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OPTIONVOLATILITY
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Advanced Trading
     
 
Strategies and Techniques
McGraw-Hill
New York San Francisco Washington, D.C. Auckland BogotaCaracas Lisbon London Madrid Mexico City MilanMontreal New Delhi San Juan Singapore
Sydney Tokyo Toronto© 1994, Richard D. Irwin, a Times Mirror Higher Education Group, Inc.company
ALL RIGHTS RESERVED. No part of this publication may be reproduced,stored ina retrieval system, or transmitted, in any form or by any means, elec-tronic, mechanical, photocopying, recording, or otherwise, without the priorwritten permission of the publisher and the authors.
This publication is designed to provide accurate and authoritative informationin regard to the subject matter covered. It is sold with the understanding that theauthor and the publisher are not engaged in rendering legal, accounting, orother professional advice.
ISBN 1-55738-486-X
Printed in the United States of America
BB
22 21 20 19 18 17
CB/TAQ/BIS
McGraw-HillA Disiston of The McGraw-Hill CompantesTo Paul, for convincing me to become an options trader;To Hen and Jerry, for their financial help when | needed it;
To Eddie, who encouraged me to finish the book andget off the computer so he could do his homework;
And most of all to Leona, for her support and encouragement.¢ Table of Contents +
Preface to the First EditionPreface to the Second Edition
e1¢
The Language of Options
Contract SpecificationsExercise and AssignmentMarket Integrity
Margin RequirementsSettlement Procedures
e2¢
Elementary Strategies
Simple Buy and Sell StrategiesRisk/Reward CharacteristicsCombination StrategiesConstructing an Expiration Graph
o3%
Introduction to Theoretical Pricing Models
Expected ReturnTheoretical Value
A Word on Models
A Simple ApproachExercise Price
Time to ExpirationPrice of the UnderlyingInterest RatesDividends
Volatilityvi Table of Contents
oat
Volatility 51Random Walks and Normal Distributions 51Mean and Standard Deviation 56Underlying Price as the Mean of a Distribution 60Volatility as a Standard Deviation 60Lognormal Distributions 61Daily and Weekly Standard Deviations 65Volatility and Observed Price Changes 67A Note on Interest Rate Products 68Types of Volatilities 69eo 5%
Using an Option’s Theoretical Value 8176%
Option Values and Changing Market Conditions 95The Delta 99The Gamma 103The Theta 111The Vega or Kappa 113The Rho 116Summary 118e7%
Introduction to Spreading 127What Is a Spread? 127Why Spread? 132Spreading as a Risk Management Tool 133eB
Volatility Spreads 137Backspread (also referred to as a ratio backspread or long ratio spread) 138Ratio Vertical Spread (also referred to as a ratio spread, short ratio spread,
vertical spread, or front spread) 139Straddle 141
Strangle 143Table of Contents vii
Butterfly 145Time Spread (also referred to as a calendar spread or horizontal spread) 148The Effect of Changing Interest Rates and Dividends 154Diagonal Spreads 157Other Variations 157Spread Sensitivities 159Choosing an Appropriate Strategy 161Adjustments 168Entering a Spread Order 16979%
Risk Considerations 173Choosing the Best Spread 173Practical Considerations 181How Much Margin for Error? 187Dividends and Interest 188What Is a Good Spread? 192Adjustments 193A Question of Style 195Liquidity 196#104
Bull and Bear Spreads 199Naked Positions 199Bull and Bear Ratio Spreads 199Bull and Bear Butterflies and Time Spreads 201Vertical Spreads 202#11 %
Option Arbitrage 213Synthetic Positions , 213Conversions and Reversals 217Arbitrage Risk 223Boxes 228Jelly Rolls 231Using Synthetics in Volatility Spreads 233
Trading without Theoretical Values 235vitt
124%Early Exercise of American OptionsFutures OptionsStock OptionsThe Effect of Early Exercise on Trading Strategies
a I
Hedging with OptionsProtective Calls and PutsCovered WritesFencesComplex Hedging StrategiesPortfolio Insurance
© 144%Volatility RevisitedSome Volatility CharacteristicsVolatility ForecastingA Practical ApproachSome Thoughts on Implied Volatility
e154Stock Index Futures and OptionsWhat Is an Index?Calculating an IndexReplicating an IndexStock Index FuturesIndex ArbitrageIndex OptionsBiases in the Index Market
+ 16%
Intermarket SpreadingAn Intermarket HedgeVolatility RelationshipsIntermarket Volatility SpreadsOptions on Spreads
Table of Contents
241241243250
257258260263205268
273273279282290
301301302304305309313326
331335336339351Table of Contents ix
17%
Position Analysis 353Some Simple Examples 353Graphing a Position 358A Complex Position 367Futures Option Positions 372218%
Models and the Real World 385Markets Are Frictionless 386Interest Rates Are Constant over the Life of an Option 388Volatility Is Constant over the Life of the Option 390Trading Is Continuous 304Volatility Is Independent of the Price of the Underlying Contract 399
Over small periods of time the percent price changes in an underlyingcontract are normally distributed, resulting in a lognormal distribution
of underlying prices at expiration 400Skewness and Kurtosis 402Volatility Skews 405A Final Thought 416“ Appendix A *
A Glossary of Option and Related Terminology 419* Appendix B +
The Mathematics of Option Pricing 431Option Pricing Models 431Normal Distributions 439Volatility Calculations 442The Extreme Value Method 443The Exponential and Natural Logarithm Functions 446Appendix C +
Characteristics of Volatility Spreads 449
* Appendix D #What’s the Right Strategy? 451x Table of Contents
“+ Appendix E +
Synthetic and Arbitrage Relationships 453Arbitrage Values for European Options (no early exercise permitted) 455Other Useful Relationships: 456
> Appendix F
Recommended Reading 457Elementary Books 457Intermediate Books 459Advanced Books 461
“ Index + 463« Preface to the First Edition +
Within the last decade trading options has increased at an explosive rate. Not only havetraditional market participants, speculators, hedgers, and arbitrageurs all become ac-tively involved in option markets, but the number of individual floor traders willing torisk their own capital in these markets has grown dramatically. Yet the trader enteringan option market for the first time may find that his initial efforts are less than totallysuccessful. Indeed, the learning period in options during which a trader gains fullconfidence in his ability to survive and thrive under all types of market conditions mayrequire many months or even years of trading experience. Unfortunately, the greatmajority of traders do not survive this learning period. The usual characteristics ofoptions, the subleties of the marketplace, and the unforseen risks, all seem to conspireagainst the inexperienced trader and eventually lead to his demise.
Much of the pain experienced by a new trader could be avoided if the trader werebetter prepared for the realities of option trading. Unfortunately, existing option litera-ture has tended to take either a highly theoretical approach best suited to an academicenvironment, or a simplistic approach presenting options as just another way of tradingstocks or commodities. Neither approach is likely to meet the needs of the serious trader.The former approach is not only mathematically beyond the capabilities of most traders,but relies heavily on theoretical assumptions which are too often violated in the realworld. The latter approach cannot possibly prepare a serious trader for the wide varietyof strategies with which he must be familiar, nor with the very real risks to which hewill be exposed.
This book was written with the hope of filling the void in the traditional optionliterature by combining theory and real-world practice. Moreover, it was writtenPrimarily with the serious trader in mind. This includes traders whose firms are activelyInvolved in option markets, either by choice or by necessity, or individual traders whowish to make the most of the opportunities offered by options. This is not meant todiscourage those who are casually or peripherally involved in options markets fromTeading this book. Additional insight into any subject is always worthwhile. Butunderstanding options requires substantial effort. The serious trader, because hislivelihood often depends on this understanding, wil! usually be more willing to investthe time and energy required to attain this goal.
; In preparing the reader for the option marketplace, the author has tried to combinean iMtuitive approach to option theory with a discussion of the real-life problems withWhich he will be confronted. Of course, the reader who is comfortable with mathemat-Ics is in no way discouraged from delving more deeply into the theory of option pricing
xtxii Preface
in many of the excellent academic presentations of the subject. But the important pointis that such a rigorous opproach is not necessary for success in option trading. Indeed,the great majority of successful option traders have never even looked at a mathematicalpresentation of option theory. Nor would many of them be capable of understandingthe complex mathematics if they did.
Much of the presentation in this book will necessarily be colored by the author’spersonal experiences as a floor trader. Sophisticated hedging strategies, such as portfolioinsurance, and complex intermarket spreading strategies are touched upon only briefly,if at all. Yet the principles of option evaluation which enable a floor trader to successfullyparticipate in an option market are the same principles which will enable any participantto make the best use of options, regardless of the reasons for entering the market.Additionally, the author is able to place special emphasis on a lesson which floor tradersquickly learn but which casual traders too often forget. Without a very healthy respectfor the risks of option trading and a full understanding of risk management techniques,today’s profits can quickly turn into tomorrow’s losses.
Because of the more recent introduction of listed options on futures contracts andthe increased interest in these markets, the author has tended to concentrate theexamples in the text on these options. However, the principles which lead to successin futures options are equally valid in commodity, stock, and index option markets.
The core material in this book was developed in classes taught by the author totraders at the Chicago Board of Trade. In expanding the material into book form theauthor has tried to draw on a wide variety of other sources. Foremost among these arethe many floor traders who offered their comments and criticisms. In addition, specialthanks go to Greg Monroe of the Chicago Board of Trade Education Department andMark Rzepczynski of the Chicago Mercantile Exchange Research Department for theircomments on the text, and to David Isbister of Monetary Investments International forpreparation of some of the values used in the tables.
Finally, my thanks to the staff at Probus Publishing for their encouragement,patience, and assistance in dealing with a first time author.
Sheldon NatenbergChicago+ Preface to the Second Edition +
In 1986, when I first discussed with Probus Publishing the idea of an option book forprofessional traders, there was considerable doubt as to whether there would besufficient interest to justify publication of such a book. After all, how many professionaloption traders are there? To everyone’s (pleasant) surprise, when the book came out notonly did it turn out that a large number of professionals were purchasing the book, butmany non-professionals also seemed to be very interested in this approach.
The revised edition is no different in its focus. The new material is likely to be ofgreatest interest to the serious option trader. While the material may also be of interestto the non-professional, it is the professional, whose livelihood depends on a completeunderstanding of options, who will be most willing to spend the time required to masterthe material.
In the new edition J have tried to incorporate the comments and suggestions whichtraders have made concerning the first edition. Some of the more important additions:
Expanded coverage of stock options—When I sat down to write the first editionthe emphasis was on commodity options. This was primarily a marketing decision. Atthe time there were several books available on stock options, but hardly any commodityoptions. However, with the success of the first edition, and at the suggestion of manyfriends at the CBOE, I felt it would be worthwhile giving stock options equal emphasis.
More on volatility—Given its importance, a second chapter on volatility has beenadded with more detailed discussion of volatility characteristics and considerations.
A chapter on stock index futures and options—These markets have become so
important, and are so interconnected, that some discussion is mandatory in any bookon options. While one chapter cannot possibly cover every aspect of index markets, Ihave tried to touch on how these markets differ from traditional option markets, andthe effect of these differences on trading strategies.___ A discussion of intermarket spreading—Much of the most sophisticated tradinginvolves spreading options in one underlying market against options in a differentunderlying market. I have included a discussion on the relationship between similarunderlying markets, and the methods traders use to construct spreads when a relation-ship appears to be mispriced.
A more detailed discussion of volatility skews—This is probably the one area aboutWhich I am most often asked, the tendency of different exercise prices to trade atdifferent implied volatilities. I have tried to include a discussion of this phenomenon,and several methods by which traders deal with this problem.
xiiixiv Preface
I have also deleted two appendicies:
A guide to software—New software is being introduced so quickly that it did notseem practical to include a list of vendors and products as | did in the first edition. Noram I familiar with every piece of software available, so it would be unfair to thosevendors who have good products but whom I might inadvertantly omit. The best wayfor traders to choose software is to talk to other traders and to read some of the industryperiodicals to find out what programs are being used to evaluate options.
Historical volatilities—When the first edition came out I suspected that some newtraders might not have access to any volatility data, so I included some historicalvolatility graphs for selected futures contracts. Now, however, volatility data in someform is available to almost all option traders so I did not feel that volatility charts, whichwould quickly become outdated, would be worth including.
As in the first edition, I make no claims to being a theoretician, and this book is notintended to take the place of a good book on option theory. But theory is only importantas a means to an end—the actual trading of options in the marketplace. Whatever theoryis in the book, | have tried to present in non-technical language. For a more completediscussion of option pricing theory, the reader can consult any of the advanced booksto be found in Appendix F.
Nor is it my intention to make decisions for the reader or to tell the reader how totrade. There are many ways to trade successfully in an option market. Regardless of atrader’s own style, without a complete familiarity with the necessary tools, and aproficiency in their use, it is almost impossible to be successful in options. I have triedto explain what these tools are, how they work, and the variety of ways in which tradersuse them to make decisions that fit their own individual needs and trading styles. Indoing so, I have attempted, as much as possible, to avoid contaminating the reader withmy own personal preferences and prejudices.
In a sense, nothing in either this or the first edition of Option Volatility and PricingStrategies is new. All the theory, trading strategies, and risk management considera-tions, are familiar to experienced traders in one form or another. My goal has been toput all this material together and present it in an orderly, easily understandable formatwhich I hope will form a solid foundation upon which an aspiring option trader canbuild a successful career.
This book is a result not only of my efforts, but of the efforts of the many traderswho were kind enough to read this material and offer their comments and suggestions.Without their help I could not hope to cover all the important aspects of options. To allof them, and to the editors at Probus Publishing Company, who displayed patienceabove and beyond the call of duty, I offer my thanks and enduring gratitude.
Sheldon NatenbergChicagoJune 1994Ye 1 &
The Language of Options
Every option market brings together traders and investors with different expectationsand goals. Some enter the market with an opinion on which direction prices will move.Some intend to use options to protect existing positions against adverse price move-ment. Some hope to take advantage of price discrepancies between similar or relatedproducts. Some act as middlemen, buying and selling as an accommodation to othermarket participants and hoping to profit from the difference between the bid and askrice.
, Even though expectations and goals differ, every trader’s education must beginwith an introduction to the terminology of option trading, and to the rules andregulations which govern trading activity. Without a facility in the language of options,a trader will find it impossible to communicate his desire to buy or sell in themarketplace. Without a clear understanding of the terms of an option contract, and hisrights and responsibilities under that contract, a trader cannot hope to make the bestuse of options, nor will he be prepared for the very real risks of trading,
CONTRACT SPECIFICATIONS
Options are of two types. A call option is the right to buy or take a long position in agiven asset (typically a security, commodity, index, or futures contract) at a fixed priceon or before a specified date. A put optionis the right to sell or take a short position ina given asset.
Note the difference between an option and a futures contract. A futures contractTequires delivery at a fixed price. The buyer and seller of a futures contract both haveobligations which they must meet. The seller must make delivery and the buyer musttake delivery of the asset. The buyer ofan option, however, has a choice. He can chooseto take delivery (a call) or make delivery (a put). If the buyer of an option chooses toeither make or take delivery, the seller of the option is obligated to take the other side.In option trading all rights lie with the buyer and all obligations with the seller.
The asset to be bought or sold under the terms of the option is the underlying assetOr, More simply, the underlying. The exercise price, or strike price, is the price at whichthe underlying will be delivered should the holder of an option choose to exercise hisTight to buy or sell, The date after which the option may no longer be exercised is theexpiration date.2 Chapter I
If an option is purchased directly from a bank or other dealer, the quantity of theunderlying to be delivered, the exercise price, and the expiration date can all be tailoredto meet the buyer’s individual requirements. If the option is purchased on an exchange,the quantity of the underlying to be delivered, as well as the exercise price andexpiration date, are predetermined by the exchange.!
As an example of an exchange traded option, the buyer of a crude oil October 21call on the New York Mercantile Exchange has the right to take a long position in oneOctober crude oil futures contract for 1,000 barrels of crude oil (the underlying), at aprice of $21 per barrel (the exercise price), on or before October expiration (theexpiration date). The buyer of a General Electric March 80 put on the Chicago BoardOptions Exchange has the right to take a short position in 100 shares of General Electricstock (the underlying) at a price of $80 per share (the exercise price}, on or before Marchexpiration (the expiration date).
Since stock has no expiration date, the underlying asset for a stock option is simplysome number of shares in the underlying stock. In the case of futures options, however,the situation can be somewhat confusing, since a futures contract has a limited life span.The underlying asset for an option on a futures contract is usually the futures monthidentical to the expiration month of the option. The underlying asset for a crude oilOctober 21 call on the NYMEX is one October crude oil futures contract. Theunderlying asset fora Treasury Bond June 96 put on the Chicago Board of Trade is oneJune Treasury Bond futures contract.
Some futures exchanges also list serial options, whereby options with differentexpiration dates have identical underlying futures contracts. When there is no futurescontract with the same expiration month as the option, the underlying contract for thatoption is the nearest futures contract after the expiration of the option. For example,the underlying for a December Deutschemark option on the Chicago MercantileExchange is one December Deutschemark futures contract. With no October orNovember futures contract available, the underlying for an October or NovemberDeutschemark option is also one December futures contract. December is the nearestfutures month after the expiration of October and November options.
Expiration dates for exchange traded contracts are not uniform, but are set by eachindividual exchange. The expiration date for stock options in the United States is usuallythe third Saturday after the third Friday of the expiration month. For options on futurescontracts, however, the expiration need not coincide with the delivery month specifiedin the option contract. In some cases the exact expiration date for a futures option canpredate the delivery month of the underlying futures contract by several weeks. A crudeoil option on the NYMEX will typically expire the first Saturday of the preceding month,so that an October option will actually expire the first Saturday in September.
1. Several exchanges have recently introduced flex options, which permit the buyer and seller to negotiateboth the exercise price and expiration date. These are still considered exchange traded options sincethe contracts are guaranteed by the exchange.The Language of Options 3
Figure 1-1: Contract Specifications
Crude Oil* October 2i1 Call| Expiration Exercise |
Underlying Date Price TypeGE March 80 Put
*If this is a futures option, the underlying is a futures contract rather than the physical commodity.
 
Figure 1-2: An Option Buy Order
 4 Chapter I
Figure 1-3: An Option Sell Order
 
EXERCISE AND ASSIGNMENT
A trader who owns a call or a put option has the right to exercise that option prior toits expiration date, thereby converting the option into a long underlying position, in thecase of a call, or a short underlying position, in the case of a put. A trader who exercisesa crude oil October 21 call has chosen to take a long position in one October crude oilfutures contract at $21 per barrel. A trader who exercises a GE March 80 put has chosento take a short position in 100 shares of GE stock at $80 per share. Once an option isexercised it ceases to exist, just as if it had been allowed to expire unexercised.
A trader who intends to exercise an option must submit an exercise notice to eitherthe seller of the option, if purchased from a dealer, or to the guarantor of the option, ifpurchased on an exchange. When a valid exercise notice is submitted, the seller of theoption is assigned. Depending on the type of option, he will pe required to take a longor short position in the underlying contract at the specified exercise price.
In addition to its underlying contract, exercise price, expiration date, and type, anoption is further identified by the conditions of exercise. An option is either American,The Language of Options
Figure 1-4: The Exercise and Assignment Process
> —_-———— | Clearing House | —————>
 
Clearing firm notifies theclearing house that thebuyer wishes to exercise
eeBuyer's Clearing Firm
t
Buyer notifies his clearing firmthat he wishes to exercise hisoption thereby taking @ long(call) or short (put) position
in the underlying instrumentat the exercise price
'
 
 
Holder of a LongOption Position(Buyer)
Figure 1-5: An Exercise Notice
 
Clearing house chooses a
seller at random and notifiesthe seller's clearing firm thatthe seller has been assigned
| Seller's Clearing Firm
Seller is notified by his clearingfirm that he has been assigned,and that he now has a short(call) or long (put) position
in the underlying instrument
at the exercise price
Y
Holder of a ShortOption Position(Seller)
      
 
 
 
 
 
 
 
 
___DATE EXERCISE __TIME STAMPNOTICEPUTQTy STK/COMM MONTH once ror bAY10 DM Mar 5 |" x Initials: SOHNAccount #Firm #Broker #
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Per
 
 6 Chapter I
Figure 1-6: An Assignment Notice
 
 
 
 
 
 
 
 
_ DATE ASSIGNMENTNOTICEQTy STK/COMM MONTH once PUT CALL15 [Gude Ort} Oct 8 xInitials: RIN5 |7-Bonds | Dec 1 |X Account #Firm #
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
whereby the holder can exercise the option at any time prior to expiration, or European,whereby the holder can exercise the option only on expiration day.2 The great majorityof exchange traded options throughout the world are American options, carrying withthem the right of early exercise. Indeed, all U.S. exchange traded stock and futuresoptions are American?
As in any competitive market, an option’s price, or premium, is determined bysupply and demand. Buyers and sellers make competitive bids and offers in themarketplace. When a bid and offer coincide, a trade is made. The premium paid for anoption can be separated into two components, the intrinsic value and the time value.An option’s intrinsic value is the amount which would be credited to the option holder’saccount if he were to exercise the option and close out the position against theunderlying contract at the current market price. For example, with gold trading at $435per ounce, the intrinsic value of a $400 call is $35. By exercising his option, the holderof the $400 call can buy gold at $400 per ounce. If he sells gold at the market price of
2. Since exchanges need time to process exercise and assignment notices, the holder of an exchangetraded option must usually submit an exercise notice no later than the close of business on the day priorto expiration.
3. Certain index options, such as the S&P 500 traded on the Chicago Board Options Exchange, and theMajor Market traded on the American Stock Exchange, are European. Some foreign currency optionstraded on the Philadelphia Stock Exchange are also European.
 the Language of Options 7
$435 per ounce, $35 per ounce will be credited to his account. With a certain stocktrading at $62, the intrinsic value ofa $70 put is $8. By exercising his option, the holderof the put can sell the stock at $70 per share. If he then buys the stock back at the marketprice of $62, he will show a total credit of $8.
A call will only have intrinsic value if its exercise price is less than the currentmarket price of the underlying contract. A put will only have intrinsic value if its exerciseprice is greater than the current market price of the underlying contract. The amountof intrinsic value is the amount by which the call’s exercise price is less than the currentunderlying price, or the amount by which the put’s exercise price is greater than thecurrent underlying price. No option can have an intrinsic value less than zero.
Usually an option’s price in the marketplace will be greater than its intrinsic value.The additional amount of premium beyond the intrinsic value which traders are willingto pay for an option is the time value, sometimes also referred to as the option’s timepremium or extrinsic value. As we shall see, market participants are willing to pay thisadditional amount because of the protective characteristics afforded by an option overan outright long or short position in the underlying contract.
An option’s premium is always composed of precisely its intrinsic value and its timevalue. If a $400 gold call is trading at $50 with gold at $435 per ounce, the time valueof the call must be $15, since the intrinsic value is $35. The two components must addup to the option’s total premium of $50. If a $70 put ona stock is trading for $9 withthe stock at $62, the time value of the put must be $1, since the intrinsic value is $8.The intrinsic value and the time value must add up to the option’s premium of $9.
Even though an option’s premium is always composed of its intrinsic value and itstime value, it is possible for one or both of these components to be zero. If the optionhas no intrinsic value, its price in the marketplace will consist solely of time value. If theoption has no time value, its price will consist solely of intrinsic value. In the latter case,We say that the option is trading at parity.
While an cption’s intrinsic value can never be less than zero, it is possible for anoption, if it is European, to have a negative time value. (More about this when we lookat early exercise in Chapter 12.) When this happens the option can trade for less thanparity. Usually, however, an option’s premium will reflect some non-negative amountof intrinsic and time value.
Any option which has a positive intrinsic value is said to be in-the-money by theamount of the intrinsic value. With a stock at $44, a $40 call is $4 in-the-money. WithDeutschemarks at 57.75, a 59 put is 1.25 in-the-money. An option which has nointrinsic value is said to be out-of-the-money. The price of an out-of-the-money optionConsists solely of time value. In order to be in-the-money, a call (put) must have anexercise price lower (higher) than the current price of the underlying contract. Notethat if a call is in-the-money, a put with the same exercise price and underlying contractMust be out-of the-money. Conversely, if the put is in-the-money, a call with the sameexercise price must be out-of-the-money.
Finally, an option whose exercise price is identical to the current price of theUnderlying contract is said to be at-the-money. Technically, such an option is alsoOUt-of the-money since it has no intrinsic value. We make the distinction between an8 Chapter |
Figure 1-7: In- and Out-of-the-Money Options
 
 
CurrentUnderlyingPrice
Lower Exercise Prices Higher Exercise Prices
~~? >In-the-Money Calls Out-of-the-Money Calls
Out-of-the-Money Puts In-the-Money Puts
~—_? _
 
at-the-money and out-of-the-money option because an at-the-money option has thegreatest amount of time premium and is usually traded very actively.
If we want to be very precise, the exercise price of an option must be identical tothe current price of the underlying contract for the option to be at-the-money. However,for exchange-traded options, the term is commonly applied to the call and put whoseexercise price is closest to