CHAPTER 22
OPTIONS AND CORPORATE FINANCE
SLIDES
22.1 Key Concepts and Skills
22.2 Chapter Outline
22.3 Options
22.4 Options
22.5 Call Options
22.6 Call Option Pricing at Expiry
22.7 Call Option Payoffs
22.8 Call Option Profits
22.9 Put Options
22.10 Put Option Pricing at Expiry
22.11 Put Option Payoffs
22.12 Put Option Profits
22.13 Option Value
22.14 Selling Options
22.15 Call Option Payoffs
22.16 Put Option Payoffs
22.17 Option Diagrams Revisited
22.18 Option Quotes
22.19 Option Quotes
22.20 Option Quotes
22.21 Option Quotes
22.22 Option Quotes
22.23 Option Quotes
22.24 Option Quotes
22.25 Combinations of Options
22.26 Protective Put Strategy (Payoffs)
22.27 Protective Put Strategy (Profits)
22.28 Covered Call Strategy
22.29 Long Straddle
22.30 Short Straddle
22.31 Put-Call Parity: P0 + S0 = C0 + E/(1+ r)T
22.32 Put-Call Parity
22.33 Put-Call Parity
22.34 Valuing Options
22.35 American Call
22.36 Option Value Determinants
22.37 An Option Pricing Formula
22.38 Binomial Option Pricing Model
SLIDES – CONTINUED
CHAPTER WEB SITES
Section Web Address
22.1 www.optionseducation.org
22.4 www.cboe.com
22.39 Binomial Option Pricing Model
22.40 Binomial Option Pricing Model
22.41 Binomial Option Pricing Model
22.42 Binomial Option Pricing Model
22.43 Binomial Option Pricing Model
22.44 Binomial Option Pricing Model
22.45 Delta
22.46 Delta
22.47 The Risk-Neutral Approach
22.48 The Risk-Neutral Approach
22.49 The Risk-Neutral Approach
22.50 Example of Risk-Neutral Valuation
22.51 Example of Risk-Neutral Valuation
22.52 Example of Risk-Neutral Valuation
22.53 Example of Risk-Neutral Valuation
22.54 Risk-Neutral Valuation and the Replicating Portfolio
22.55 The Black-Scholes Model
22.56 The Black-Scholes Model
22.57 The Black-Scholes Model
22.58 The Black-Scholes Model
22.59 Stocks and Bonds as Options
22.60 Stocks and Bonds as Options
22.61 Stocks and Bonds as Options
22.62 Mergers and Diversification
22.63 Example
22.64 Example
22.65 Example
22.66 M&A Conclusions
22.67 Options and Capital Budgeting
22.68 Example: Low NPV
22.69 Example: Low NPV
22.70 Example: Negative NPV
22.71 Example: Negative NPV
22.72 Example: Negative NPV
22.73 Options and Capital Budgeting
22.74 Investment in Real Projects and Options
22.75 Quick Quiz
www.nasdaq.com
www.kcbt.com
www.euronext.com
22.5 www.cboe.com
22.7 www.nasdaqtrader.com
www.ivolatility.com
22.8 www.numa.com
www.margrabe.com/optionpricing.html
CHAPTER ORGANIZATION
22.1 Options
22.2 Call Options
The Value of a Call Option at Expiration
22.3 Put Options
The Value of a Put Option at Expiration
22.4 Selling Options
22.5 Option Quotes
22.6 Combinations of Options
22.7 Valuing Options
Bounding the Value of a Call
The Factors Determining Call Option Values
A Quick Discussion of Factors Determining Put Option Values
22.8 An Option Pricing Formula
A Two-State Option Model
The Black-Scholes Model
22.9 Stocks and Bonds as Options
The Firm Expressed in Terms of Call Options
The Firm Expressed in Terms of Put Options
A Resolution of the Two Views
A Note about Loan Guarantees
22.10 Options and Corporate Decisions: Some Applications
Mergers and Diversification
Options and Capital Budgeting
22.11 Investment in Real Projects and Options
ANNOTATED CHAPTER OUTLINE
Slide 22.0 Chapter 22 Title Slide
Slide 22.1 Key Concepts and Skills
Slide 22.2 Chapter Outline
1. Options
Slide 22.3 Options
Option – a contract that gives the owner the right, without the obligation,
to buy or sell a specified asset on or before a specified date at a specified
price.
Slide 22.4 Options
Option Terminology:
1. Exercising the option – using the option to buy or sell the underlying
asset
2. Strike or exercise price – fixed price at which the underlying asset may
be bought (sold)
3. Expiration date (Expiry) – the last day that the option can be exercised
4. American option – the option can be exercised any time up to and
including the expiration date
5. European option – the option can only be exercised on the expiration
date
6. In-the-money: option has value
7. Out-of-the-money: option would have a negative value if exercised
8. At-the-money: zero payoff if exercised (i.e., stock price is exactly equal
to the exercise price)
Lecture Tip: There has been a great deal of innovation in the derivatives
field over the years. In the options area, a number of interesting twists on
the standard option contract provide interesting class discussion topics.
Consider the growing credit derivatives sector, which had a substantial
impact on the recent financial crisis. A couple of examples are
“price/spread” options, which are triggered by changes in the spread
between the value of emerging market debt and U.S. Treasuries and
“default puts,” for which payment occurs upon the default of a third party.
Lecture Tip: Students are often fascinated by the topics of hedging and
speculation. Options provide an excellent opportunity to introduce the
differences between these terms. Hedging occurs when you use options (or
some other security) to offset a position you already have. For example, if
you own 100 shares of GM stock and the price has risen nicely, you might
want to hedge against a price decline by buying a put option contract.
Speculators do not hold offsetting positions. Instead, they take a single
(naked) position hoping the price will move in the direction they want. If
you expect the price of GM to decline, you could buy put options and then
profit if you are correct. If you are incorrect, then your loss is limited to
the price that you paid for the options.
Both investors bought put options, but for very different reasons. The
first is protecting against a loss, like insurance. The second is hoping to
profit by “guessing” at the direction of the price movement.
Corporations are using options and other derivative securities to hedge
much more frequently than they have done in the past. If done properly,
this should reduce the variability in the firm’s earnings. FASB 133
provides the accounting guidelines for the use of derivatives, and the
guidelines are different depending on whether or not the company is
hedging or speculating.
2. Call Options
Call option – gives the owner the right, but not the obligation, to buy the
underlying asset at a fixed price before the option expires
Slide 22.5 Call Options
A. The Value of a Call Option at Expiration
Call: An option is in-the-money when the stock price is higher than the
strike price (profitable to exercise), at-the-money when the stock price and
the strike price are the same, and out-of-the-money when the stock price is
less than the strike price.
Value of a Call Option at Expiration
Notation:
S1 = stock price at expiration
S0 = stock price today
C1 = value of call at expiration
C0 = call premium today
E = exercise price
If S1 E, then C1 = 0
If S1 E, then C1 = S1 – E
Intrinsic value (IV) = value if exercised immediately
IV(call) = max(ST – E, 0)
The profit from buying a call is equal to the intrinsic value (payoff) less
the premium paid.
Slide 22.6 Call Option Pricing at Expiry
Slide 22.7 Call Option Payoffs
Slide 22.8 Call Option Profits
3. Put Options
Put option – gives the owner the right, but not the obligation, to sell the
underlying asset at a fixed price before the option expires
Slide 22.9 Put Options
A. The Value of a Put Option at Expiration
Put: An option is in-the-money when the stock price is less than the strike
price, at-the-money when they are the same, and out-of-the-money when
the stock price is greater than the strike price.
If S1 ≥ E, then P1 = 0
If S1 ≥ E, then P1 = E – S1
Intrinsic value (IV) = value if exercised immediately
IV(put) = max(E – ST , 0)
The profit from buying a put is equal to the intrinsic value (payoff) less the
premium paid.
Slide 22.10 Put Option Pricing at Expiry
Slide 22.11 Put Option Payoffs
Slide 22.12 Put Option Profits
Lecture Tip: Although the concepts are similar for puts and calls, students
generally have more difficulty working with puts. An example showing
what happens to the intrinsic value of both a put and a call when the stock
price changes may be helpful.
At expiration, the call value will be equal to max(0, S – E). If the strike
price is greater than the stock price, the option will not be exercised and
the value is zero. If the stock price is greater than the strike price, then the
option will be exercised and the owner will gain the difference between
the two.
At expiration, the put value will be equal to max(0, E – S). If the strike
price is less than the stock price, the option will not be exercised (you
could sell it for more in the market) and the option value is zero. If the
stock price is less than the strike price, then the owner will exercise the
option and the gain will be the difference between the two.
Example: Consider options with a strike price of $30.
Strike Price Stock Price Call Value Put Value
30 20 0 10
30 25 0 5
30 30 0 0
30 35 5 0
30 40 10 0
The price paid for an option (the premium) is greater than or equal to the
intrinsic value, with the difference being referred to as the speculative (or
time) premium.
Slide 22.13 Option Value
4. Selling Options
The person who sold the option is called the option writer and has an
obligation to fulfill the agreement if the option is exercised. In other
words, the writer must sell (buy) the underlying asset if the call (put) is
exercised.
Slide 22.14 Selling Options
Lecture Tip: You may wish to emphasize the asymmetrical nature of
options payoffs by contrasting the positions of options buyers and options
writers. For example, call buyers hope that the value of the underlying
asset rises before their option expires. Their potential gain is unlimited,
while their loss is limited to the price paid (the premium) for the option
contract.
Call writers, on the other hand, hope that the value of the underlying
asset falls (or, at least, doesn’t rise); their gain is limited to the premium
received, while their potential (opportunity) loss is unlimited. Writers of
covered calls possess the underlying asset at the time the call is written, so
the cost of delivering the underlying asset, should it become necessary, is
known. However, the opportunity cost of having to sell the asset at a
below market price is unknown and unlimited. Writers of naked calls do
not own the underlying asset and must purchase it at the prevailing
market price if the option is exercised. Their actual potential cost (the
amount of cash they have to come up with) is unknown and unlimited. For
this reason, many people view writing naked options as much riskier than
writing covered options.
Options are a zero-sum game (ignoring transaction costs). This is because
one person gains and one person loses by the same amount. The
transaction occurs because you don’t know which you will be ex ante.
Thus, to calculate the gain or loss for a seller, you can calculate the gain or
loss for the buyer and change the sign. This makes the payoff diagrams
mirror images.
Slide 22.15 Call Option Payoffs
Slide 22.16 Put Option Payoffs
Slide 22.17 Option Diagrams Revisited
5. Option Quotes
Chicago Board Options Exchange (CBOE) – the largest organized stock
options exchange. Virtually all listed options are American options. (Even
in Europe, most options are American, not European.) An option is
described as “Firm/Expiration month/ Strike price/Type.”
Contracts are generally for 100 shares (index options provide their basis in
the quote), so a contract will cost 100*price.
Options expire on the Saturday following the third Friday of the expiration
month.
Slide 22.18 –
Slide 22.24 Option Quotes
6. Combinations of Options
Once you understand options, they can be combined in ways to create
desired outcomes, either for hedging or speculative purposes. This is
referred to as financial engineering.
Slide 22.25 Combinations of Options
Protective put – buy stock and put (stock price insurance)
Slide 22.26 Protective Put Strategy (Payoffs)
Slide 22.27 Protective Put Strategy (Profits)
Covered call – buy stock and sell call. This is a strategy for building
income in a portfolio. The tradeoff is limited upside potential.
Slide 22.28 Covered Call Strategy
Long straddle – buy put and call. Benefit with large price swings, either up
or down.
Slide 22.29 Long Straddle
Short straddle – sell put and call. Earn the premium income, but lose if
price swings dramatically.
Slide 22.30 Short Straddle
Put-Call Parity
Recall the protective put strategy:
Buy one share of stock at price, S.
Buy one put option with strike, E, and put premium, P.
Example: Suppose you buy Citigroup stock for $45, and at the same time,
you purchase a put option with a strike price of $40.
You pay $1.80 for the option, and it expires in one year. You plan to sell
the stock in one year.
Consider the following possible payoffs:
Stock
Price
Put Value Combined Value Total Gain or Loss
25 15 40 -6.80
Stock
Price
Put Value Combined Value Total Gain or Loss
30 10 40 -6.80
35 5 40 -6.80
40 0 40 -6.80
45 0 45 -1.80
50 0 50 +3.20
55 0 55 +8.20
60 0 60 +13.20
65 0 65 +18.20
The maximum loss has been limited to $6.80.
Alternatively, suppose, instead, you buy a call option with a strike price of
E and a call price of C. You invest the rest in a Treasury Bill.
Example: A call option on Citigroup stock is selling for $7.78 and the T–
bill has an interest rate of 2.5%. We want to look at the same investment as
in part A, so you invest a total of $46.80. So, you invest 46.80 – 7.78 =
39.02 in T-bills. Consider the payoffs.
Stock
Price
Call Value T-bill
39.02(1.025)
Combined Value Total Gain or Loss
25 0 40 40 -6.80
30 0 40 40 -6.80
35 0 40 40 -6.80
40 0 40 40 -6.80
45 5 40 45 -1.80
50 10 40 50 +3.20
55 15 40 55 +8.20
60 20 40 60 +13.20
65 25 40 65 +18.20
The payoffs are the same with both strategies.
The Result: If the combined value is the same at the end, under all
situations, then the cost today must be the same.
This leads to the famous put-call parity (PCP) condition:
S + P = C + PV(E)
where the present value is computed using the risk-free rate.
The PCP condition can be rearranged to solve for any of the components.
Slide 22.31 –
Slide 22.33 Put-Call Parity
7. Valuing Options
Slide 22.34 Valuing Options
A. Bounding the Value of a Call
Upper bound: C0 S0. A call option can never sell for more than the stock.
Lower bound: 0 or S0 – E, whichever is larger. To prevent arbitrage, the
value of a call must be greater than the stock price minus the exercise
price. Otherwise, buy the option, pay the exercise price, and get the stock
for less than it sells for in the market.
Intrinsic value = max(0, S0 – E), i.e., option value just before expiration.