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Investments: Analysis

and Behavior

Chapter 18- Options Marketsand Strategies

2010 McGraw-Hill/Irwin

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2

Learning Objectives

Understand the characteristics of call and put options

Know the uses of index options

Be able to implement covered call and protective putstrategies

Utilize Black-Scholes option pricing

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3

Options Markets

Derivative securities: value is derived or stemsfrom changes in the value of some other assets.

Call option: the right (but not obligation) to buy

Put option: the right (but not obligation) to sell

Total volume nearly 3 billion contracts in 2007

The most popular options - equity options

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Figure 18.1 Trading Activity in Equity Options Contracts Has Risen Sharply

0

500,000,000

1,000,000,000

1,500,000,000

2,000,000,000

2,500,000,000

3,000,000,000

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

OCCT

otalYearlyClearedC

ontractVolum

Total Contract Volume

Equity Options

Non-Equity Options

Source: O tions Clearin Cor oration

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5

Characteristics of Exchange Traded Options

Four types of underlying assets

Equity securities

Stock indexes

government debt securities

foreign currencies

Have standardized terms

Trading activity is determined by supply and demand

Open interest: number of outstanding options

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Exercise price (orStrike price): Promised

or predetermined price for underlyingassets

At-the-money: when option price equals

current market price of underlying assets

In-the-money: when the strike price is less

(more) than the market price of the underlying

asset for a call (put)

Out-of-money: when the strike price is more(less) than the market price of the underlying

asset for call (put)

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Option premium: price at which the contract

trades (the amount paid for the option)

Long-term Equity AnticiPation Securities

(LEAPS): expiration dates up to three years.

Long-term calls and puts.

Trading symbol for stock options combinationof the stock ticker symbol, plus a letter to indicate

the month of the year, plus a final letter toindicate strike price

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Expiration Months Code

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

Calls A B C D E F G H I J K L

Puts M N O P Q R S T U V W X

Strike Price Codes

A B C D E F G H I J K L M

5 10 15 20 25 30 35 40 45 50 55 60 65

105 110 115 120 125 130 135 140 145 150 155 160 165

205 210 215 220 225 230 235 240 245 250 255 260 265

305 310 315 320 325 330 335 340 345 350 355 360 365

405 410 415 420 425 430 435 440 445 450 455 460 465

505 510 515 520 525 530 535 540 545 550 555 560 565

605 610 615 620 625 630 635 640 645 650 655 660 665

705 710 715 720 725 730 735 740 745 750 755 760 765

N O P Q R S T U V W X Y Z

70 75 80 85 90 95 100 7.50 12.50 17.50 22.50 27.50 32.50

170 175 180 185 190 195 200 37.50 42.50 47.50 52.50 57.50 62.50

270 275 280 285 290 295 300 67.50 72.50 77.50 82.50 87.50 92.50

370 375 380 385 390 395 400 97.50 102.50 107.50 112.50 117.50 122.50

470 475 480 485 490 495 500 127.50 132.50 137.50 142.50 147.50 152.50

570 575 580 585 590 595 600 157.50 162.50 167.50 172.50 177.50 182.50

670 675 680 685 690 695 700 187.50 192.50 197.50 202.50 207.50 212.50

770 775 780 785 790 795 800 217.50 222.50 227.50 232.50 237.50 242.50

Table 18.2 Option Ticker Codes

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Options Clearing Corporation (OCC)

Sole issuer of all securities options listed onexchanges and NASD

All option transactions are ultimately clearedthrough OCC

OCC takes the opposite side of every optiontraded

Guarantees contract performance and reducesthe credit risk.

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Option concept

Option contracts are a zero sum game

before commissions and other transaction

costs.

Hedged position: option transaction to offsetthe risk inherent in some other investment (tolimit risk)

Speculative position: option transaction to profitfrom the inherent riskiness of some underlyingasset.

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Option style and settlement

Option holder: long the option position Option writer: short the option position

StyleAmerican style option: exercised at any time (All stock options in

the US)

European style option: only exercised on the expiration date.

Delivery Physical delivery option: actual delivery of the underlying asset

takes place

Cash-settle option: cash payment based on difference betweenexercise price and current determined price of the underlyingasset

Contract size: usually for 100 shares of stock

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Option types

Stock Options: generally cover 100 shares ofunderlying securities. Adjustment made for stockdividend, stock split, merger, etc.

Index options: Standard and Poors 100 Index(OEX) are the most actively traded.

Debt OptionsPhysical delivery price-based options: right to

purchase (sell) a debt security

Cash settled price-based options: right to receive

cash based on the value of debt securityYield based options: cash settled based on the

difference between the exercise price and value of anunderlying yield.

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Index

Index

Value CALL Last

Volum

e

Open

Interest PUT Last Volume

Open

Interest

S&P 100 581.85 Aug 580.0 8.90 1124 2994 Aug580.0 9.60 1917 3873

Dow Jones Industrial

Average 113.11 Aug 112.0 2.45 4034 3382 Aug112.0 1.02 50 4217

Nasdaq-100 1809.84 Aug 1825 26.00 471 2312 Aug 1825 43.00 185 4041

Russell 2000 708.6 Sep 710.0 26.70 372 11474 Sep710.0 28.15 257 10328

Source: www.cboe.com

Table 18.3 Sample of Index Options, August 4, 2008

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Call Option strategies

Long position: the right (but not obligation) tobuy the underlying asset at a strike price for alimited period of time.

The right to buy stock at a fixed price becomes morevaluable as price of stock increases (in the moneywhen current stock price > exercise price)

Risk for buyer is limited to the call premium andpotential is unlimited

Short position: payoff mirror image of longposition (zero sum game)

Covered call: sale of a call option on a stock thatis owned.

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Put option strategies

Long position: the right, but not obligation, to sell

an underlying asset at strike price.

The right to sell stock at a fixed price becomes

valuable as price of the stock decreases (in themoney when current price < exercise price)

Risk for buyer is limited to the premium and profit is

also limited (price cannot be below zero)

Short position: mirror image of long position, butinvolves obligation to transact if buyer so

chooses.

Protective put: insurance against a sharp

correction. Purchase of a stock and put option

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Combinations Spread: both buyer and writer of the same type

of option on the same underlying asset

Price spread: purchase or sale of options on the

same underlying asset but different exercise price

Time spread: purchase or sale of options on the sameunderlying asset but different expiration dates

Bull call spread: purchase of a low strike price

call and sale of a high strike price call.

Bull put spread: sale of high strike price put andpurchase or a low strike price put

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PayoffLong call

Short call

Bull call spread

PayoffLong put

Short put

Bull put spread

Payoff

Long call Short put

Straddle

Straddle : purchasing a call and

Writing a put on the same asset,

exercise price, and expiration date

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Option pricing

Factors contributing value of an option price of the underlying stock

time until expiration

volatility of underlying stock price

cash dividend

prevailing interest rate.

Intrinsic value: difference between an in-the-moneyoptions strike price and current market price

Time value: speculative value.

Call price = Intrinsic value + time value

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Black-Scholes Option Pricing Model

Where C: current price of a call option

S: current market price of the underlying stock

X: exercise price

r: risk free rate

t: time until expiration

N(d1) and N (d2) : cumulative density functions for d1 and d2

)()( 21 dNe

XdNSC

rt

fundsinvestedof

costyOpportunit

potentialupside

ofValue

price

Call

t

trXSd

2

1

5.0ln tdd 12

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ExampleCurrent stock price: 50 exercise price : 55

Risk free rate: 6.25% time to expiration: 6 monthsVolatility: 40% What is the call price?

Solution

0851.02828.0

0713.00953.0

5.04.0

5.04.05.00625.05550lnd

2

1

3679.0

5.04.00851.0d2

N(d1) = 0.4661 N(d2) = 0.3564

30.4$]3564.0[55

]4661.0[50

)()(priceCall

)5.0)(0625.0(

21

e

dNe

XdNS

rt

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Put call parity

Relationship between the price of a putoption and the price of a call option on the

same underlying equity.

Using the same values before,

CSrteXpricePut

61.7$30.450e

55pricePut.5)(0.0625)(0

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Option risks

Delta: the sensitivity of option value to a unitchange in the underlying asset (hedge ratio)

Gamma: The responsiveness of delta to unitchanges in the value of the underlying asset

Theta: The sensitivity of option value tochange in time

Vega: The sensitivity of option value to changein volatility

Rho: The sensitivity of option value to changesin interest rate

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Such values are presented in CBOE Option

Calculator ( www.cboe.com )

http://www.cboe.com/http://www.cboe.com/

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VIX

If you know the price of the option, youcan calculate the volatility that the priceimplies, called implied volatility.

The VIX is the scaled implied volatility ofthe S&P 500 Index option.

Say the VIX is at 22.06

Means the S&P500 index is expected tomove by 6.35% (= 22% 12) in the nextmonth.

The VIX is known as the fear index and is

a tradable product