Options

22.1 Options

Many corporate securities are similar to the stock options that

22.1 Options Contracts: Preliminaries

An option gives the holder the right, but

22.1 Options Contracts: Preliminaries

Exercising the Option
The act of buying or selling

Options Contracts: Preliminaries

In-the-Money
The exercise price is less than the spot price

Options Contracts: Preliminaries

Intrinsic Value
The difference between the exercise price of the

22.2 Call Options

Call options gives the holder the right, but not

Basic Call Option Pricing Relationships at Expiry

At expiry, an American call

Call Option Payoffs

-20

100

90

80

70

60

0

10

20

30

40

50

-40

20

0

-60

40

60

Stock price ($)

Option payoffs ($)

Buy a call

Exercise price =

Call Option Payoffs

Write a call

Exercise price = $50

Call Option Profits

Write a call

Buy a call

Exercise price = $50; option

22.3 Put Options

Put options give the holder the right, but not

Basic Put Option Pricing Relationships at Expiry

At expiry, an American put

Put Option Payoffs

-20

100

90

80

70

60

0

10

20

30

40

50

-40

20

0

-60

40

60

Stock price ($)

Option payoffs ($)

Buy a put

Exercise price =

Put Option Payoffs

-20

100

90

80

70

60

0

10

20

30

40

50

-40

20

0

-60

40

60

Option payoffs ($)

write a put

Exercise price = $50

Stock price

Put Option Profits

-20

100

90

80

70

60

0

10

20

30

40

50

-40

20

0

-60

40

60

Stock price ($)

Option profits ($)

Buy a put

Write a put

Exercise

22.4 Selling Options

The seller (or writer) of an option has an

22.5 Stock Option Quotations

22.5 Stock Option Quotations

This option has a strike price of $8;

A

22.5 Stock Option Quotations

This makes a call option with this exercise

22.5 Stock Option Quotations

On this day, 15 call options with this

22.5 Stock Option Quotations

The holder of this CALL option can sell

22.5 Stock Option Quotations

Buying this CALL option costs $2.10.

Since the option

22.5 Stock Option Quotations

On this day, there were 660 call options

22.6 Combinations of Options

Puts and calls can serve as the building

Protective Put Strategy: Buy a Put and Buy the Underlying Stock:

Protective Put Strategy Profits

Buy a put with exercise price of $50

Covered Call Strategy

Sell a call with exercise price of $50 for

Long Straddle: Buy a Call and a Put

Buy a put with

Short Straddle: Sell a Call and a Put

Sell a put with

Long Call Spread

Sell a call with exercise price of $55 for

Put-Call Parity

Sell a put with an exercise price of $40

Buy the

22.7 Valuing Options

The last section concerned itself with the value of

Option Value Determinants

Call Put
Stock price + –
Exercise price – +
Interest rate + –
Volatility

Market Value, Time Value, and Intrinsic Value for an American Call

CaT

22.8 An Option‑Pricing Formula

We will start with a binomial option pricing

Binomial Option Pricing Model

Suppose a stock is worth $25 today and

Binomial Option Pricing Model

A call option on this stock with exercise

Binomial Option Pricing Model

Borrow the present value of $21.25 today and

Binomial Option Pricing Model

The levered equity portfolio value today is

Binomial Option Pricing Model

We can value the option today as half

The Binomial Option Pricing Model

If the interest rate is 5%, the

The Binomial Option Pricing Model

If the interest rate is 5%, the

Binomial Option Pricing Model

the replicating portfolio intuition.

Many derivative securities can be

The Risk-Neutral Approach to Valuation

We could value V(0) as the value

The Risk-Neutral Approach to Valuation

S(0) is the value of the underlying

The Risk-Neutral Approach to Valuation

The key to finding q is to

Example of the Risk-Neutral Valuation of a Call:

Suppose a stock is

Example of the Risk-Neutral Valuation of a Call:

The next step would

Example of the Risk-Neutral Valuation of a Call:

After that, find the

Example of the Risk-Neutral Valuation of a Call:

Finally, find the value

Risk-Neutral Valuation and the Replicating Portfolio

This risk-neutral result is consistent with

The Black-Scholes Model

The Black-Scholes Model is

Where
C0 = the value of a

The Black-Scholes Model

Find the value of a six-month call option on

The Black-Scholes Model

Let’s try our hand at using the model. If

The Black-Scholes Model

N(d1) = N(0.52815) = 0.7013
N(d2) = N(0.31602) = 0.62401

Assume S = $50, X = $45, T = 6 months,

22.9 Stocks and Bonds as Options

Levered Equity is a Call Option.
The

22.9 Stocks and Bonds as Options

Levered Equity is a Put Option.
The

22.9 Stocks and Bonds as Options

It all comes down to put-call

22.10 Capital-Structure Policy and Options

Recall some of the agency costs of

Balance Sheet for a Company in Distress

Assets BV MV Liabilities BV MV
Cash $200 $200 LT bonds $300 ?
Fixed Asset $400 $0 Equity $300 ?
Total $600 $200 Total $600 $200
What happens if

Selfish Strategy 1: Take Large Risks (Think of a Call Option)

The

Selfish Stockholders Accept Negative NPV Project with Large Risks

Expected cash flow

22.11 Mergers and Options

This is an area rich with optionality, both

22.12 Investment in Real Projects & Options

Classic NPV calculations typically ignore

22.13 Summary and Conclusions

The most familiar options are puts and calls.
Put