berk chapter 20: financial options

Copyright © 2011 Pearson Prentice Hall. All rights reserved.

Chapter 20

Financial Options

Copyright © 2011 Pearson Prentice Hall. All rights reserved.20-2

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. 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.

2. Compute the value of a call or a put option at expiration.

3. List the rights and obligations of the buyer of the option and the seller of the option.

4. Use put-call parity to solve for the call premium, the put premium, the stock price, the strike price, or the dividend.

5. Discuss the following factors that influence call and put option values: stock price, strike price, and volatility.


Learning Objectives (cont'd)

6. Describe arbitrage bounds for option prices.

7. 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.

8. Explain the use of option modeling to value equity.

9. 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

• 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 (cont'd)

• 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

• 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 (cont'd)

• 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 (cont'd)

• 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

• 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 Amazon.com Stock


Interpreting Stock Option Quotations (cont'd)

• 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 (cont'd)

• 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


Textbook Example 20.1 (cont'd)


Alternative Example 20.1

• Problem– It is December 30, 2009 and you have decided

to purchase 25 February put contracts on the DJIA with an exercise price of $106.

CallsLast Sale Net Bid Ask Vol

Open Int Puts

Last Sale Net Bid Ask Vol

Open Int

10 Jan 104.00 (DJV1016A104-E) 2.06 -0.03 1.79 2.3 6 5411 10 Jan 104.00 (DJV1016M104-E) 0.71 -0.07 0.6 0.9 164 2712

10 Jan 105.00 (DJV1016A105-E) 1.37 -0.13 1.2 1.62 14 3866 10 Jan 105.00 (DJV1016M105-E) 1.03 -0.07 1 1.3 25 3640

10 Jan 106.00 (DJV1016A106-E) 0.81 -0.11 0.67 1.04 1 1960 10 Jan 106.00 (DJV1016M106-E) 1.44 0 1.5 1.8 0 584

10 Jan 107.00 (DJV1016A107-E) 0.48 -0.09 0.34 0.55 263 4657 10 Jan 107.00 (DJV1016M107-E) 2.2 0.25 1.9 2.3 14 251

10 Feb 104.00 (DJV1020B104-E) 2.76 0 2.8 3.3 0 349 10 Feb 104.00 (DJV1020N104-E) 2.33 0 1.9 2.3 0 54

10 Feb 105.00 (DJV1020B105-E) 2.67 0 2.25 2.66 0 229 10 Feb 105.00 (DJV1020N105-E) 2.6 0.23 2.3 2.7 21 98



DJX (DOW JONES INDU AVG INDEX) 105.49 Dec 30, 2009 @ 17:19 ET



• Problem (continued)

– How much money will this purchase cost you?

– Is this option in-the-money or out-of-the-money?



• Solution

– The ask price is $3.30 per contract.

– The total cost is:• 25 × $3.30 × 100 = $8,250

– Since the strike price exceeds the current price, ($105.49) the put option is in-the-money.


Options on Other Financial Securities

• 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 NYSE index, are also traded.


Options on Other Financial Securities (cont'd)

• 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

• 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

max ( , 0)C S K


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


20.2 Option Payoffs at Expiration (cont'd)

• 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

max ( , 0)P K S



• Problem– You own a put option on Dell stock with an

exercise price of $17.50 that expires today. Plot the value of this option as a function of the stock price.


Alternative Example 20.2 (cont'd)

• Solution– Let S be the stock price and P be the value of

the put option. The value of the option is P= max(12.50 - S,0)


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


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


Returns for Holding an Option to Expiration

• 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 (cont'd)

• 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

(a) The return on the expiration date from purchasing one of the August call options in Table 20.1 on July 8, 2009, and holding the position until the expiration date; (b) the same return for the August put options in the table.


Combinations of Options

• 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


Combinations of Options (cont'd)

• 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



• Butterfly Spread

– A portfolio that is long two call options with differing strike prices, and short two call options with a strike price equal to the average strike price of the first two calls

• While 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



• 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 Amazon 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 Amazon with a strike price of $45 (the green dashed line is the bond payoff).


20.3 Put-Call Parity

• Consider the two different ways to construct portfolio insurance discussed above.– 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 (cont'd)

• 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

( ) S P PV K C



• 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.

( )C P S PV K



• Problem

– Assume:• You want to buy a one-year call option and put option

on Dell.

• The strike price for each is $15.

• The current price per share of Dell is $14.79.

• 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?



• Solution– Put-Call Parity states:

( ) S P PV K C

$15$14.79 $2.23

1.025P

$2.07P



• If the stock pays a dividend, put-call parity becomes

( ) ( )C P S PV K PV Div


20.4 Factors Affecting Option Prices

• 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.


20.4 Factors Affecting Option Prices (cont'd)

• 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.


Arbitrage Bounds on Option Prices

• 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.


Arbitrage Bounds on Option Prices (cont'd)

• 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


Arbitrage Bounds on Option Prices (cont'd)

• Time Value

– The difference between an option’s price and its intrinsic value

• An American option cannot have a negative time value.


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


Option Prices and Volatility

• The value of an option generally increases with the volatility of the stock.


20.5 Exercising Options Early

• Although an American option cannot be worth less than its European counterpart, they may have equal value.


Non-Dividend-Paying Stocks

• 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

( )C P S PV K

Intrinsic value Time value

( ) C S K dis K P


Non-Dividend-Paying Stocks (cont'd)

• Because dis(K) and P must be positive before the expiration date, a European call always has a positive time value.

– Since 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.



• 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.



( ) P K S dis K C


• However, it may be optimal to exercise a put option on a non-dividend paying stock early.



• 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.


Table 20.2 Cisco Option Quotes


Dividend-Paying Stocks

• 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.


( ) ( )C S K dis K P PV Div


Dividend-Paying Stocks (cont'd)

• 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.


Table 20.3 Option Quotes for GE on December 21, 2005



( ) ( )P K S C dis K PV Div

Dividend-Paying Stocks (cont'd)

• 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.


Table 20.4 Two-Year Call and Put Options on the S&P 500 Index


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.


Figure 20.8 Equity as a Call Option


Debt as an Option Portfolio

• 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.


Debt as an Option Portfolio (cont'd)

• 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.


Figure 20.9 Debt as an Option Portfolio


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:

Risk-free debt = Risky debt + Put option on firm assets

• This put option is called a credit default swap (or CDS).• 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.


Figure 20.10 Google Call Option Quotes and Implied Debt Yields


Agency Conflicts

• 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.


Agency Conflicts

• When the firm makes new investments that increase the value of its assets, the value of the put option will decline.

• Since 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.


Discussion of Data Case Key Topic

Instead of a straddle, suppose you recommend a strangle for your uncle, where the call option purchased is the one with the strike price right above the current price, and the put option purchased is the one with the strike price right below the current price. Repeat parts a-f for that option strategy. How does that strategy compare with the straddle? Why? Option prices are at:www.cboe.com www.finra.org


Chapter Quiz

1. Does the holder of an option have to exercise it?2. Why does an investor who writes (shorts) an

option have an obligation?3. Explain how you can use put options to create

portfolio insurance. How can you create portfolio insurance using call options?

4. If a put option trades at a higher price from the value indicated by the put-call parity equation, what action should you take?

5. What is the intrinsic value of an option?


Chapter Quiz

6. How does the volatility of a stock affect the value of puts and calls written on the stock?

7. When might it be optimal to exercise an American put option early?

8. When might it be optimal to exercise an American call early?

9. Explain how equity can be viewed as a call option on the firm.

10.Explain how debt can be viewed as an option portfolio.

berk chapter 20: financial options

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