2. FINANCIAL OPTIONS AND APPLICATIONS IN CORPORATE FINANCE
CHAPTER 19
FINANCIAL OPTIONS AND APPLICATIONS IN CORPORATE FINANCE

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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
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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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6. 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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8. 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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9. 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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10. Option Terminology (cont’d)
Buyer Seller
Call Option Right to buy asset Obligation to sell asset
Put Option Right to sell asset Obligation to buy asset
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11. 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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12. 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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13. 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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14. 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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15. 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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16. 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
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17. Exercise Value of Option
Price of
stock (a)
Strike
price (b)
Exercise value
of option (a)–(b)
$25.00
$0.00
30.00
25.00
5.00
35.00
10.00
40.00
15.00
45.00
20.00
50.00
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Market Price of Option
Price of
stock (a)
Strike
price (b)
Exer.
val. (c)
Mkt. Price
of opt. (d)
$25.00
$0.00
$3.00
30.00
25.00
5.00
7.50
35.00
10.00
12.00
40.00
15.00
16.50
45.00
20.00
21.00
50.00
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
$0.00
$3.00
30.00
25.00
5.00
7.50
2.50
35.00
10.00
12.00
2.00
40.00
15.00
16.50
1.50
45.00
20.00
21.00
1.00
50.00
25.50
0.50
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20. Call Time Value Diagram
Option value 30 25 20 15 10 5
Market price
Exercise value
Stock price
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21. 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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22. 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
Length of option
Volatility of stock price
Level of interest rates
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23. 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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24. Binomial Option Pricing
Five steps involved in the process:
Define the possible ending prices of the stock.
Find the range of option values at expiration.
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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25. Binomial Option Pricing (cont’d)
Create a riskless hedged investment. The value of the portfolio stays regardless of whether stock goes up or down, so the portfolio is riskless.
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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26. 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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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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OPM Equations
V = P[N(d1)] – Xe -rRFt[N(d2)]
d1 =
 t 0.5
d2 = d1 –  t 0.5
ln(P/X) + [rRF + (2/2)]t
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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) + [( /2)](0.25)} ÷ {(0.4)(0.25)0.5}
d1 = ( )/0.2 = 0.180
d2 = d1 – (0.4)(0.25)0.5
d2 = – 0.20 =–0.020
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31. Second: Find N(D1) and N(D2)
Note: Values obtained from Excel using NORMSDIST function. For example: N(d1) = NORMSDIST(0.180) =
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32. 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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33. 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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34. 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
0.25
6.4%
0.16
$1.74
↑P by $5 25 20
$5.57
↑x by $5
$0.34
↑t to 6 months
0.5
$2.54
↑rRF to 9%
9.0%
$1.81
↑σ2 to 0.25
$2.13
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36. 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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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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38. Portfolio Payoffs at Expiry Date T for PT<X and PT≥X
Stock PT
Put
X – PT
Call
PT – X
Cash X
Total
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39. Put-Call Parity Relationship
Portfolio payoffs are equal, so portfolio values also must be equal.
Put + Stock = Call + PV of Exercise Price
Put + P = V + Xe
-rRFt
Put = V – P + Xe
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40. 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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41. Applications of Option Pricing in Corporate Finance
Option pricing is used in four major areas in corporate finance:
Real options analysis for project (real asset) evaluation and strategic decisions
Risk management (options serve as insurance)
Capital structure decisions (equity seen as a call and option-like securities)
Compensation plans (stock option)
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