX XTotalXXPTPT

25. 47
Put-Call Parity Relationship
Portfolio payoffs are equal, so portfolio values also must be
equal.
Put + Stock = Call + PV of Exercise Price
Put + P = VC + Xe
-rRFt
Put = VC – P + Xe
-rRFt
Sheet11. Deeble Construction Co.'s stock is trading at $30 a
share. Call options on the company's stock are also available,
some with a strike price of $25 and some with a strike price of
$35. Both options expire in three months. Which of the
following best describes the value of these options?2. Suppose
you believe that Delva Corporation's stock price is going to
decline from its current level of $82.50 sometime during the
next 5 months. For $510.25 you could buy a 5-month put option
giving you the right to sell 100 shares at a price of $85 per
share. If you bought this option for $510.25 and Delva's stock

26. price actually dropped to $60, what would your pre-tax net
profit be?3. The exercise price on one of Flanagan Company's
options is $15, its exercise value is $23, and its time value is
$4. What are the option's market value and the price of the
stock?Market value$ Price of the stock$ 4. Which of the
following statements is CORRECT?5. Which of the following
statements is CORRECT?6. A call option on the stock of
Bedrock Boulders has a market price of $6. The stock sells for
$30 a share, and the option has an exercise price of $25 a
share.What is the exercise value of the call option?$ What is
the option's time value?$ 7. Call options on XYZ Corporation's
common stock trade in the market. Which of the following
statements is most correct, holding other things constant?8. The
current price of a stock is $50, the annual risk-free rate is 6%,
and a 1-year call option with a strike price of $55 sells for
$7.20. What is the value of a put option, assuming the same
strike price and expiration date as for the call option?9. An
option that gives the holder the right to sell a stock at a
specified price at some future time is
Week 7 Cengage Homework
1. Deeble Construction Co.'s stock is trading at $30 a share.
Call options on the company's stock are also available, some
with a strike price of $25 and some with a strike price of $35.
Both options expire in three months. Which of the following
best describes the value of these options?
a. The options with the $25 strike price have an exercise value
greater than $5.
b. The options with the $35 strike price have an exercise value
greater than $0.

27. c. The options with the $25 strike price will sell for less than
the options with the $35 strike price.
d. If Deeble's stock price rose by $5, the exercise value of the
options with the $25 strike price would also increase by $5.
e. The options with the $25 strike price will sell for $5.
2. Suppose you believe that Delva Corporation's stock price is
going to decline from its current level of $82.50 sometime
during the next 5 months. For $510.25 you could buy a 5-month
put option giving you the right to sell 100 shares at a price of
$85 per share. If you bought this option for $510.25 and Delva's
stock price actually dropped to $60, what would your pre-tax
net profit be?
a. $1,989.75
b. $2,193.70
d. $2,089.24
e. $2,303.38
3. Problem 8-2
Options
The exercise price on one of Flanagan Company's options is

28. $15, its exercise value is $23, and its time value is $4. What are
the option's market value and the price of the stock?
Market value
$
Price of the stock
$
4. Which of the following statements is CORRECT?
a. An option holder is not entitled to receive dividends unless
he or she exercises their option before the stock goes ex
dividend.
b. Put options give investors the right to buy a stock at a certain
strike price before a specified date.
c. LEAPS are very short-term options that were created
relatively recently and now trade in the market.
d. Call options give investors the right to sell a stock at a
certain strike price before a specified date.
e. Options typically sell for less than their exercise value.
5. Which of the following statements is CORRECT?
a. An option's value is determined by its exercise value, which
is the market price of the stock less its striking price. Thus, an
option can't sell for more than its exercise value.
b. Issuing options provides companies with a low cost method
of raising capital.

29. c. The market value of an option depends in part on the option's
time to maturity and also on the variability of the underlying
stock's price.
d. As the stock's price rises, the time value portion of an option
on a stock increases because the difference between the price of
the stock and the fixed strike price increases.
e. The potential loss on an option decreases as the option sells
at higher and higher prices because the profit margin gets
bigger.
6. Problem 8-1
Options
A call option on the stock of Bedrock Boulders has a market
price of $6. The stock sells for $30 a share, and the option has
an exercise price of $25 a share.What is the exercise value of
the call option?
$
What is the option's time value?
$
7. Call options on XYZ Corporation's common stock trade in the
market. Which of the following statements is most correct,
holding other things constant?
a. Assuming the same strike price, an XYZ call option that
expires in one month will sell at a higher price than one that
expires in three months.
b. The price of these call options is likely to rise if XYZ's stock
price rises.

30. c. If XYZ pays a dividend, then its option holders will not
receive a cash payment, but the strike price of the option will be
reduced by the amount of the dividend.
d. The higher the strike price on XYZ's options, the higher the
option's price will be.
e. If XYZ's stock price stabilizes (becomes less volatile), then
the price of its options will increase.
8. The current price of a stock is $50, the annual risk-free rate
is 6%, and a 1-year call option with a strike price of $55 sells
for $7.20. What is the value of a put option, assuming the same
strike price and expiration date as for the call option?
a. $7.71
b. $8.12
c. $8.55
d. $7.33
e. $9.00
9. An option that gives the holder the right to sell a stock at a
specified price at some future time is

31. a. a call option.
b. a covered option.
c. an out-of-the-money option.
d. a put option.
e. a naked option.
Ch08 P08 Build a Model Spring 2, 20137/22/12Chapter 8. Ch
08 P08 Build a ModelExcept for charts and answers that must
be written, only Excel formulas that use cell references or
functions will be accepted for credit. Numeric answers in cells
will not be accepted.You have been given the following
information on a call option on the stock of Puckett Industries:P
=$65X =$70t =0.5rRF =4%s =50.00%a. Using the Black-
Scholes Option Pricing Model, what is the value of the call
option?First, we will use formulas from the text to solve for d1
and d2.Hint: use the NORMSDIST function.(d1)=N(d1)
=(d2)=N(d2) =Using the formula for option value and the values
of N(d) from above, we can find the call option value.VC=b.
Suppose there is a put option on Puckett's stock with exactly the
same inputs as the call option. What is the value of the put?Put
option using Black-Scholes modified formula =Put option using
put-call parity =
Sheet27/22/12