April 19, 2022

This week’s reading gives an overview of financial options and describes payoffs to various options strategies. The factors that affect option pri

This week's 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 400-word description in which you discuss and answer the above questions.

Cite and use APA format if you use outside sources.
Describe how this discussion will change your thought process of how you will view business in the future.
Leave a question for peers in your answer.

Berk_DeMarzo_cf5_ppt_20_accessible.pptx

Corporate Finance

Fifth Edition

Chapter 20

Financial Options

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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

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.

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.

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.

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

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

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

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

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

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

Table 20.1 Option Quotes for eBay Stock

Source: Chicago Board Options Exchange at

www.cboe.com

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.

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

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

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?

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.

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

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

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?

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.

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.

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

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.

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

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).

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.

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.

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

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).

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.

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

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.

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.

Figure 20.2 Short Position in a Call Option at Expiration

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).

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?

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:

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).

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.

Figure 20.3 Profit from Holding a Call Option to Expiration

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).

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.

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.

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).

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.

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.

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

• 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).

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.

Figure 20.5 Payoff and Profit from a Straddle

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.

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

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.

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.

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.

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.

Figure 20.6 Butterfly Spread

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).

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

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).

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.

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.

20.3 Put-Call Parity (2 of 4)

Therefore,

Where K is the st

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This week’s reading gives an overview of financial options and describes payoffs to various options strategies. The factors that affect option pri

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