<s> TradingOptionsas aProfessional
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TradingOptionsas aProfessionalTECHNIQUES FORMARKET MAKERS ANDEXPERIENCED TRADERS
JAMES B. BITTMAN
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Copyright © 2009 by James B. Bittman. All rights reserved. Except as permitted under the United StatesCopyright Act of 1976, no part of this publication may be reproduced or distributed in any form or byany means, or stored in a database or retrieval system, without the prior written permission of the publisher.ISBN: 978-0-07-164283-5MHID: 0-07-164283-8The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-146505-2,MHID: 0-07-146505-7.All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after everyoccurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of thetrademark owner, with no intention of infringement of the trademark. Where such designations appearin this book, they have been printed with initial caps.McGraw-Hill eBooks are available at special quantity discounts to use as premiums and salespromotions, or for use in corporate training programs. To contact a representative please visit the ContactUs page at www.mhprofessional.com.This publication is designed to provide accurate and authoritative information in regard to the subjectmatter covered. It is sold with the understanding that neither the author nor the publisher is engaged inrendering legal, accounting, or other professional service. If legal advice or other expert assistance isrequired, the services of a competent professional person should be sought.—From a Declaration of Principles jointly adopted by a Committee ofthe American Bar Association anda Committee of Publishers.TERMS OF USEThis is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGraw-Hill”) and its licensorsreserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted underthe Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill’s priorconsent. You may use the work for your own noncommercial and personal use; any other use of the workis strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms.THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF ORRESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATIONTHAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, ANDEXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOTLIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free.Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error oromission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has noresponsibility for the content of any information accessed through the work. Under no circumstancesshall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them hasbeen advised of the possibility of such damages. This limitation of liability shall apply to any claim orcause whatsoever whether such claim or cause arises in contract, tort or otherwise.
For my wife, Laura,Thank you for loving me,and for understanding my passion for trading.For our daughter, Grace,whose joy in discovering the world thrills me every day.And for all traders,who have opened my eyes to the camaraderie of riding the market.I want you all to know that trading is like life. Look for opportunities,weigh the risks, and go with your instincts. Mistakes are inevitable;learn and grow from them. Work hard at it, and enjoy the process. Thatis the path to success.
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DISCLOSURES ANDDISCLAIMERS
hroughout this book, hypothetical examples are used. Althoughthey are meant to represent realistic scenarios, any strategies discussed, including examples using actual securities and/or actual pricedata, are strictly for illustrative and educational purposes only. Theyare not to be construed as an endorsement, recommendation, or solicitation to buy or sell securities or to employ any speciﬁc strategy.In order to simplify computations, commissions and other transaction costs have not been included in the examples used in this book.Commissions will affect the outcome of stock and option strategiesand should be considered in real-world situations. The investor considering options should consult a tax advisor as to how taxes may affectthe outcome of any option transactions.Options involve risk and are not suitable for everyone. Prior to buying or selling an option, a person must receive a copy of Characteristics and Risks of Standardized Options. Copies may be obtained fromyour broker or from Op-Eval, 2406 North Clark Street, Box 154,Chicago, IL 60614. A prospectus, which discusses the role of theOptions Clearing Corporation, is also available without charge onrequest addressed to the Options Clearing Corporation, One NorthWacker Drive, Suite 500, Chicago, IL 60606.
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CONTENTS
Acknowledgments xvIntroduction—Learning to Trade Options as a Professional xviiChapter 1
Option Market Fundamentals 1Fundamental Terms 1The Market—Deﬁnition 1 10The Market—Deﬁnition 2 11National Best Bid and Best Offer 13Margin Accounts and Related Terms 16Proﬁt/Loss Diagrams 19Summary 29
Chapter 2
Operating the Op-Eval Pro SoftwareOverview of Program Features 31Installing the Software 32Choices of Pricing Formulas 34Features of Op-Eval Pro 35The Single Option Calculator 36Calculating Implied Volatility 39The Spread Positions Screen 39Theoretical Graph Screen 42Theoretical Price Table 44The Portfolio Screen 45
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31
x • Contents
The Distribution Screen 46Summary 48Chapter 3
The Basics of Option Price Behavior 49The Insurance Analogy 49Option Pricing Formulas 53Call Values and Stock Prices 54Put Values and Stock Prices 56Call Values Relative to Put Values 59Option Values and Strike Price 60Option Values and Time to Expiration 62Time Decay Is Complicated 64Time Decay and Volatility 64Option Values and Interest Rates 67Option Values and Dividends 69Option Values and Volatility 69Extreme Volatility 71Dynamic Markets 71Three-Part Forecasts 72Trading Scenarios 72Summary 75
Chapter 4
The Greeks 77Overview 77Delta 78Gamma 80Vega 83Theta 85Rho 87How the Greeks Change 89How Delta Changes 92How Gamma Changes 99How Vega Changes 104How Theta Changes 108How Rho Changes 111
Contents • xi
Position Greeks 118Summary 131Chapter 5
Synthetic Relationships 135Synthetic Relationships 135Synthetic Long Stock 137Synthetic Short Stock 139Synthetic Long Call 141Synthetic Short Call 144Synthetic Long Put 146Synthetic Short Put 148When Stock Price ≠ Strike Price 151The Put-Call Parity Equation 153Applying the Effective Stock Price Concept 155The Role of Interest Rates and Dividends 156Summary 160
Chapter 6
Arbitrage Strategies 163Arbitrage—the Concept 163The Conversion 165Pin Risk 167Pricing a Conversion 168Pricing a Conversion with Dividends 173Pricing Conversions by Strike Price 176The Concept of Relative Pricing 177The Reverse Conversion 178Pricing a Reverse Conversion 181Pricing a Reverse Conversion withDividends 185Box Spreads 188The Long Box Spread 188Pricing a Long Box Spread 193The Short Box Spread 196Pricing a Short Box Spread 199Summary 203
xii • Contents
Chapter 7
Volatility 205Volatility Deﬁned 206Historic Volatility 206Another Look at Daily Returns 213Realized Volatility 216The Meaning of “30 Percent Volatility” 216Converting Annual Volatility to DifferentTime Periods 217Calendar Days Versus Trading Days 220Implied Volatility 222Expected Volatility 230Using Volatility 231“Overvalued” and “Undervalued” 232An Alternative Focus 234Volatility Skews 234Summary 238
Chapter 8
Delta-Neutral Trading: Theory and Reality 241Delta-Neutral Deﬁned 242The Theory of Delta-Neutral Trading 247Delta-Neutral Trading—LongVolatility Example 248Delta-Neutral-Trading—ShortVolatility Example 256Simulated “Real” Delta-Neutral Trade 1 263Simulated “Real” Delta-Neutral Trade 2 267Delta-Neutral Trading—Opportunities and Risksfor Speculators 272Delta-Neutral Trading—Opportunities and Risksfor Market Makers 275Summary 277
Chapter 9
Setting Bid-Ask Prices 279The Theory of the Bid-Ask Spread 280The Need to Adjust Bid and Ask Prices 284
Contents • xiii
The Process of Adjusting Bid and Ask Prices 285The Limit on Adjusting Bid and Ask Prices 288Estimating Option Prices as Volatility Changes 290Expressing Bid and Ask Prices in VolatilityTerms 292Trading Exercises Introduced 294Exercise 1: Buying Calls Delta-Neutral 296Exercise 2: Creating a Butterﬂy Spread inThree Trades 298Exercise 3: Creating a Reverse Conversion inTwo Trades 302Exercise 4: Creating a Long Box Spread inTwo Trades 306Summary 310Chapter 10 Managing Position Risk 311Calculating Position Risks 312Managing Directional Risk with Delta 314Vertical Spreads versus OutrightLong Options 320Vertical Spreads—How the Risks Change 321Greeks of Delta-Neutral Positions 327Neutralizing Position Greeks 329Neutralizing Greeks when Interest RatesAre Positive 333Establishing Risk Limits 337Summary 340EpilogueIndex
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ACKNOWLEDGMENTS
his book, like all major projects, is not the product of one person’seffort. Many people assisted me with editing, advice, and encouragement.Anton Karadakov wrote the Op-Eval Pro software that accompaniesthis text. It is more than an update of previous versions. With severalnew features, it is a valuable tool for both advanced traders and beginners. If you are looking for a software developer, Anton has an amazing ability to turn ideas into computer program reality. He can bereached at karadakov@yahoo.com.Lisa Harms edited the entire manuscript and made numerous contributions to both the writing style and the outline. Floyd Fulkersonveriﬁed that numbers in tables and text matched. He also madenumerous suggestions about organization and reinforcing key ideas.Debra Peters, vice president of the CBOE and director of TheOptions Institute, deserves special thanks for allowing me to juggle thework of this book with my main responsibilities of talking to individualinvestors, professional money managers, and brokers. Options are valuable investing and trading tools, and Debra motivates all of us at TheOptions Institute to produce high-quality courses—in person andonline—that spread this message. Visit us at www.cboe.com and clickon “Learning Center.”Jeanne Glasser, my editor at McGraw-Hill, kept her composure andmaintained her enthusiasm while tolerating my delays in submittingthe manuscript.
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xvi • Acknowledgments
My wife, Laura, once again has been extremely understanding andsupportive. She tended to our young daughter alone on too manyweekends while I was holed up in my ofﬁce trying to make the wordsfor this book come out. No more books, honey—for a while.The following people also made contributions in a variety of waysfrom feedback to moral support:William BrodskyEd TillyEd JoyceEd ProvostRichard DufourMarc AllaireMike BellaviaLaura JohnsonBarbara KalickiJames KarlsMichelle KaufmanMarty KearneyPeter LuskShelly NatenbergBrian OverbyDan PassarelliJohn RusinLaurel SorensonGreg StevensFelecia TatumGary Trennepohl
INTRODUCTION—LEARNING TO TRADEOPTIONS AS APROFESSIONAL
f you are a market maker in training or an individual trader who isserious about trading options, there are eight option topics you needto master. These are what I call the eight essentials:
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• Option market fundamentals• Option price behavior, including the Greeks• Synthetic relationships• Pricing arbitrage strategies• Volatility• Delta-neutral trading• Setting bid and ask prices• Managing position riskThis book is intended to give prospective market makers a thoroughgrounding in all advanced topics related to options trading fromvolatility to delta-neutral trading to setting bid and ask prices to managing position risk. For individual traders it will demonstrate how to• xvii •
xviii • Introduction—Learning to Trade Options as a Professional
plan option trades and how to use volatility to estimate stock-priceranges, to pick stock-price targets, and to choose option strike prices.The insights into how market makers think are designed to help individual traders enter orders for outright long and short option tradesand for spreads.Unfortunately, a thorough understanding of each essential topicrequires at least a minimal understanding of one or more of the othertopics. A sequential discussion, therefore, with one topic building onanother, is impossible. Consider, for example, the topics of option pricebehavior and volatility. Because volatility is an intermediate to advancedsubject in options, that chapter follows the discussion of option pricebehavior. Volatility, however, affects an option’s price, so some understanding of volatility is necessary to understand option price behavior.Similarly, volatility and delta-neutral trading possess numerous overlapping concepts. Discussing either one before the other is problematic.Nevertheless, the topics must have some order. When you gain a greaterunderstanding of each topic as you proceed through this book, you mayﬁnd a review of previous chapters to be helpful.The eight essentials will be explained in-depth with examples toillustrate each concept. Chapter 1 assumes a basic level of optionsknowledge and presents only a brief review of market fundamentalsand strategies discussed later. Chapter 1, however, also discusses theintricacies of margin accounts, short stock rebate, and the concept ofthe national best bid and best offer (NBBO). Chapter 2 reviews themany features of the Op-Eval Pro software that accompanies this text,which was used to create the tables and exhibits in all chapters. Thefeatures of the software include tools for analyzing option prices, asking “what if?” questions, evaluating the risk of simple and complexpositions, graphing multilegged positions, and many other criticaltasks performed by option traders.Chapter 3 explains why options have value, how the values changeas market conditions change, and the differences between planningstock trades and planning option trades. Chapter 4 delves deeper into
Introduction—Learning to Trade Options as a Professional • xix
option price behavior by discussing the Greeks: delta, gamma, vega,and theta. These factors explain the impact of various pricing components. If you understand the Greeks, you will grasp the nuances ofadvanced spread strategies.Chapter 5 discusses synthetic relationships, an understanding ofwhich will reinforce your knowledge of option price behavior. Synthetic relationships also can play an important role in risk management. Chapter 6 expands on synthetic relationships, moving up tothe more advanced level of arbitrage strategies, conversions, reverseconversions, and box spreads. Arbitrage is a key element of optionsmarket making.Chapter 7 tackles the concept of volatility. It ﬁrst demonstrateshow historic volatility is calculated and then discusses the dynamics of implied volatility. The review of the statistics involved withexpected stock-price distributions will help to clarify what is theessence of volatility. The chapter ends by introducing the subjectof volatility skew. Chapter 8 presents four in-depth delta-neutraltrading exercises that demonstrate the theory and reality of this strategy and how speculators and market makers might use it. The exercises reveal some important relationships between option prices andstock-price ﬂuctuations.In its discussion of setting and adjusting bid and ask prices,Chapter 9 brings together the topics of volatility and synthetic relationships to illustrate how market makers set bid and ask prices andevaluate alternatives for entering and exiting positions. Chapter 10demonstrates how position Greeks are calculated and how they mightbe used to analyze position risk and to set risk limits. Neutralizing theGreeks, identifying which Greek to emphasize, and determining howto choose risk-reducing trades conclude the discussion.By the end of Chapter 10, the goal is that you will have gainedknowledge about option price behavior, advanced option strategies,and volatility that will increase your trading conﬁdence. Arbitrage,using delta-neutral trading to set and adjust bid and ask prices, and
xx • Introduction—Learning to Trade Options as a Professional
managing position risk are the skills that option market makers intraining need to learn. The insights into volatility and how marketmakers trade are designed to improve the individual trader’s ability toanticipate how option strategies perform.I can be reached at JamesBittman@gmail.com
TradingOptionsas aProfessional
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Chapter 1OPTION MARKETFUNDAMENTALSs stated in the Introduction to this book, a familiarity with optionmarket fundamentals is the ﬁrst of eight essentials that advancedoption traders must master. This chapter reviews brieﬂy the basicterminology of options and then explains the mechanics of marginaccounts, short stock rebate, and calculation of the national best bidand best offer (NBBO). Proﬁt and loss diagrams of four basic strategiesand eight intermediate and advanced strategies are presented withexplanations. A thorough understanding of the mechanics of thesestrategies is a necessary foundation for the discussions in later chapters.
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Fundamental TermsOptions are contracts between buyers and sellers. Option buyers geta limited-time right to buy or sell some underlying instrument at a speciﬁc price. For this right, they pay a premium, or price. The seller ofan option receives payment from the buyer and assumes the obligation to fulﬁll the terms of the contract if the buyer exercises the right.A call option gives the buyer the right to buy the underlying instrument at the strike price until the expiration date. The seller of a calloption is obligated to sell the underlying instrument at the strike priceuntil the expiration date if the call buyer exercises the right to buy.• 1 •
2 • Trading Options As a Professional
A put option gives the buyer the right to sell the underlying instrument at the strike price until the expiration date. The seller of a putis obligated to buy the underlying instrument at the strike price untilthe expiration date if the put buyer exercises the right to sell.The underlying instrument, or, simply, the underlying, can be astock, a futures contract, a physical commodity, or a cash value basedon some index. The strike price, or exercise price, is the speciﬁc priceat which the underlying can be bought or sold, and the expiration dateis the last day that an option can be exercised. After the expiration date,the option contract and the right cease to exist. An option not exercisedby the expiration date expires worthless.As an example, consider an “XYZ December 50 Call” that trades ata price of 3.00. The underlying is “XYZ,” which, in the United States,is typically 100 shares of XYZ stock. “December” indicates the expiration date, which, for stock options traded in the United States, is thethird Friday of the stated month. The strike price of “50” is the priceper share the buyer who exercises the call will pay for that XYZ stock.“3.00” represents the price per share of the option, so the purchaser ofthis option would pay $300 ($3 on 100 shares) to the seller.
Stock Trades Compared with Option TradesStock trades and option trades are similar in many ways, but option tradescan be much more complicated transactions. The amount of information an option trader must convey to a broker is, by itself, signiﬁcantlymore than in a stock trade. To illustrate this difference, the upper sectionof Table 1-1 shows that a typical stock trade requires four pieces of information or decisions, and the lower section shows that a typical optiontrade requires seven pieces of information or decisions.As indicated by the numbers, there are four parts to the stock trader’sinstruction, “Buy long 1,500 XYZ at 63.50.” The ﬁrst part of the instruction describes the action to take. In this example, “Buy long” is theaction. For stock trades, there are four possible actions or types of trades.
Option Market Fundamentals • 3
Table 1-1
Stock Trades versus Option Trades
Stock trade:
Buy long1,500121 Action:Buy longBuy to coverSell longSell short2 Quantity:Number of shares3 Stock name: Ticker symbol4 Price:The price per share
XYZ3
@ 63.504
Option trade:
Buy to open15XYZJan65Calls@ 2.8012345671 Action:Buy to openBuy to closeSell to openSell to close2 Quantity:Number of contracts3 Underlying: Typically 100 shares of the stock*4 Expiration: The Saturday following the third Friday of the stated month5 Strike price: The price per share at which stock is traded if the option isexercised or assigned6 Option type: Call The right to buy the underlying for the option owner and theobligation to sell the underlying for the option writerPut The right to sell the underlying for the option owner and theobligation to buy the underlying for the option writer7 Price:The price per underlying share paid for the option* The underlying instrument of an option contract is typically 100 shares of stock, but there are manyexceptions; for example, after a three-for-two stock split, the underlying might change to 150 shares.Also, for cash-settled options, the underlying is a cash value.
Buy long means that the stock is being newly purchased. Buy to covermeans that a short stock position is being closed. Sell long indicates thata trader wants to close a long stock position. Sell short indicates that atrader wants to create a new short stock position. In a short sale, the brokerage ﬁrm borrows shares on behalf of the trader and sells them in themarket. The stock lender holds the cash proceeds from the sale. Thistype of action will be discussed in greater detail later in this chapter.
4 • Trading Options As a Professional
The second part of the stock instruction represents the quantity tobe bought or sold. In this example, “1,500” is the quantity, or number, of shares being traded. The third part, “XYZ,” is the ticker symbol of the stock being traded. Finally, the last part of the instruction,“at 63.50,” is the price per share at which the stock is to be purchased.Essentially, a stock trader has to decide which stock, the action or typeof trade, how many shares, and at what price to trade them.In the bottom portion of Table 1-1, the option instruction is “Buyto open 15 XYZ Jan 65 Calls at 2.80.” This instruction contains sevenparts. As with stock trades, “Buy to open” describes the action. Alsosimilar to stock trades, option trades may consist of four possibleactions. Buy to open indicates that a new long option position is beingcreated. Buy to close means that an existing short option position isbeing closed. Sell to open indicates that a new short option positionis being created, and Sell to close means that an existing long optionposition is being closed.When a trader sells options to open, a brokerage ﬁrm has no needto borrow anything, unlike with a short sale of stock. Options are simply contracts containing rights and obligations that are created bymutual agreement between buyers and sellers. The payment made byan option buyer is made for the right contained in the contract, notfor ownership of the underlying. The option seller receives cash fromthe buyer in return for assuming an obligation that may or may not befulﬁlled in the future. To demonstrate an ability to fulﬁll the terms ofthe contract, an option seller must deposit cash with the brokerageﬁrm. This deposit is known as a margin deposit and will be discussedin greater detail later in this chapter.The second part of the option instruction, “15,” is the number ofoption contracts being traded. The third part, “XYZ,” is the ticker symbol of the underlying stock. Typically, an option covers 100 sharesof that stock. The fourth part of the instruction consists of the expiration month of the option, and in this example, the options expire in“January.” Options on stocks usually stop trading on the third Friday
Option Market Fundamentals • 5
of the month and expire on the next day, a Saturday. Cash-settledindex options typically stop trading on the Thursday before the thirdFriday, with the ﬁnal settlement value determined by Friday morningopening prices. Option traders can ﬁnd detailed information aboutsettlement procedures from the exchange where an option is traded.The ﬁfth piece of the instruction shown in the bottom portion ofTable 1-1 is “65.” This number is the strike price, or the price at whichthe underlying stock is traded if the option is exercised or assigned.Exercise is the action taken by option owners if they want to invokethe right contained in the option contract. Assignment is the selectionprocess by which a person holding a short option position is chosento fulﬁll the obligation of the short option contract.The word Call denotes the type of option, and “Call” is the sixthcomponent in the instruction. There are, of course, call and putoptions. Finally, the last part of the instruction, “at 2.80,” is the priceper share at which the option is being traded. Assuming that 100 sharesof stock is the underlying, then an option traded at “2.80” actuallycosts $280 plus transaction costs.In addition to the four decisions that a stock trader must make—thestock, the type of trade, how many shares, and the price—option tradersalso must decide on an option’s type, its strike price, and its expirationdate. As will be discussed in later chapters, this seemingly small difference of three more decisions for option traders has profound implications for the range of strategy alternatives, the importance of time inthe market forecast, and the need for a speciﬁc stock price target.
PremiumOption traders commonly refer to the price of an option as the premium, a term that originates from the insurance industry and reﬂectsone of many similarities between the language of options and the language of insurance. The similarities, in fact, extend beyond languagebecause there are many analogies between options and insurance.
6 • Trading Options As a Professional
As will be discussed in later chapters, volatility in options is analogousto risk in insurance, option payoffs are similar to claims paid by insurance policies, and time decay of option values is similar to insurancepremiums varying with length of coverage.The terms buyer, long, and owner are interchangeable, and alldescribe the position of the option purchaser. Hence an option buyeralso can be described as having a “long option position” or as beingan “option owner.”The terms seller, short, and writer are also interchangeable anddescribe the position of the person who is obligated by an option contract. Hence an option seller is described as having a “short position”or as being the “option writer.” The term writer also originates fromthe insurance industry.When an option is traded, the buyer pays the premium to the seller.When an option is exercised, a transaction in the underlying occurs atthe strike price. Consequently, if one XYZ January 50 Call trades at aprice of 3, then the buyer of this call has obtained the right to buy 100shares of XYZ stock at a price of $50 per share until the expiration datein January. For this right, the buyer pays $3 per share ($300 per option)to the seller, who assumes the obligation of selling 100 shares of XYZstock. If the call owner exercises the right, then a stock transactionoccurs; the call owner purchases 100 shares of XYZ stock at $50 per shareand pays $5,000 plus commissions to the call writer, who delivers theshares and receives the payment.The situation for puts is similar. If one QRS August 30 Put tradesat a price of 2, then the buyer of this put has the right to sell 100 sharesof QRS stock at a price of $30 per share until the expiration date inAugust. For this right, the buyer pays $2 per share ($200 per option)to the seller, who assumes the obligation of buying 100 shares of QRSstock. If the owner of the put exercises, then a stock transaction occurs.The put owner sells 100 shares of QRS stock at $30 per share andreceives $3,000 less commissions from the put writer, who buys theshares and makes the payment.
Option Market Fundamentals • 7
The Process of Exercise and AssignmentWhen an option is exercised, a random process, known as assignment,selects an option writer to fulﬁll the terms of the option. An optionowner triggers this process when he or she notiﬁes a brokerage ﬁrm ofan intent to exercise the option. The ﬁrm then notiﬁes the OptionsClearing Corporation (OCC), which is the central clearinghousefor listed options in the United States. The OCC randomly selects abrokerage ﬁrm holding one or more short positions in the option beingexercised. Finally, that ﬁrm selects a customer from among it appropriate option writers, and that customer is given an assignment notice. Theappropriate transfer of cash and shares between the option exerciser andthe assigned option writer completes the transaction.
Categories of OptionsOptions fall into two broad categories, physical-delivery options andcash-settled options. Physical-delivery options require the transfer ofsome underlying instrument when exercise and assignment occur.The underlying for equity options in the United States, for example,is typically 100 shares of stock. The underlying for futures options is