OPTIONS MARKETS: INTRODUCTION

Derivative SecuritiesOption contracts are written on common stock, stock indexes, foreign exchange, agricultural commodities, precious metals and interest rate futures

THE OPTION CONTRACTTHE OPTION CONTRACT

A call option gives its holder the right A call option gives its holder the right to purchase an asset for a specified to purchase an asset for a specified price, called exercise, or strike price, price, called exercise, or strike price, on or before some specified expiration on or before some specified expiration date.date.

A put option gives its holder the right A put option gives its holder the right to sell an asset for a specified price, to sell an asset for a specified price, called exercise, or strike price, on or called exercise, or strike price, on or before some specified expiration date.before some specified expiration date.

Example 20.1 Profits and Losses on a Example 20.1 Profits and Losses on a Call Option.Call Option.Value at expiration = Stock price – Value at expiration = Stock price – Exercise price = $23.50 - $22.50 = $1Exercise price = $23.50 - $22.50 = $1Despite the $1 payoff at maturity, the Despite the $1 payoff at maturity, the investor sell realizes a loss of $.15 on the investor sell realizes a loss of $.15 on the call because it cost $1.15 to purchasecall because it cost $1.15 to purchaseProfit = Final value – Original investment Profit = Final value – Original investment = $1 - $1.15 = -$.15 = $1 - $1.15 = -$.15

In the money; describes an option whose In the money; describes an option whose exercise would produce profits. Out of exercise would produce profits. Out of the money describes an option where the money describes an option where exercise would not be profitableexercise would not be profitable

American and European Options

• An American option allows its holder to exercise the right to purchase (if a call) or sell (if a put) the underlying asset on or before the expiration date. European options allow for exercise of the option only on the expiration date.

VALUES OF OPTIONS AT VALUES OF OPTIONS AT EXPIRATIONEXPIRATION

Suppose you hold a call option on IBM stock Suppose you hold a call option on IBM stock with an exercise price of $100, and IBM is now with an exercise price of $100, and IBM is now selling at $110. You can exercise your option selling at $110. You can exercise your option to purchase the stock at $100 and to purchase the stock at $100 and simultaneously sell the shares at the market simultaneously sell the shares at the market price of $110, clearing $10 per share. Yet if price of $110, clearing $10 per share. Yet if the shares sell below $100, you can sit on the the shares sell below $100, you can sit on the option and do nothing, realizing no further option and do nothing, realizing no further gain or loss.gain or loss.

Payoff to call holder = SPayoff to call holder = STT – X if S – X if STT >> X X0 if S0 if STT ≤≤ X XSSTT is the value of the stock at expiration is the value of the stock at expirationX is the exercise priceX is the exercise price

The value at expiration of the call on The value at expiration of the call on IBM with exercise price $100 is given IBM with exercise price $100 is given by the scheduleby the scheduleIBM value:IBM value: $90$90 $100$100 $110$110 $120$120 $130$130

Option value:Option value: 0 0 10 20 300 0 10 20 30

Payoff to call writer = - (SPayoff to call writer = - (STT – X) if S – X) if STT >> X X

0 if S0 if STT ≤≤ XX

Call Option PayoffsCall Option Payoffs

–20

12020 40 60 80 100

–40

20

40

60

Stock price ($)

Op

tion

pay

offs

($) Buy

a ca

ll

Exercise price = $50

50

Call Option PayoffsCall Option Payoffs

–20

12020 40 60 80 100

–40

20

40

60

Stock price ($)

Op

tion

pay

offs

($)

Sell a call

Exercise price = $50

50

Call Option ProfitsCall Option Profits

Exercise price = $50; option premium = $10

Sell a call

Buy a call

–20

12020 40 60 80 100

–40

20

40

60

Stock price ($)

Op

tion

pay

offs

($)

50–10

10

Put optionsPut options

If IBM shares were to fall to $90, a If IBM shares were to fall to $90, a put option with exercise price $100 put option with exercise price $100 could be exercised to clear $10 for its could be exercised to clear $10 for its holder.holder.

Payoff to put holder = 0 if SPayoff to put holder = 0 if STT ≥ ≥ XX

X - SX - STT if S if STT < < XX

Basic Put Option Pricing RelationshipsBasic Put Option Pricing Relationshipsat Expiryat Expiry

At expiry, an American put option is At expiry, an American put option is worth the same as a European option worth the same as a European option with the same characteristics.with the same characteristics.

If the put is in-the-money, it is worth If the put is in-the-money, it is worth X X –– S STT..

If the put is out-of-the-money, it is If the put is out-of-the-money, it is worthless.worthless.

PP = = MaxMax[[X X –– S STT, 0], 0]

Put Option PayoffsPut Option Payoffs

–20

0 20 40 60 80 100

–40

20

0

40

60

Stock price ($)

Op

tion

pay

offs

($)

Buy a put

Exercise price = $50

50

50

Put Option PayoffsPut Option Payoffs

–20

0 20 40 60 80 100

–40

20

0

40

–50

Stock price ($)

Op

tion

pay

offs

($)

Sell a put

Exercise price = $50

50

Put Option ProfitsPut Option Profits

–20

20 40 60 80 100

–40

20

40

60

Stock price ($)

Op

tion

pay

offs

($)

Buy a put

Exercise price = $50; option premium = $10

–10

10Sell a put

50

Selling OptionsSelling Options

Exercise price = $50; option premium = $10 Sell a call

Buy a call

50 6040 100

–40

40

Stock price ($)

Op

tion

pay

offs

($)

Buy a put

Sell a put

The seller (or writer) of an option has an obligation.

The purchaser of an option has an option.

–10

10

Buy a call

Sell a

put

Buy a put

Sell a call

Option versus stock investmentOption versus stock investment

Why would you purchase a call Why would you purchase a call option rather than buy IBM stock option rather than buy IBM stock directly?directly?

- Strategy A:Strategy A:- Strategy B:Strategy B:- Strategy C:Strategy C:

OPTION STRATEGYOPTION STRATEGYProtective put; purchase of stock Protective put; purchase of stock combined with a put option that combined with a put option that guarantees minimum proceeds equal to guarantees minimum proceeds equal to the put’s exercise pricethe put’s exercise priceTable 20.1 Value of Protective Put Portfolio Table 20.1 Value of Protective Put Portfolio at Option Expirationat Option Expiration

SSTT ≤≤ X S X STT >> X X

Stock Stock S ST T SSTT

+ Put+ Put X - S X - ST T 00

Total X STotal X STT

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

ExpiryExpiry

Buy a put with an exercise price of $50

Buy the stock

Protective Put payoffs

$50

$0

$50

Value at expiry

Value of stock at expiry

Protective Put Strategy ProfitsProtective Put Strategy Profits

Buy a put with exercise price of $50 for $10

Buy the stock at $40

$40

Protective Put strategy

$40

$0

-$40

$50

Value at expiry

Value of stock at expiry

-$10

Covered call; a combination of selling Covered call; a combination of selling a call on a stock together with buying a call on a stock together with buying the stockthe stock

Table 20.2 Value of Covered Call Table 20.2 Value of Covered Call Position at Option ExpirationPosition at Option Expiration

SSTT ≤≤ X S X STT >> X X

Payoff of stockPayoff of stock S ST T SSTT

+ Payoff of written call+ Payoff of written call -0 -(S -0 -(ST T – X)– X)

Total STotal ST T XX

Covered Call StrategyCovered Call Strategy

Sell a call with exercise price of $50 for $10

Buy the stock at $40

$40

Covered Call strategy

$0

-$40

$50

Value at expiry

Value of stock at expiry

-$30

$10

Straddle; a combination of buying Straddle; a combination of buying both a call and a put on the same both a call and a put on the same asset, each with the same exercise asset, each with the same exercise price and expiration date. The price and expiration date. The purpose is to profit from expected purpose is to profit from expected volatility. volatility.

Long Straddle: Buy a Call and a Long Straddle: Buy a Call and a PutPut

30 40 60 70

30

40

Stock price ($)

Op

tion

pay

offs

($)

Buy a put with exercise price of $50 for $10

Buy a call with exercise price of $50 for $10

A Long Straddle only makes money if the stock price moves $20 away from $50.

$50

–20

Long Straddle: Buy a Call and a Long Straddle: Buy a Call and a PutPut

–30

30 40 60 70

–40

Stock price ($)

Op

tion

pay

offs

($)

$50

This Short Straddle only loses money if the stock price moves $20 away from $50.

Sell a put with exercise price of$50 for $10

Sell a call with an exercise price of $50 for $10

20

bond

Put-Call Parity: Put-Call Parity: pp00 + + SS00 = = cc00 + + EE/(1+ /(1+ rr))TT

25

25

Stock price ($)

Op

tion

pay

offs

($)

Consider the payoffs from holding a portfolio consisting of a call with a strike price of $25 and a bond with a future value of $25.

Call

Portfolio payoffPortfolio value today = c0 +(1+ r)TE

Put-Call Parity: Put-Call Parity: pp00 + + SS00 = = cc00 + + EE/(1+ /(1+ rr))TT

25

25

Stock price ($)

Op

tion

pay

offs

($)

Consider the payoffs from holding a portfolio consisting of a share of stock and a put with a $25 strike.

Portfolio value today = p0 + S0

Portfolio payoff

Put-Call Parity: Put-Call Parity: pp00 + + SS00 = = cc00 + + EE/(1+ /(1+ rr))TT

Since these portfolios have identical payoffs, they must have the same value today: hence

Put-Call Parity: c0 + E/(1+r)T = p0 + S0

25

25

Stock price ($)

Opt

ion

payo

ffs

($)

25

25

Stock price ($)

Opt

ion

payo

ffs

($) Portfolio value today

= p0 + S0

Portfolio value today

(1+ r)T

E= c0 +

Warrants are essentially call options Warrants are essentially call options issued by a firm. issued by a firm.

One important difference between One important difference between calls and warrants is that exercise of calls and warrants is that exercise of a warrant requires the firm to issue a a warrant requires the firm to issue a new share of stock – the total new share of stock – the total number of shares outstanding number of shares outstanding increasesincreases