The reading gives an overview of financial options and describes payoffs to various options strategies. The factors that affect option prices are also discussed. Finally, the equity and debt of the firm are modeled as options. What part of the chapter rea

PeterDruckerWeek12.1 Berk_DeMarzo_cf5_ppt_20_accessible1.pptx
 

The reading gives an overview of financial options and describes payoffs to various options strategies. The factors that affect option prices are also discussed. Finally, the equity and debt of the firm are modeled as options. What part of the chapter readings was most significant to you? 

Task Requirement:

Write a 500-word description in which you discuss and answer the above questions.

12/28/21, 3:25 PM

The Be

s

t Of Peter Drucker

https://www.forbes.com/sites/stevedenning/2014/07/29/the-best-of-peter-drucker/?sh=773c46305a96 1/8

Leadership Strategy

I write about 21st century leadership, Agile, innovation & narrative.
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The Best Of Peter Drucker

Jul 29, 2014, 08:33pm EDT

Steve Denning Senior Contributor

Everyone knows that Peter Drucker was the founder of modern
management. But how do we come to terms with the writings of a man who
wrote 39 books? Even to read his 811-page classic, Management: Tasks,
Responsibilities, Practices (1973) or the revised edition of 572 pages (2008),
is more than most readers get round to. Inevitably most of us pick and
choose.

An excellent introduction to Drucker’s thinking—and one of the real “raisins
in the cake”— which was recently flagged by Jim Hays, is Peter Drucker’s
nine-page paper for The Economist in November 2001: “Will The
Corporation Survive?” Drucker’s answer to his own question was: “Yes, but
not in the form that we know it.” The paper was incorporated into the 2008
edition of Drucker’s Management, but it is also available here.

Five basic assumptions of the 20 Century

The paper, written 13 years ago,  is almost as fresh as if it was written
yesterday. It argues that for “most of the time since the corporation was
invented around 1870, the following five basic points have been assumed to
apply:”

1. “The corporation is the ‘master’, the employee is the ‘servant’,
because the corporation owns the means of production… “

2. “The great majority of employees work full-time for the corporation…
“

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https://www.forbes.com/sites/stevedenning/

http://www.economist.com/node/770874

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3. “The most efficient way to produce anything is to bring together
under one management as many as possible of the activities needed
to turn out the product,” because, as Ronald Coase argued, this lowers
transaction costs.

4. “Suppliers and especially manufacturers have market power because
they have information about a product or a service that the customer
does not and cannot have… “

5. “To any one particular technology pertains one and only one industry,
and conversely, to any one particular industry pertains one and only
one technology.”

Competition was very orderly with “everything in its place.” Thus “everybody
took it for granted that every product or service had a specific application,
and that for every application there was a specific product or material…
Competition therefore took place mainly within an industry. By and large, it
was obvious what the business of a given company was and what its markets
were.”

The assumptions upended

Now, each of those assumptions has been turned upside down:

1. The corporation is no longer the master of the employee because “the
means of production is knowledge, which is owned by knowledge
workers and is highly portable.”

2. “A growing number of people who work for an organisation will not
be full-time employees but part-timers, temporaries, consultants or
contractors… or employees of, an outsourcing contractor.”

3. It no longer makes sense to bring everything under one management,
because (a) “the knowledge needed for any activity has become highly
specialised. It is therefore increasingly expensive, and also
increasingly difficult, to maintain.” (b) Transaction costs are
drastically reduced, particularly the cost communications.C

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4. “The customer now has the information…. the manufacturer will
cease to be a seller and instead become a buyer for the customer.”

5. “There are few unique technologies. Increasingly, the knowledge
needed in a given industry comes out of some totally different
technology.”

“One thing is almost certain: in future,” Drucker wrote, “there will be not
one kind of corporation but several different ones.” In the 20 Century,
banks everywhere were very much alike and so were hospitals and retailers.
In future, “different banks may be quite different from one another,
depending on how each of them responds to the changes in its workforce,
technology and markets. A number of different models is likely to emerge…”
Confederations of different kinds of organizations will emerge.

Top management is powerful but failing

Drucker saw that the importance of top management would increase in this
emerging world:

“As the corporation moves towards a confederation or a syndicate, it will
increasingly need a top management that is separate, powerful and
accountable. This top management’s responsibilities will cover the entire
organisation’s direction, planning, strategy, values and principles; its
structure and its relationship between its various members; its alliances,
partnerships and joint ventures; and its research, design and
innovation.”

Yet while the demands on top management were increasing, Drucker saw
that top management was not getting the job done.

“The recent failure rate of chief executives in big American companies
points in the same direction. A large proportion of CEOs of such
companies appointed in the past ten years were fired as failures within a
year or two… This suggests that the jobs they took on had become

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undoable. The American record suggests not human failure but systems
failure. Top management in big organisations needs a new concept.”

Drucker cites a few possible examples of rearranging managerial
responsibilities at the top. With the wisdom of hindsight, none of them look
particularly plausible or sustainable, e.g. GE under Jack Welch.

The failure of top management relates less to any particular configuration of
management responsibilities and more to another of Drucker’s central
themes: the role of the corporation in society.

The role of the corporation in society

Drucker had a clear vision of the corporation as an agent of society:

“An equally important task for top management in the next society’s
corporation will be to balance the three dimensions of the corporation:
as an economic organisation, as a human organisation and as an
increasingly important social organisation. Each of the three models of
the corporation developed in the past half-century stressed one of these
dimensions and subordinated the other two. The German model of the
“social market economy” put the emphasis on the social dimension, the
Japanese one on the human dimension and the American one
(“shareholder sovereignty”) on the economic dimension.”

“None of the three is adequate on its own. The German model achieved
both economic success and social stability, but at the price of high
unemployment and dangerous labour-market rigidity. The Japanese
model was strikingly successful for 20 years, but faltered at the fir

st

serious challenge; indeed it has become a major obstacle to recovery
from Japan’s present recession. Shareholder sovereignty is also bound to
flounder. It is a fair-weather model that works well only in times of
prosperity.”

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Interestingly, Germany took action to deal with the issue of labor flexibility,
and this one of the key success factors for Germany today. Meanwhile most
big US corporations are still wedded to shareholder sovereignty.

A different kind of leadership is needed

“Corporations will have to pay attention,” Drucker argued, “both to their
short-term business results and to their long-term performance…”

Drucker’s hope was that the pension funds and mutual funds would lead the
way.

“By 2000, pension funds and mutual funds had come to own the
majority of the share capital of America’s large companies. This has
given shareholders the power to demand short-term rewards. But the
need for a secure retirement income will increasingly focus people’s
minds on the future value of the investment.”

What Drucker didn’t fully foresee is that the managers of pension funds and
mutual funds would themselves have powerful incentives to focus on short-
term shareholder value and the stock price. Their compensation is often
geared to it, and the success of their fund sometimes depends on it–at least
in the near term.

Nor could he have foreseen the massive shift in CEO compensation that was
to occur by 2014. “In 1993, some 20 percent of executive compensation was
based on stock,” Eduardo Porter wrote recently in the NYT. “Today, equity
accounts for about 60 percent of the remuneration of executives at
companies in the S&P 500-stock index. With so much money tied up in
stock options and the like, it is not surprising that executives will do almost
anything to give their share price a boost regardless of what costs this might
incur after their options have vested.”

Nor could Drucker have foreseen how severely the system would be
degraded by self-interest. Thus in a recent study published in the Accounting

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http://info.equilar.com/rs/equilar/images/equilar-2014-ceo-pay-strategies-report ?mkt_tok=3RkMMJWWfF9wsRojuKTNZKXonjHpfsX67%2BgqXrHr08Yy0EZ5VunJEUWy3YoITtQ%2FcOedCQkZHblFnV0PSq28UaoNoqIK%20

http://aaajournals.org/doi/abs/10.2308/accr-50734

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Review, an astonishing 62 percent of directors, who had a disclosed
friendship with the CEO, said they would cut the budget for research and
development in order to assure the bonus for their friend, the CEO. Instead
of senior managers acting as responsible stewards of societal resources, as
Drucker optimistically envisaged, we see leaders driven by greed and
nepotism. Instead of wise statesmen capable of balancing social interests, we
have inherited the mean-spirited and the narrow-minded.

A different kind of management

To accomplish the kind of positive future that Drucker envisaged, it is now
much clearer in today than in 2001 that a different kind of leadership and
management is needed for our corporations.

It means a fundamental shift in how leaders think, speak and act in the
workplace. Whereas the 20 Century economy flourished with an ethos of
efficiency and control, accentuated in recent decades by values of self-
interest and self-aggrandisement, the economy of the 21 Century will
require an ethos of imagination, exploration, experiment, discovery and
collaboration, driven by a commitment to make a positive difference in the
world.

It implies:

th
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a shift from a goal of making money to the goal of delighting
customers profitably. Innovation is not an option: it’s an imperative.
The only question is how.

a shift from controlling individuals to inspiring collaboration among
self-organizing teams, networks and ecosystems.;

a shift from coordinating work by hierarchical bureaucracy to
dynamic linking, with iterative approaches to development with
direct customer feedback and interaction with teams and networks.Co

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Of course, Drucker recognized all along that management is not a static
pursuit. “The demands on the skill, knowledge, performance, responsibility
and integrity of the manager have doubled in every generation during the
past half century,” he wrote in The Practice of Management, his 1954
classic. That is even more true in 2014.

Other short introductions to Peter Drucker

Other short introductions to the world of Peter Drucker include:

And read also:

Why The World’s Dumbest Idea Is (Finally) Dying

The Origin Of The Dumbest Idea In The World

How America lost the capacity to compete

Can Management Get Us Out Of The Mess It Has Created?

The five surprises of radical management

a shift from a preoccupation with economic value to an embrace of
values that will grow the firm and the accompanying ecosystems,
particularly radical transparency, continuous improvement and
sustainability.

a shift from top-down communications to horizontal conversations.
Instead of telling people what to do, leaders inspire people across
organizational boundaries to work together on common goals.

“The Coming of the New Organization” by Peter Drucker: (HBR
article, 1988)

“The American CEO,” by Peter Drucker (December 2004)

“A time to rediscover Peter F Drucker”, by Richard Straub (2009)

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http://www.forbes.com/sites/stevedenning/2014/06/17/why-the-worlds-dumbest-idea-is-finally-dying/

http://www.forbes.com/sites/stevedenning/2013/06/26/the-origin-of-the-worlds-dumbest-idea-milton-friedman/

http://www.forbes.com/sites/stevedenning/2013/01/17/the-boeing-debacle-seven-lessons-every-ceo-must-learn/

http://www.forbes.com/sites/stevedenning/2014/03/14/can-management-open-the-path-to-prosperity/

http://www.forbes.com/sites/stevedenning/2011/02/25/measuring-businesss-new-bottom-line-customer-delight/

http://hbr.org/1988/01/the-coming-of-the-new-organization/ar/1

http://online.wsj.com/news/articles/SB113207479262897747

http://www.druckersociety.at/files/reaching-out-coming-home

12/28/21, 3:25 PM The Best Of Peter Drucker

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________________________

Follow Steve Denning on Twitter @stevedenning

This article was prepared with assistance from Jim Hays, Richard Straub
and Rick Wartzman

Steve Denning Follow

My book, “The Age of Agile” was published by HarperCollins in 2018 and was selected by

the Financial Times as one of the best business books of 2018. I… Read More

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Corporate Finance

Fifth Edition

Chapter 20

Financial Options

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
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Slides in this presentation contain hyperlinks. JAWS users should be able to get a list of links by using INSERT+F7
1

Chapter Outline
20.1 Option Basics
20.2 Option Payoffs at Expiration
20.3 Put-Call Parity
20.4 Factors Affecting Option Prices
20.5 Exercising Options Early
20.6 Options and Corporate Finance

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved

2

Learning Objectives (1 of 3)
Define the following terms: call option, put option, exercise price, strike price, exercising the option, expiration date, American option, European option, in-the-money, and out-of-the-money.
Compute the value of a call or a put option at expiration.
List the rights and obligations of the buyer of the option and the seller of the option.

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Learning Objectives (2 of 3)
Use put-call parity to solve for the call premium, the put premium, the stock price, the strike price, or the dividend.
Discuss the following factors that influence call and put option values: stock price, strike price, and volatility.
Describe arbitrage bounds for option prices.

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Learning Objectives (3 of 3)
Explain why it is never optimal to exercise an American call option early on a non-dividend-paying stock, and why it is sometimes optimal to exercise an American put option early.
Explain the use of option modeling to value equity.
Describe how corporate debt can be viewed as a portfolio of riskless debt and a short position in a put option.

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
20.1 Option Basics (1 of 2)
Financial Option
A contract that gives its owner the right (but not the obligation) to purchase or sell an asset at a fixed price as some future date
Call Option
A financial option that gives its owner the right to buy an asset

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
20.1 Option Basics (2 of 2)
Put Option
A financial option that gives its owner the right to sell an asset
Option Writer
The seller of an option contract

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Understanding Option Contracts (1 of 3)
Exercising an Option
When a holder of an option enforces the agreement and buys or sells a share of stock at the agreed-upon price
Strike Price (Exercise Price)
The price at which an option holder buys or sells a share of stock when the option is exercised
Expiration Date
The last date on which an option holder has the right to exercise the option

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Understanding Option Contracts (2 of 3)
American Option
Options that allow their holders to exercise the option on any date up to, and including, the expiration date
European Option
Options that allow their holders to exercise the option only on the expiration date
Note: The names American and European have nothing to do with the location where the options are traded

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Understanding Option Contracts (3 of 3)
The option buyer (holder)
Holds the right to exercise the option and has a long position in the contract
The option seller (writer)
Sells (or writes) the option and has a short position in the contract
Because the long side has the option to exercise, the short side has an obligation to fulfill the contract if it is exercised.
The buyer pays the writer a premium

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Interpreting Stock Option Quotations (1 of 3)
Stock options are traded on organized exchanges.
By convention, all traded options expire on the Saturday following the third Friday of the month.
Open Interest
The total number of contracts of a particular option that have been written

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Table 20.1 Option Quotes for eBay Stock
Source: Chicago Board Options Exchange at
www.cboe.com

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
A table displays the option quotes for E Bay incorporated on September 10 2018 at 12 33 E T, 33.75, negative 0.235. Bid 33.75, Ask 33.76. Size 18 by 14. Volume. 2108011. The table for calls is as follows. The table has 10 Rows and 7 columns. The columns have the following headings from left to right. Calls, Last sale, Net, Bid, Ask, Volume, Open. The Row entries are as follows. Row 2. 20 18 September 21 32.00, E BAY 1821132, 1.86, blank 1.86, 1.96, blank 534. Row 3. 20 18 September 21 33.00, E BAY 1821133, 1.04, blank 1.03, 1.08, 15, 827. Row 4. 20 18 September 21 34.00, E BAY 1821134, 0.45, negative 0.09, 0.42, 0.43, 110, 4959. Row 5. 20 18 September 21 35.00, E BAY 1821135, 0.15, negative 0.06, 0.14, 0.15, 258, 7199. Row 6. 20 18 September 21 36.00, E BAY 1821136, 0.05, negative 0.03, 0.05, 0.06, 268, 13279. Row 7. 20 19 January 1 30.00, E BAY 1821130, 4.75, blank 4.7, 4.8, blank 737. Row 8. 20 19 January 1 33.00, E BAY 1821133, 2.7, negative 0.12, 2.62, 2.68, 2, 467. Row 9. 20 19 January 1 35.00, E BAY 1821135, 1.73, 0.1, 1.61, 1.66, 6, 2079. Row 10. 20 19 January 1 37.00, E BAY 1821137, 0.96, blank 0.91, 0.96, 1, 2324. Row 11. 20 19 January 1 40.00, E BAY 1821140, 0.39, blank 0.34, 0.38, blank 3455. The table for puts is as follows. The table has 10 Rows and 7 columns. The columns have the following headings from left to right. Puts, Last Sale, Net, Bid, Ask, Volume, Open I n t. The Row entries are as follows. Row 1. 20 18 September 21 32.00, E BAY 1821132, 0.09, negative 0.02, 0.09, 0.1, 2, 2122. Row 2. 20 18 September 21 33.00, E BAY 1821133, 0.25, negative 0.06, 0.24, 0.26, 2, 2927. Row 3. 20 18 September 21 34.00, E BAY 1821134, 0.62, 0.03, 0.63, 0.65, 35, 5631. Row 4. 20 18 September 21 35.00, E BAY 1821135, 1.13, negative 0.22, 1.34, 1.39, 1, 3594. Row 5. 20 18 September 21 36.00, E BAY 1821136, 2.28, negative 0.07, 2.15, 2.3, 2, 1481. Row 6. 20 19 January 1 30.00, E BAY 1821130, 0.74, blank 0.65, 0.68, blank 7912. Row 7. 20 19 January 1 33.00, E BAY 1821133, 1.55, negative 0.05, 1.55, 1.58, 129, 7562. Row 8. 20 19 January 1 35.00, E BAY 1821135, 2.47, blank, 2.51, 2.57, blank 15795. Row 9. 20 19 January 1 37.00, E BAY 1821137, 3.8, 0.65, 3.85, 3.9, 79, 17202. Row 10. 20 19 January 1 40.00, E BAY 1821140, 5.6, Blank 6.3, 6.4, Blank 6093.
12

Interpreting Stock Option Quotations (2 of 3)
At-the-money
Describes an option whose exercise price is equal to the current stock price
In-the-money
Describes an option whose value, if immediately exercised, would be positive
Out-of-the-money
Describes an option whose value, if immediately exercised, would be negative

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Interpreting Stock Option Quotations (3 of 3)
Deep in-the-money
Describes an option that is in-the-money and for which the strike price and the stock price are very far apart
Deep out-of-the-money
Describes an option that is out-of-the-money and for which the strike price and the stock price are very far apart

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved

14

Textbook Example 20.1 (1 of 2)
Purchasing Options
Problem
It is the afternoon of September 10, 2018, and you have decided to purchase 10 January call contracts on eBay stock with an exercise price of $35. Because you are buying, you must pay the ask price. How much money will this purchase cost you? Is this option in-the-money or out-of-the-money?

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Textbook Example 20.1 (2 of 2)
Solution
From Table 20.1, the ask price of this option is $1.66. You are purchasing 10 contracts and each contract is on 100
shares, so the transaction will cost

(ignoring any brokerage fees). Because this is a call option and the exercise price is above the current stock price ($33.75), the option is currently out-of-the-money.

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Alternative Example 20.1 (1 of 3)
Problem
You have decided to purchase 2/15/2019 put contracts on the D J I A with an exercise price of $246.
Source:
CBOE.com

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
As on January 21, 2019 at 15:52 ET, LAST 247. 06
There are three tables shown. One table shows the Calls values and another shows the Puts value. In between both the tables a table shows the Strike values as on February 02, 2015.
The Calls table has nine columns with four rows. The information given in the Calls table is as follows:
Last: 4.1
• Net: positive 1.405
• Bid: 4.35
• Ask: 4.55
• Vol: 3
• IV: 0.1432
• Delta: 0.5427
• Gamma: 0.0406
• Int: 15
Last: 4
• Net: positive 1.73
• Bid: 3.75
• Ask: 3.95
• Vol: 401
• IV: 0.1406
• Delta: 0.5016
• Gamma: 0.0416
• Int: 17
Last: 3.2
• Net: positive 1.31
• Bid: 3.25
• Ask: 3.45
• Vol: 14
• IV: 0.1403
• Delta: 0.46
• Gamma: 0.0415
• Int: 2
Last: 2.7
• Net: positive 1.14
• Bid: 2.77
• Ask: 2.92
• Vol: 1
• IV: 0.1411
• Delta: 0.4197
• Gamma: 0.0406
• Int: 5
The second table titled February 02, 2019. The table consists of one column and four rows.
The Strike values are as follows:
• DJX 246.000
• DJX 247.000
• DJX 248.000
• DJX 249.000
The Puts table has nine columns consisting of four rows. The last column has a negative symbol over it. The information given in the Puts table is as follows:
Last: 3.75
• Net: negative 1.6
• Bid: 3.45
• Ask: 3.65
• Vol: 10
• IV: 0.1514
• Delta: negative 0.457
• Gamma: 0.0384
• Int: 50
Last: 4.32
• Net: negative 1.58
• Bid: 3.85
• Ask: 4.1
• Vol: 2
• IV: 0.1499
• Delta: minus 0.4957
• Gamma: 0.039
• Int: 0
Last: 0
• Net: 0
• Bid: 4.3
• Ask: 4.6
• Vol: 0
• IV: 0.1487
• Delta: minus 0.5351
• Gamma: 0.0392
• Int: 0
Last: 0
• Net: 0
• Bid: 4.85
• Ask: 5.1
• Vol: 0
• IV: 0.147
• Delta: minus 0.5748
• Gamma: 0.0391
• Int: 3
17

Alternative Example 20.1 (2 of 3)
Problem
How much money will this purchase cost you?
Is this option in-the-money or out-of-the-money?

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Alternative Example 20.1 (3 of 3)
Solution
The ask price is $3.65 per contract.
The total cost is

Because the strike price ($246) is less than the current price ($247.06), the put option is out-of-the-money.

Copyright © 2020, 2017, 2014 Pearson Education, Inc. All Rights Reserved
Options on Other Financial Securities (1 of 2)
Although the most commonly traded options are on stocks, options on other financial assets, like the S&P 100 index, the S&P 500 index, the Dow Jones Industrial index, and the N Y S E index, are also traded.

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Options on Other Financial Securities (2 of 2)
Hedge
To reduce risk by holding contracts or securities whose payoffs are negatively correlated with some risk exposure
Speculate
When investors use contracts or securities to place a bet on the direction in which they believe the market is likely to move

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21

20.2 Option Payoffs at Expiration (1 of 2)
Long Position in an Option Contract
The value of a call option at expiration is

Where S is the stock price at expiration, K is the exercise price, C is the value of the call option, and max is the maximum of the two quantities in the parentheses.

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Figure 20.1 Payoff of a Call Option with a Strike Price of $20 at Expiration

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The x-axis shows the stock price from 0 to 60 in increments of 10. The y-axis shows the payoff in dollars from 0 to 40 in increments of 10. The graph shows that the curve starts at (0, 0) and at the strike price (20, 0) it starts to rise and stops at (60, 40).
23

20.2 Option Payoffs at Expiration (2 of 2)
Long Position in an Option Contract
The value of a put option at expiration is

Where S is the stock price at expiration, K is the exercise price, P is the value of the put option, and max is the maximum of the two quantities in the parentheses.

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Textbook Example 20.2 (1 of 2)
Payoff of a Put Option at Maturity
Problem
You own a put option on Oracle Corporation stock with an exercise price of $20 that expires today. Plot the value of this option as a function of the stock price.

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Textbook Example 20.2 (2 of 2)
Solution
Let S be the stock price and P be the value of the put option. The value of the option is

Plotting this function gives

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The x-axis shows the stock price from 0 to 40 in increments of 10. The y-axis shows the payoff in dollars from 0 to 20 in increments of 10. The graph shows that the curve starts at (0, 20) and at the strike price (20, 0) it becomes parallel to the x-axis and stops at (40, 0).
26

Alternative Example 20.2 (1 of 2)
Problem
You own a put option on Dell stock with an exercise price of $12.50 that expires today. Plot the value of this option as a function of the stock price.

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Alternative Example 20.2 (2 of 2)
Solution
Let S be the stock price and P be the value of the put
option. The value of the option is

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The y-axis ranges from 0 through 14. The graph starts at (0, 12.5), falls diagonally through (6, 6.5) to a point at (12.5, 0) labeled, strike price, then moves horizontally through (20, 0). All values estimated.
28

Short Position in an Option Contract
An investor that sells an option has an obligation.
This investor takes the opposite side of the contract to the investor who bought the option.
Thus the seller’s cash flows are the negative of the buyer’s cash flows.

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Figure 20.2 Short Position in a Call Option at Expiration

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The x-axis shows the stock price from 0 to 60 in increments of 10. The y-axis (downward) shows payoff in dollars from 0 to minus 40 in reduction of 10. The graph shows that the curve stars at (0, 0) and is parallel to x-axis, till (20, 0) when it starts to drop and ends at (60, minus 40).
30

Textbook Example 20.3 (1 of 2)
Payoff of a Short Position in a Put Option
Problem
You are short in a put option on Oracle Corporation stock with an exercise price of $20 that expires today. What is your payoff at expiration as a function of the stock price?

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Textbook Example 20.3 (2 of 2)
Solution
If S is the stock price, your cash flows will be

If the current stock price is $30, then the put will not be exercised and you will owe nothing. If the current stock price is $15, the put will be exercised and you will lose $5. The figure plots your cash flows:

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The x-axis shows the stock price from 0 to 40 in increments of 10. The y-axis (downward) shows payoff in dollars from 0 to minus 20 in reduction of 5. The graph shows that the curve stars at (40, 0) and is parallel to x-axis, till (20, 0) when it starts to drop and ends at (0, minus 20).
32

Profits for Holding an Option to Expiration
Although payouts on a long position in an option contract are never negative, the profit from purchasing an option and holding it to expiration could be negative because the payout at expiration might be less than the initial cost of the option.

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Figure 20.3 Profit from Holding a Call Option to Expiration

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The y-axis shows profit at expiration in dollars from minus 5 to 10 in increments of 5 with x-axis originating at 0. The graph shows the following data:
• 2019 Jan 18 30.00 Call: The curve originates at (25, minus 5), runs parallel to x-axis till (30, minus 5) after which it starts to increase and ends at (45, 10).
• 2019 Jan 18 33.00 Call: The curve originates at (25, minus 2.5), runs parallel to x-axis till (33, minus 2.5) after which it starts to increase and ends at (45, 9).
• 2019 Jan 18 35.00 Call: The curve originates at (25, minus 1.5), runs parallel to x-axis till (35, minus 1.5) after which it starts to increase and ends at (45, 8).
• 2019 Jan 18 37.00 Call: The curve originates at (25, minus 1), runs parallel to x-axis till (35.5, minus 1) after which it starts to increase and ends at (45, 7).
• 2019 Jan 18 40.00 Call: The curve originates at (25, minus 0.5), runs parallel to x-axis till (40, minus 0.5) after which it starts to increase and ends at (45, 5).
34

Textbook Example 20.4 (1 of 2)
Profit on Holding a Position in a Put Option Until Expiration
Problem
Assume you decided to purchase each of the January put options quoted in Table 20.1 on September 10, 2018, and you financed each position by shorting a two-month bond with a yield of 2.5%. Plot the profit of each position as a function of the stock price on expiration.

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Textbook Example 20.4 (2 of 2)
Solution
Suppose S is the stock price on expiration, K is the strike price, and P is the price of each put option on September 10th. Then your cash flows on the expiration date will be

The plot is shown below. Note the same trade-off between the maximum loss and the potential for profit as for the call options.

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expiration in dollars from minus 10 to 10 in increments of 5 with x-axis originating at 0. The graph shows the following data:
• 2019 Jan 18 40.00 Put: The curve starts at (25, 8) and drops to (40, minus 6), after which it runs parallel to x-axis till (45, minus 6).
• 2019 Jan 18 37.00 Put: The curve starts at (25, 7.5) and drops to (36.5, minus 5), after which it runs parallel to x-axis till (36.5, minus 5).
• 2019 Jan 18 35.00 Put: The curve starts at (25, 7) and drops to (35, minus 3), after which it runs parallel to x-axis till (45, minus 3).
• 2019 Jan 18 33.00 Put: The curve starts at (25, 6.5) and drops to (32.5, minus 2), after which it runs parallel to x-axis till (45, minus 2).
• 2019 Jan 18 30.00 Put: The curve starts at (25, 4) and drops to (30, minus 0.5), after which it runs parallel to x-axis till (45, minus 0.5).
36

Returns for Holding an Option to Expiration (1 of 2)
The maximum loss on a purchased call option is 100% (when the option expires worthless).
Out-of-the money call options are more likely to expire worthless, but if the stock goes up sufficiently, it will also have a much higher return than an in-the-money call option.
Call options have more extreme returns than the stock itself.

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Returns for Holding an Option to Expiration (2 of 2)
The maximum loss on a purchased put option is 100% (when the option expires worthless).
Put options will have higher returns in states with low stock prices.
Put options are generally not held as an investment, but rather as insurance to hedge other risk in a portfolio.

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Figure 20.4 Option Returns from Purchasing an Option and Holding It to Expiration

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• 2019 Jan 18 40.00 Call: The line originates at (25, minus 100) and runs parallel to the x-axis till (40, minus 100) after which it increases to (41, 500). • 2019 Jan 18 37.00 Call: The line originates at (37, minus 100) and increases to (42, 500). • 2019 Jan 18 35.00 Call: The line originates at (35, minus 100) and increases to (45, 500). • 2019 Jan 18 33.00 Call: The line originates at (34, minus 100) and increases to (45, 350). • 2019 Jan 18 30.00 Call: The line originates at (30, minus 100) and increases to (45, 200).

• 2019 Jan 18 30.00 Put: The line originates at (45, minus 100) and runs parallel to the x-axis till (40, minus 100) after which it increases to (25, 130). • 2019 Jan 18 33.00 Put: The line originates at (40, minus 100) and runs parallel to the x-axis till (37, minus 100) after which it increases to (25, 200). • 2019 Jan 18 35.00 Put: The line originates at (37, minus 100) and runs parallel to the x-axis till (34, minus 100) after which it increases to (25, 299). • 2019 Jan 18 37.00 Put: The line originates at (34, minus 100) and runs parallel to the x-axis till (33, minus 100) after which it increases to (25, 405). • 2019 Jan 18 40.00 Put: The line originates at (33, minus 100) and runs parallel to the x-axis till (30, minus 100) after which it increases to (27, 500).
39

Combinations of Options (1 of 4)
Straddle
A portfolio that is long a call option and a put option on the same stock with the same exercise date and strike price
This strategy may be used if investors expect the stock to be very volatile and move up or down a large amount but do not necessarily have a view on which direction the stock will move.

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Figure 20.5 Payoff and Profit from a Straddle

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The x-axis shows the Stock price in dollars with strike price K marked on the x-axis. The lines for Put and call payoff originate from different ends of the graph and coincide at K on the x-axis, forming a V. The lines for Put and call payoff originate from different ends of the graph and coincide below K on the x-axis, forming a V.
41

Combinations of Options (2 of 4)
Strangle
A portfolio that is long a call option and a put option on the same stock with the same exercise date but the strike price on the call exceeds the strike price on the put

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Textbook Example 20.5 (1 of 2)
Strangle
Problem
You are long both a call option and a put option on Hewlett-Packard stock with the same expiration date. The exercise price of the call option is $40; the exercise price of the put option is $30. Plot the payoff of the combination at expiration.

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Textbook Example 20.5 (2 of 2)
Solution
The red line represents the put’s payouts and the blue line represents the call’s payouts. In this case, you do not receive money if the stock price is between the two strike prices. This option combination is known as a strangle.

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The x-axis shows the Stock price in dollars from 0 to 80 in increments of 20. The y-axis shows the payoff in dollars from 0 to 40 in increments of 10. The graph shows that the line for put originates at 30 on the y-axis and coincides with the x-axis on 30. The line for call originates at (80, 40) and coincides with the x-axis on 40.
44

Combinations of Options (3 of 4)
Butterfly Spread
A portfolio that is long two call options with differing strike prices and is short two call options with a strike price equal to the average strike price of the first two calls
Although a straddle strategy makes money when the stock and strike prices are far apart, a butterfly spread makes money when the stock and strike prices are close.

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Figure 20.6 Butterfly Spread

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The x-axis shows the stock price in dollars from 0 to 45. The y-axis shows the payoff in dollars from minus 30 to 30 in increments of 5 and the x-axis drawn at 0. The graph shows that the line for 20 call originates at 0 and runs along the x-axis till 20, after which it starts to increase and ends at (45, 20). The line for 40 call originates at 0 and runs along the x-axis till 40, after which it starts to increase and ends at (45, 5). The line for payoff originates at 0 and runs along the x-axis till 30, after which it decreases to (45, minus 30). The line for payoff of the entire combination originates at 0 and runs along the x-axis till 20, after which it increases to (30, 10) before dropping again to (40, 0).
46

Combinations of Options (4 of 4)
Protective Put
A long position in a put held on a stock you already own
Portfolio Insurance
A protective put written on a portfolio rather than a single stock
When the put does not itself trade, it is synthetically created by constructing a replicating portfolio.
Portfolio insurance can also be achieved by purchasing a bond and a call option

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Figure 20.7 Portfolio Insurance
The plots show two different ways to insure against the possibility of the price of Tripadvisor stock falling below $45. The orange line in (a) indicates the value on the expiration date of a position that is long one share of Amazon stock and one European put option with a strike of $45 (the blue dashed line is the payoff of the stock itself). The orange line in (b) shows the value on the expiration date of a position that is long a zero-coupon riskfree bond with a face value of $45 and a European call option on Tripadvisor with a strike price of $45 (the green dashed line is the bond payoff).

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A line graph a, plots pay off in dollars versus stock price in dollars. The Vertical axis shows payoff in dollars from 0 to 75 in increment of 15, and the Horizontal axis shows stock price in dollars from 0 to 75 in increment of 15. A doted curve starts from origin and ends at point (75, 75). Curve labeled as stock plus put starts from point (0, 45), becomes parallel with the horizontal axis till point (45, 45). Thereafter, it converges with the doted curve. All values are estimated.

A line graph b, plots pay off in dollars versus stock price in dollars. The Vertical axis shows payoff in dollars from 0 to 75 in increment of 15, and the Horizontal axis shows stock price in dollars from 0 to 75 in increment of 15. A doted curve labeled as riskless bond starts from the point (0, 45), becomes parallel with the horizontal axis till point (75, 45). Curve labeled as riskless bond plus call starts from point (0, 45), and converges with the horizontal axis till point (45, 45). Thereafter, the curve is upward sloping till point (75, 75). All values are estimated.
48

20.3 Put-Call Parity (1 of 4)
Consider the two different ways to construct portfolio insurance discussed previously
Purchase the stock and a put
Purchase a bond and a call.
Because both positions provide exactly the same payoff, the Law of One Price requires that they must have the same price.

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20.3 Put-Call Parity (2 of 4)
Therefore,

Where K is the strike price of the option (the price you want to ensure that the stock will not drop below), C is the call price, P is the put price, and S is the stock price.

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20.3 Put-Call Parity (3 of 4)
Rearranging the terms gives an expression for the price of a European call option for a non-dividend-paying stock:

This relationship between the value of the stock, the bond, and call and put options is known as put-call parity.

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Textbook Example 20.6 (1 of 3)
Using Put-Call Parity
Problem
You are an options dealer who deals in non-publicly traded options. One of your clients wants to purchase a one-year European call option on H A L Computer Systems stock with a strike price of $20. Another dealer is willing to write a one-year European put option on H A L stock with a strike price of $20, and sell you the put option for a price of $3.50 per share. If H A L pays no dividends and is currently trading for $18 per share, and if the risk-free interest rate is 6%, what is the lowest price you can charge for the option and guarantee yourself a profit?

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Textbook Example 20.6 (2 of 3)
Solution
Using put-call parity, we can replicate the payoff of the one-year call option with a strike price of $20 by holding the following portfolio: Buy the one-year put option with a strike price of $20 from the dealer, buy the stock, and sell a one-year risk-free zero-coupon bond with a face value of $20. With this combination, we have the following final payoff
depending on the final price of H A L stock in one year,

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The columns have the following headings from left to right. Blank, S sub 1 is less than $20, S sub 1 is greater than $20. The Row entries are as follows. Row 1. Buy Put Option, 20 minus S sub 1, 0. Row 2. Buy Stock, S sub 1. S sub 1.. Row 3. Sell Bond, Negative 20, Negative 20. Row 4. Portfolio, 0, S sub 1 minus 20. Row 5. Sell Call Option, 0, Negative left parenthesis S sub 1 minus 20 right parenthesis. Row 6. Total Payoff, 0, 0.
53

Textbook Example 20.6 (3 of 3)
Note that the final payoff of the portfolio of the three securities matches the payoff of a call option. Therefore, we can sell the call option to our client and have future payoff of zero no matter what happens. Doing so is worthwhile as long as we can sell the call option for more than the cost of the portfolio, which is

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Alternative Example 20.6 (1 of 2)
Problem
Assume
You want to buy a one-year call option and put option on Dellibar.
The strike price for each is $15.
The current price per share of Dellibar is $14.79.
Dellibar does not pay a dividend.
The risk-free rate is 2.5%.
The price of each call is $2.23.
Using put-call parity, what should be the price of each put?

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Alternative Example 20.6 (2 of 2)
Solution
Put-Call Parity states

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20.3 Put-Call Parity (4 of 4)
If the stock pays a dividend, put-call parity becomes

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Textbook Example 20.7 (1 of 2)
Using Options to Value Near-Term Dividends
Problem
It is February 2016 and you have been asked, in your position as a financial analyst, to compare the expected dividends of several popular stock indices over the next several years. Checking the markets, you find the following closing prices for each index, as well as for options expiring December 2018.
Index Feb 2016 Index Value Dec 2018 Index Options Strike Price Dec 2018 Index Options Call Price Dec 2018 Index Options Put Price
DJIA 164.85 160 19.78 22.73
S&P 500 1929.80 1900 243.25 278.00
Nasdaq 100 4200.66 4200 636.35 666.85
Russell 2000 1022.08 1000 150.10 166.80

If the current risk-free interest rate is 0.90% for a December 2018 maturity, estimate the relative contribution of the near-term dividends to the value of each index.

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Textbook Example 20.7 (2 of 2)
Solution
Rearranging the Put-Call Parity relation gives

Applying this to the D J I A, we find that the expected present value of its dividends over the next 34 month is

Therefore, expected dividends through December 2018 represent

of the current value of D J I A index. Doing a similar
calculation for the other indices, we find that near-term dividends account for 5.8% of the value of the S&P 500, 3.2% of the N A S D A Q 100, and 6.2% of the Russell 2000.

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20.4 Factors Affecting Option Prices (1 of 2)
Strike Price and Stock Price
The value of a call option increases (decreases) as the strike price decreases (increases), all other things held constant.
The value of a put option increases (decreases) as the strike price increases (decreases), all other things held constant.

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60

20.4 Factors Affecting Option Prices (2 of 2)
Strike Price and Stock Price
The value of a call option increases (decreases) as the stock price increases (decreases), all other things held constant.
The value of a put option increases (decreases) as the stock price decreases (increases), all other things held constant.

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61

Arbitrage Bounds on Option Prices (1 of 3)
An American option cannot be worth less than its European counterpart.
A put option cannot be worth more than its strike price.
A call option cannot be worth more than the stock itself.

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62

Arbitrage Bounds on Option Prices (2 of 3)
Intrinsic Value
The amount by which an option is in-the-money, or zero if the option is out-of-the-money.
An American option cannot be worth less than its intrinsic value.

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63

Arbitrage Bounds on Option Prices (3 of 3)
Time Value
The difference between an option’s price and its intrinsic value.
An American option cannot have a negative time value.

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64

Option Prices and the Exercise Date
For American options, the longer the time to the exercise date, the more valuable the option.
An American option with a later exercise date cannot be worth less than an otherwise identical American option with an earlier exercise date.
However, a European option with a later exercise date can be worth less than an otherwise identical European option with an earlier exercise date.

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Option Prices and Volatility
The value of an option generally increases with the volatility of the stock.

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Textbook Example 20.8 (1 of 2)
Option Value and Volatility
Problem
Two European call options with a strike price of $50 are written on two different stocks. Suppose that tomorrow, the low-volatility stock will have a price of $50 for certain. The high-volatility stock will be worth either $60 or $40, with each price having equal probability. If the exercise date of both options is tomorrow, which option will be worth more today?

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Textbook Example 20.8 (2 of 2)
Solution
The expected value of both stocks tomorrow is $50 ̶ the low-volatility stock will be worth this amount for sure, and the high-
high-volatility stock has an expected value of

However, the options have very different values. The option on the low-volatility stock is worth nothing because there is no chance it will expire in-the-money (the low-volatility stock will be worth $50 and the strike price is $50). The option on the high-volatility stock is worth a positive amount because there is a 50% chance that it
will be worth

and a 50% chance that it will be
worthless. The value today of a 50% chance of a positive payoff (with no chance of a loss) is positive.

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Alternative Example 20.8 (1 of 2)
Problem
You are considering investing in Finray, which currently trades at $13.10 per share.
A one-year call option with a strike price of $13 costs $0.87, while a put option with the same strike price and expiration costs $0.98.
If the risk-free rate is 0.10%, what is Finray’s expected dividend?

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Alternative Example 20.8 (2 of 2)
Solution
Put-Call Parity states

Solving for PV(Div) yields

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20.5 Exercising Options Early
Although an American option cannot be worth less than its European counterpart, they may have equal value.

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Non-Dividend-Paying Stocks (1 of 5)

For a non-dividend paying stock, Put-Call Parity can be written as

Where dis(K) is the amount of the discount from face value of the zero-coupon bond K.

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Non-Dividend-Paying Stocks (2 of 5)
Because dis(K) and P must be positive before the expiration date, a European call always has a positive time value.
Because an American option is worth at least as much as a European option, it must also have a positive time value before expiration.
Thus, the price of any call option on a non-dividend-paying stock always exceeds its intrinsic value prior to expiration.

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Non-Dividend-Paying Stocks (3 of 5)
This implies that it is never optimal to exercise a call option on a non-dividend paying stock early.
You are always better off just selling the option.
Because it is never optimal to exercise an American call on a non-dividend-paying stock early, an American call on a non-dividend paying stock has the same price as its European counterpart.

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Non-Dividend-Paying Stocks (4 of 5)
However, it may be optimal to exercise a put option on a non-dividend paying stock early

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Non-Dividend-Paying Stocks (5 of 5)
When a put option is sufficiently deep in-the-money, dis(K) will be large relative to the value of the call, and the time value of a European put option will be negative.
In that case, the European put will sell for less than its intrinsic value.
However, its American counterpart cannot sell for less than its intrinsic value, which implies that an American put option can be worth more than an otherwise identical European option.

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Textbook Example 20.9 (1 of 2)
Early Exercise of a Put Option on a Non-Dividend-Paying Stock
Problem
Table 20.2 lists the quotes from the C B O E on July 20, 2018, for options on Alphabet stock (Google’s holding company) expiring in September 2018. Alphabet will not pay a dividend during this period. Identify any option for which exercising the option early is better than selling it.

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Textbook Example 20.9 (2 of 2)
Solution
Because Alphabet pays no dividends during the life of these options (July 2018 to September 2018), it should not be optimal to exercise the call options early. In fact, we can check that the bid price for each call option exceeds that option’s intrinsic value, so it would be better to sell the call than to exercise it. For
example, the payoff from exercising a call with a strike of 1000 early is

while the option can be sold for $204.90.
On the other hand, an Alphabet shareholder holding a put option with a strike price of $1360 or higher would be better off exercising—rather than selling—the option. For example, by exercising the 1400 put the shareholder would receive $1400 for her stock, whereas by selling the stock and the option she would only
receive

The same is not true of the puts with strikes
below $1360, however. For example, the holder of the 1320 put option who exercises it early would receive $1320 for her stock, but would net

by selling the stock and the put instead. Thus, early exercise
is only optimal for the deep in-the-money put options.

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Table 20.2 Alphabet Option Quotes
Source: Chicago Board Options Exchange at
www.cboe.com

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GOOGL (ALPHABET INC (A)) 1197.88 minus 1.22
Jul 20 2018 @ 17:59 ET Bid 1197 Ask 1198.78 Size 1 into 1 Vol 1896554
Calls Bid Ask Open Int Puts Bid Ask Open Int
2018 Sep 21 1000.00 (GOOGL182111000) 204.9 206.4 576 2018 Sep 21 1000.00 (GOOGL1821U1000) 3.2 3.6 834
2018 Sep 21 1040.00 (GOOGL182111040) 166.9 169.7 132 2018 Sep 21 1040.00 (GOOGL1821 U1040) 5.3 6 141
2018 Sep 21 1080.00 (GOOGL182111080) 127.5 136.9 226 2018 Sep 21 1080.00 (GOOGL1821U1080) 9.3 9.9 342
2018 Sep 21 1120.00 (GOOGL182111120) 95.1 104.5 196 2018 Sep 21 1120.00 (GOOGL1821U1120) 16.1 16.9 277
2018 Sep 21 1160.00 (GOOGL182111160) 70 71 345 2018 Sep 21 1160.00 (GOOGL1821U1160) 27.2 28.1 176
2018 Sep 21 1200.00 (GOOGL182111200) 46.3 47.3 1295 2018 Sep 21 1200.00 (GOOGL1821U1200) 43.6 44.5 345
2018 Sep 21 1280.00 (GOOGL182111280) 16.1 16.6 202 2018 Sep 21 1280.00 (GOOGL1821U1280) 89.7 99 10
2018 Sep 21 1320.00 (GOOGL182111320) 8.4 8.9 150 2018 Sep 21 1320.00 (GOOGL1821U1320) 127 128 10
2018 Sep 21 1360.00 (GOOGL182111360) 4.1 4.6 109 2018 Sep 21 1360.00 (GOOGL1821U1360) 159 169 1
2018 Sep 21 1400.00 (GOOGL182111400) 2.1 2.35 265 2018 Sep 21 1400.00 (GOOGL1821U1400) 198 207.5 0
79

Dividend-Paying Stocks (1 of 3)
The put-call parity relationship for a dividend-paying stock can be written as

If PV(Div) is large enough, the time value of a European call option can be negative, implying that its price could be less than its intrinsic value.
Because an American option can never be worth less than its intrinsic value, the price of the American option can exceed the price of a European option.

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Dividend-Paying Stocks (2 of 3)
With a dividend paying stock, it may be optimal to exercise the American call option early.
When a company pays a dividend, investors expect the price of the stock to drop.
When the stock price falls, the owner of a call option loses.
Unlike the owner of the stock, the option holder does not get the dividend as compensation.
However, by exercising early and holding the stock, the owner of the call option can capture the dividend.

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Textbook Example 20.10 (1 of 2)
Early Exercise of Options on a Dividend-Paying Stock
Problem
General Electric (G E) stock went ex-dividend on December 22, 2005 (only equity holders on the previous day are entitled to the dividend). The dividend amount was $0.25. Table 20.3 lists the quotes for G E options on December 21, 2005. From the quotes, identify the options that should be exercised early rather than sold.

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Textbook Example 20.10 (2 of 2)
Solution
The holder of a call option on G E stock with a strike price of $32.50 or less is better off exercising ̶ rather than selling ̶ the option. For example, exercising
the 06 January 10 call and immediately selling the stock would net

The option itself can be sold for $25.40, so the holder is better off by
$0.12 by exercising the call rather than selling it. To understand why early exercise can be optimal in this case, note that interest rates were about 0.33% per month, so the value of delaying payment of the $10 strike price until January was worth only $0.033, and the put option was worth less than $0.05. Thus, from Eq. 20.7, the benefit of delay was much less than the $0.25 value of the dividend.
On the other hand, all of the put options listed have a positive time value and thus should not be exercised early. In this case, waiting for the stock to go ex-dividend is more valuable than the cost of delaying the receipt of the strike price.

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Table 20.3 Option Quotes for G E on December 21, 2005 (G E paid $0.25 dividend with ex-dividend date of December 22, 2005)
Source: Chicago Board Options Exchange at
cboe.com

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GE 35.52 minus 0.02
Dec 21, 2005 @ 11:50 ET Vol 8103000
Calls Bid Ask Open Interest Puts Bid Ask Open Interest
06 Jan 10.00 (GE AB-E) 25.4 25.6 738 06 Jan 10.00 (GE MB-E) 0 0.05 12525
06 Jan 20.00 (GEAD-E) 15.4 15.6 1090 06 Jan 20.00 (GE MD-E) 0 0.05 8501
06 Jan 25.00 (GE AE-E) 10.4 10.6 29592 06 Jan 25.00 (GE ME-E) 0 0.05 36948
06 Jan 30.00 (GEAF-E) 5.4 5.6 37746 06 Jan 30.00 (GE MF-E) 0 0.05 139548
06 Jan 32.50 (GEAZ-E) 2.95 3.1 13630 06 Jan 32.50 (GE MZ-E) 0 0.05 69047
36 Jan 35.00 (GEAG-E) 0.7 0.75 146682 06 Jan 35.00 (GE MG-E) 0.3 0.35 140014
06 Jan 40.00 (GEAH-E) 0 0.05 84366 06 Jan 40.00 (GE MH-E) 4.7 4.8 4316
06 Jan 45.00 (GEAI-E) 0 0.05 7554 06 Jan 45.00 (GE Ml-E) 9.7 9.8 767
06 Jan 50.00 (GEAJ-E) 0 0.05 17836 06 Jan 50.00 (GE MJ-E) 14.7 14.8 383
06 Jan 60.00 (GEAL-E) 0 0.05 7166 06 Jan 60.00 (GE ML-E) 24.7 24.8 413
84

Dividend-Paying Stocks (3 of 3)
The put-call parity relationship for puts can be written as

As stated earlier, European options may trade for less than their intrinsic value.
On the next slide, note that all the puts with a strike price of $1400 or higher trade for less than their exercise value.

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Table 20.4 Two-Year Call and Put Options on the S&P 500 Index
Source: Chicago Board Options Exchange at
cboe.com

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GE 35.52 minus 0.02
Dec 21, 2005 @ 11:50 ET Vol 8103000
Calls Bid Ask Open Interest Puts Bid Ask Open Interest
06 Jan 10.00 (GE AB-E) 25.4 25.6 738 06 Jan 10.00 (GE MB-E) 0 0.05 12525
06 Jan 20.00 (GEAD-E) 15.4 15.6 1090 06 Jan 20.00 (GE MD-E) 0 0.05 8501
06 Jan 25.00 (GE AE-E) 10.4 10.6 29592 06 Jan 25.00 (GE ME-E) 0 0.05 36948
06 Jan 30.00 (GEAF-E) 5.4 5.6 37746 06 Jan 30.00 (GE MF-E) 0 0.05 139548
06 Jan 32.50 (GEAZ-E) 2.95 3.1 13630 06 Jan 32.50 (GE MZ-E) 0 0.05 69047
36 Jan 35.00 (GEAG-E) 0.7 0.75 146682 06 Jan 35.00 (GE MG-E) 0.3 0.35 140014
06 Jan 40.00 (GEAH-E) 0 0.05 84366 06 Jan 40.00 (GE MH-E) 4.7 4.8 4316
06 Jan 45.00 (GEAI-E) 0 0.05 7554 06 Jan 45.00 (GE Ml-E) 9.7 9.8 767
06 Jan 50.00 (GEAJ-E) 0 0.05 17836 06 Jan 50.00 (GE MJ-E) 14.7 14.8 383
06 Jan 60.00 (GEAL-E) 0 0.05 7166 06 Jan 60.00 (GE ML-E) 24.7 24.8 413
86

20.6 Options and Corporate Finance
Equity as a Call Option
A share of stock can be thought of as a call option on the assets of the firm with a strike price equal to the value of debt outstanding.
If the firm’s value does not exceed the value of debt outstanding at the end of the period, the firm must declare bankruptcy and the equity holders receive nothing.
If the value exceeds the value of debt outstanding, the equity holders get whatever is left once the debt has been repaid.

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Figure 20.8 Equity as a Call Option

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The x-axis shows the firm asset value in dollars from 0 to 200 in increments of 50 with required debt payment marked at 100. The y-axis shows value in dollars from 0 to 200 in increments of 50. The line for firm assets originates at (0, 0) and runs diagonally through the graph till (200, 200). The line for equity originates (0, 0) and runs parallel to the x-axis till (100, 0) after which it increases and ends at (200, 100).
88

Debt as an Option Portfolio (1 of 2)
Debt holders can be viewed as owners of the firm having sold a call option with a strike price equal to the required debt payment.
If the value of the firm exceeds the required debt payment, the call will be exercised; the debt holders will therefore receive the strike price and give up the firm.
If the value of the firm does not exceed the required debt payment, the call will be worthless, the firm will declare bankruptcy, and the debt holders will be entitled to the firm’s assets.

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Debt as an Option Portfolio (2 of 2)
Debt can also be viewed as a portfolio of riskless debt and a short position in a put option on the firm’s assets with a strike price equal to the required debt payment.
When the firm’s assets are worth less than the required debt payment, the owner of the put option will exercise the option and receive the difference between the required debt payment and the firm’s asset value.
This leaves the debt holder with just the assets of the firm.
If the firm’s value is greater than the required debt payment, the debt holder only receives the required debt payment.

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Figure 20.9 Debt as an Option Portfolio

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The x-axis shows the firm asset value in dollars from 0 to 200 in increments of 50 with required debt payment marked at 100. The y-axis shows value in dollars from 0 to 200 in increments of 50. The line for risk-free bond originates at (0, 100) and runs parallel to the x-axis. The line for firm assets originates at (0, 0) and runs diagonally through the graph till (200, 200). The line for debt originates from (0, 0) and runs diagonally through the graph till (100, 100) after which it runs parallel to x-axis. An arrow marked Less: Put Option is drawn downward from risk free bond to firm assets. An arrow marked Less: Equity Call Option is drawn upward from firm assets to debt.
91

Credit Default Swaps
By rearranging Equation 20.9, we can eliminate a bond’s credit risk by buying the very same put option to protect or insure it:

This put option is called a credit default swap (or C D S).
In a credit default swap, the buyer pays a premium to the seller and receives a payment from the seller to make up for the loss if the bond defaults.

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Textbook Example 20.11 (1 of 3)
Calculating the Yield on New Corporate Debt
Problem
As of September 2012, Google (G O O G) had no debt. Suppose the firm’s managers consider recapitalizing the firm by issuing zero-coupon debt with a face value of $163.5 billion due in January of 2014, and using the proceeds to pay a special dividend. Suppose too that Google had 327 million shares outstanding, trading at $700.77 per share, implying a market value of $229.2 billion. The risk-free rate over this horizon is 0.25%. Using the call option quotes in Figure 20.10, estimate the credit spread Google would have to pay on the debt assuming perfect capital markets.

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Textbook Example 20.11 (2 of 3)
Solution
Assuming perfect capital markets, the total value of Google’s equity and debt should remain unchanged after the recapitalization. The $163.5 billion face value of the debt is equivalent to a claim of

on Google’s current assets.
Because Google’s shareholders will only receive the value in excess of this debt claim, the value of Google’s equity after the recap is equivalent to the current value of a call option with a strike price of $500. From the quotes in Figure 20.10, such a call option has a value of approximately $222.05 per share (using the average of the bid and ask quotes). Multiplying by Google’s total number of shares, we can estimate the total
value of Google’s equity after the recap as

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Textbook Example 20.11 (3 of 3)
To estimate the value of the new debt, we can subtract the estimated equity value from Google’s total value of $229.2
billion; thus, the estimated debt value is

Because the debt matures 16 months from
the date of the quotes, this value corresponds to a yield to maturity of

Thus, Google’s credit spread for the new debt issue would
be about

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Figure 20.10 Google Call Option Quotes and Implied Debt Yields
Given the C B O E call option quotes for Google stock, we can calculate the implied debt yield given perfect markets if Google were to borrow by issuing six-month, zero-coupon bonds. Note the increase in the debt yield with the amount borrowed.

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The table shows the following data:
GOOG (GOOGLE INC) 700.77 minus 5.38
Sep 10 2012 @ 21:39 ET Vol 2560067
Calls Bid Ask Open Int
14 Jan 300.00 (GOOG1418A300-E) 402.9 405.9 4
14 Jan 350.00 (GOOG1418A350-E) 355.3 358 34
14 Jan 400.00 (GOOG1418A400-E) 308.2 311.6 471
14 Jan 450.00 (GOOG1418A450-E) 263 266.5 25
14 Jan 500.00 (GOOG1418A500-E) 220.2 223.9 229
14 Jan 550.00 (GOOG1418A550-E) 181 184.7 122
14 Jan 600.00 (GOOG1418A600-E) 145.2 148.6 303
14 Jan 650.00 (GOOG1418A650-E) 114.3 117.3 292
14 Jan 660.00 (GOOG1418A660-E) 108.5 111.6 63
14 Jan 680.00 (GOOG1418A6SO-E) 97.8 101.7 91
14 Jan 700.00 (GOOG1418A700-E) 87.6 91 508
14 Jan 750.00 (GOOG1418A750-E) 66.2 68.1 534
The line graph shows the implied debt yields.
The x-axis of the graph shows the amount borrowed in billion dollars from 100 to 200. The y-axis shows the debt yield from 0 to 12 percent in increments of 2. The graph shows that the curve starts at (100, 1) and increases to (200, 11).
96

Agency Conflicts (1 of 2)
In addition to pricing, the option characterization of debt and equity securities provides a new interpretation of agency conflicts.
Because equity is like a call option, equity holders will benefit from risky investments.
Debt is a short put option position, so debt holders will be hurt by an increase in risk.
This can potentially lead to an overinvestment problem.

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Agency Conflicts (2 of 2)
When the firm makes new investments that increase the value of its assets, the value of the put option will decline.
Because debt holders are short a put, the value of the firm’s debt will increase, so some fraction of the increase in the value of assets will go to debt holders.
This reduces equity holders’ incentive to invest, possibly leading to a debt overhang (or underinvestment) problem.

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Chapter Quiz (1 of 3)
Does the holder of an option have to exercise it?
Why does an investor who writes (shorts) an option have an obligation?
Explain how you can use put options to create portfolio insurance. How can you create portfolio insurance using call options?

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Chapter Quiz (2 of 3)
If a put option trades at a higher price from the value indicated by the put-call parity equation, what action should you take?
What is the intrinsic value of an option?
How does the volatility of a stock affect the value of puts and calls written on the stock?

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Chapter Quiz (3 of 3)
When might it be optimal to exercise an American put option early?
When might it be optimal to exercise an American call early?
Explain how equity can be viewed as a call option on the firm.
Explain how debt can be viewed as an option portfolio.

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Copyright
This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.

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