McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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Options

The right but not the obligation…

This chapter explores various options and their payoff structure.

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Basic Options

Put OptionThe right to sell an asset at a specified exercise price on or

before the exercise date

Call OptionThe right to buy an asset at a specified exercise price on or

before the exercise date

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Option Obligations

Buyer Seller

Call option Right to buy asset Obligation to sell asset

Put option Right to sell asset Obligation to buy asset

Does the seller of a call option hope the price of the underlying security moves up or down?

Does the buyer of a put option hope the price of the underlying security moves up or down?

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Option ValueOption Value: The value of an option at expiration is a function of the stock price and the exercise price.

Call Option

Put Option

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Option Value: ExampleOption values given an exercise price of $720

00060$120ValuePut

1206000$0Value Call

840780720660$600PriceStock

What are the payoff limits for call option buyers? Sellers?

What are the payoff limits for put option buyers? Sellers?

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Call Option Value

Call option value (buyer) given a $720 exercise price.

Share Price

Cal

l opt

ion

valu

e

720 840

$120

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Call Option Profit

$20 call option (buyer) given a $720 exercise price

Share Price

Cal

l opt

ion

valu

e

720 840

$100

Profit (buyer): Current Price - Exercise Price - Cost of Call

Profit = ($840 $720) $20 $100

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Call Option ValueCall option payoff (seller) given a $720 exercise price.

Share Price

Cal

l opt

ion

$ pa

yoff

720 840

$-120

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Call Option Profit

$20 call option (seller) given a $720 exercise price:

Share Price

Cal

l opt

ion

$ pa

yoff

720 840

$-120

Profit (Seller): Exercise Price - Current Price + Cost of Call

$-100

Profit = $720 $840 $20 $100

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Call Option: Example

How much must the stock be worth at expiration in order for a call holder to break even if the exercise price is $50 and the call premium

was $4?

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Put Option ValuePut option value (buyer) given a $720 exercise price:

Share Price

Put

opt

ion

valu

e

600 720

$120

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Put Option Profit

$30 put option (buyer) given a $720 exercise price:

Share Price

Put

opt

ion

valu

e

600 720

$90

Profit (buyer): Exercise Price - Current Price - Cost of Put

Profit = $720 $600 $30 $90

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Put Option Value

Put option payoff (seller) given a $720 exercise price.

Share Price

Put

opt

ion

$ pa

yoff

600 720

-$120

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Put Option Profit

$30 put option (seller) given a $720 exercise price.

Share Price

Put

opt

ion

$ pa

yoff

600 720

-$90

Profit (Seller): Current Price - Exercise Price + Cost of Put

Profit = $600 $720 $30 $90

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Put Options: Example

What is your return on exercising a put option which was purchased for $10 with an exercise price of $85? The stock price at expiration is

$81.

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Option Hedging Strategy

Protective Put:

Share Price

Pos

itio

n V

alue Protective Put

Long Put

Long Stock

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Protective Put Value

Share Price

Pos

itio

n V

alue Protective Put

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Call Option Value: Upper and Lower Limits

Stock Price Upper Limit

Lower Limit

(Stock price - exercise price) or 0whichever is higher

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Call Option Value

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Call Option Value

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Black-Scholes Option Pricing Model

OptionC = Ps[N(d1)] - S[N(d2)]e-rt

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Options on Real Assets

Real Options - Options embedded in real assets

Option to ExpandOption to Abandon

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Options on Financial Assets

Executive Stock Options

Warrants

Convertible Bonds

Callable Bonds