a 95 call to finish in-the-money threemonths from now is:
In(95/84)/(.16-V.25) = In(1.1310)/.08 = .1231/.08 = +1.5383 st. devs.
Checking a table of standard deviations, we find that there is approximately a 6.2%chance, or about one chance in 16, of an upward move of 1.5383 standard deviations.
In the case of a stock, a slight modification is necessary because the volatilityrepresents price movement away from the forward price. If P is the current stock price,t is the time period, r is the risk-free interest rate, and D is the amount of dividendsexpected over the period, the forward price of the stock, P, is:
Pp=P-et~DExample: Suppose interest rates are at 8%. If a certain non-dividend paying stock
is trading at 38 and has an annual volatility of 27%, the movement, in standarddeviations, needed for a 35 put to finish in-the-money six months (t=.5) from now is:
1n[35/(38-28 5)/(.27-V5) = 1n(35/39.55)/.191—.122/.191 = -.64 standard deviations
Checking a table of standard deviations, we find that there is approximately a 26%chance, or about one chance in four, of a downward move of .64 standard deviations.
Ut
Ut“+ Appendix C +
Characteristicsof Volatility SpreadsAppendix C
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452“* Appendix D +What’s the Right Strategy?
The following chart is designed to help the reader choose the types of strategies whichare most likely to be profitable given a trader’s opinion on market direction andvolatility. Even though several strategies may be appropriate under the same marketconditions, each strategy will have its own unique risk/reward characteristics. Thereader should refer to the text for a more detailed analysis of each strategy.
The implied volatility component, whether low, moderate, or high, is in compari-son to a trader’s own volatility forecast. If the trader believes that 15% is a reasonableforecast, but implied volatility is 13%, then implied volatility is low. If the trader believesthat 20% is a reasonable forecast, but implied volatility is 24%, then implied volatility ishigh. If the trader’s volatility forecast is approximately the same as the implied volatility,then implied volatility is moderate.
Any of the listed strategies can be done synthetically. Instead of buying (selling) acall, a trader can buy (sell) a put with the same exercise price and buy (sell) anunderlying contract (synthetic long (short) call). Instead of buying (selling) a put, a tradercan buy (sell) a call with the same exercise price and sell (buy) an underlying contract(synthetic long (short) put).
The only scenario for which there is no appropriate strategy is one in which a traderhas no opinion on either implied volatility or market direction. In such a case adisciplined trader will choose to sit on the sidelines until trading conditions becomemore opportune.
In-the-money call butterflies and time spreads, and out-of-the-money put butterfliesand time spreads, are those in which all exercise prices are lower than the current priceof the underlying contract. Out-ofthe-money call butterflies and time spreads, andin-the-money put butterflies and time spreads, are those in which all exercise prices arehigher than the current price of the underlying contract.
453Appendix D
speaids aun (ynd) jee (WO) WLI essempeyng (ind) |/e9 (WLI) WLO Angind WLY llesand WLO Angeo WLLY asqyeo WL Angispeads [ealya |jnqs}nd peyeu [jes
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454
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 + Appendix E +
Synthetic and ArbitrageRelationshipsAppendix E
456
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nd Woys + [Jed BuO] + BulALapun Woys =SuldLapun Zuo] snes + BuLALJapun Woys = uolsJaAuod aSJeAel
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SHIDALVULS FOVALIGUV UNV SLNATVAINO OLLAHLNAS457
Synthetic and Arbitrage Relationships
spuaplalp paedxe — (gold aspuexe Wua}-Woys) anfea Juaseid — (gatid asa Jexe wWJa1-8u0}) anyea quasaid =spUaplArp pajoadxe — 1XeU a} 01 uonendxe cuo woy eld asioiexe et} U0 51809 3UTALe9 = Jeyseur [104 Ala!
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SNOLLdO NVadOUuNd WOd SAN TVA qOVULIGUVYAppendix E
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SdIHSNOILV Tae TOAISN WAHLO
458** Appendix F +
Recommended Reading
This book represents only one of many possible approaches to option evaluation andtrading. The reader who desires a complete proficiency in options is strongly advised toseek out as many different sources of information as possible.
The following list includes those books which are likely to be of interest to theserious option trader. An attempt has been made to categorize books according to theirjevel of difficulty (usually in terms of the mathematics involved), although categoriza-tions are subjective and in some cases may overlap. Where possible, the primary focus ofthe book (stock options, futures options, interest rates, currencies, etc.) has also been noted.
(References to academic articles, including the original presentation of the morecommonly used pricing models, appear as footnotes in the text.]
ELEMENTARY BOOKS
Barenblat, Scot G.; and Mesler, Donald T.Stock Index Options (stock indexes)Probus Publishing Co.; Chicago, IL
1992; 206 p.
Caplan, David
The Options Advantage (futures)Probus Publishing Co.; Chicago, IL1991; 222 p.
Colburn, James T.
Trading in Options on Futures (futures)
The New York Institute of Finance; New York, NY1990; 310 p.
Frost, Ronald J.
Options on Futures, Revised Edition (futures)Probus Publishing Co.; Chicago, IL
1994; 254p.
Fuliman, Scott H.
Options: A Personal Seminar (stocks)
New York Institute of Finance; New York, NY1992; 373 p.
459460 Appendix F
Hexton, Richard
Dealing in Traded Options (stocks)
Prentice-Hall International Ltd.; Hertfordshire, UK1989; 192 p.
Luft, Carl F.; and Sheiner, Richard K.
Understanding and Trading Listed Stock Options, Rev. Ed. (stocks)Probus Publishing Co.; Chicago, IL
1994, 231 p.
Mayer, Terry S.
Commodity Options (futures)
New York Institute of Finance; New York, NY1983; 300 p.
McMillan, Lawrence G.
Options as a Strategic Investment (stocks)
The New York Institute of Finance; New York, NYThird Edition, 1993; 882 p.
The Options Institute (editor)
Options: Essential Concepts and Trading Strategies (stocks)Business One Irwin; Homewood, IL
1990; 403 p.
Smith, Courtney
Option Strategies (stocks)
John Wiley & Sons, Inc.; New York, NY1987; 256 p.
Thomsett, Michael C.
Getting Started in Options (stocks)John Wiley & Sons, Inc.; New York, NY1989; 229 p.
Walker, Joseph A.
How the Options Markets Work (stocks)New York Institute of Finance; New York, NY1991; 229 p.
Wasendorf, Russell R.; and McCafferty, Thomas A.All About Options
Probus Publishing Co.; Chicago, IL
1993; 213 p.Recommended Reading 461
INTERMEDIATE BOOKS
Baird, Allen Jan
Option Market Making (futures)
John Wiley & Sons, Inc.; New York, NY1993; 201 p.
Bookstaber, Richard M.
Option Pricing and Investment Strategies (stocks)Third Edition
Probus Publishing Co.; Chicago, IL
1991; 300 p.
Bookstaber, Richard M.; and Clarke, Roger G. :Option Strategies for Institutional Investment Management (stocks)
Addison-Wesley Publishing Co., Inc.; Menlo Park, CA
1983; 168 p.
Clasing, Henry K, Jr.; Lombard, Odile; and Marteau, DidierCurrency Options (currencies)
Business One Irwin; Homewood, IL
1992; 270 p.
Denning, Hugh
Equity Options: Valuation, Trading & Practical Strategies (stocks)Longman Professional; Melbourne, Australia
1991; 183 p.
DeRosa, David F.
Options on Foreign Exchange (currencies)Probus Publishing Co.; Chicago, IL
1992; 272 p.
Fabozzi, Frank J.
Winning the Interest Rate Game: A Guide to Debt Options (interest rates)Probus Publishing Co.; Chicago, IL
1985; 300 p.
Fabozzi, Frank J.
The Handbook of Fixed-Income Options (interest rates)Probus Publishing Co.; Chicago, IL
1989; 657 p.
Figlewski, Stephen; Silber, William L.;
and Subrahmanyam, Marti G. (editors)Financial Options: From Theory to PracticeBusiness One Irwin; Homewood, IL
1992; 579 p.462 Appendix F
Fitzgerald, Desmond M.
Financial Options (stocks)
Euromoney Publications; London, England1987; 262 p.
Gastineau, Gary
The Options Manual (stocks)McGraw Hill; New York, NYThird Edition, 1988; 440 p.
Gemmill, Gordon
Option Pricing: An International PerspectiveMcGraw-Hill; London
1993; 267 p.
Kolb, Robert W.
Options: The Investor’s Complete Toolkit (stocks)New York Institute of Finance; New York, NY1991; 216p.
Labuszewski, John W.; and Nyhoff, John E.Trading Options on Futures (futures)
John Wiley & Sons, Inc.; New York, NY1988; 264 p.
Labuszewski, John; and Sinquefield, JeanneInside the Commodity Option Markets (futures)John Wiley & Sons, Inc.; New York, NY
1985; 384 p.
Smith, A.L.H.
Trading Financial OptionsButterworths; London, England1986; 200 p.
Sutton, W. H.
Trading Currency Options (currencies)
The New York Institute of Finance; New York, NY1988; 208 p.
Tompkins, Robert
Options Explained (futures/interest rates)
MacMillan Publishers Ltd.; Basingstoke, Hants, England1991; 301 p.
Wong, M. Anthony
Trading and Investing in Bond Options (interest rates)John Wiley & Sons, Inc.; New York, NY
1991; 262 p.Recommended Reading 463
ADVANCED BOOKS
Brenner, Menachem (editor)
Option Pricing: Theory and Applications (stocks)Lexington Books; Lexington, MA
1983; 235 p.
Cox, John C.; and Rubenstein, MarkOptions Markets (stocks)Prentice-Hall; Englewood Heights, NJ1985; 498 p.
Gibson, Rajna
Option Evaluation: Analyzing and Pricing Standardized Option ContractsMcGraw-Hill, Inc.; New York, NY
1991; 304 p.
Hodges, Stewart (editor)
Options: Recent Advances in Theory and PracticeManchester University Press; Manchester, England1990; 181 p.
Hull, John C.
Options, Futures, and Other Derivative SecuritiesPrentice-Hall, Inc.; Englewood Cliffs, NJ
2nd Edition, 1993; 492 p.
Jarrow, Robert; and Rudd, AndrewOption Pricing (stocks)
Dow Jones-Irwin; Homewood, IL1983; 235 p.
Ritchken, Peter
Options: Theory, Strategy and Applications (stocks)Scott, Foresman and Co.; Glenview, IL
1987; 414p.Index
vAYAdjustment, 84, 168-169, 193-195American Stock Exchange, 6n, 303Assignment, 4-6, 224-225Arbitrage, 218, 456ARCH Model, 280Atthe-money. See Option, at-the-money* BeBackspread, 138-139, 145, 200, 452intermarket, 338Backwardation, 129Barone-Adesi, Giovanni, 248, 438nBeckers, Stan, 66n, 397n, 400nBinomial tree, 435Black, Fischer, 40n, 43, 431n, 432nBollerslav, T., 281nBox, 228-231, 254, 456~458Burghardt, Galen, 275nButterfly, 145-148, 235-236, 452, 458body of, 145nbull and bear, 201wings of, 145nBuy/write, 261% Cc %Calendar spread. See Time spreadCap, 265Carrying costs, 38, 41-42, 111, 221-223,249-250, 436. See also InterestratesChicago Board of Trade (CBOT}, 2, 6n,128, 129, 134Chicago Board Options Exchange(CBOE), 2, 43, 120, 197, 231, 323,329n, 343
Chicago Mercantile Exchange (CME), 2,120, 133, 272, 323, 324nChicago Stock Exchange, 303, 327nChristmas tree, 157-158Clearing firm, 8-9Clearing house, 8-9Collar, 265Commodity Exchange, Inc. (COMEX),105, 128, 131Condor, 158Contango relationship, 128Contingency order, 170Contract position, 360Conversion, 217-219, 456Conversion/reversal market, 219. Seealso Synthetic marketCovered write, 260-262Cox, John, 248, 400n, 434nCurvature. See GammaCylinder, 264¢D<Delta, 82, 99, 359-360American vs. European option, 250,253as a condition for early exercise, 246248as a probability, 102as a rate of change, 99as an equivalent underlying position,101-102characteristics, 118dollar ($delta), 332effect of price change. See Gammaeffect of volatility change, 106, 110,210
465466
effect of time passage, 106, 110implied, 120of an index futures contract, 311-312risk, 179, 353Delta neutral, 82, 106, 110, 137, 159,199, 227Diagonal spread, 157, 201nDiffusion process, 394-395Distribution, 400-404high volatility, 55, 56lognormal, 61-64low volatility, 54, 56normal, 52-53, 440Dividend, 38, 42, 49, 113n, 120, 244neffect on arbitrage, 228effect on early exercise, 243-245effect on index futures, 306-307Dividend play, 250-251Dollar delta neutral, 333Dowrrtick, 93Dynamic hedge, 93eEeEdge, 37, 123, 173, 175, 359Elasticity, 123-124, 126Engle, R.F., 281nExecution risk, 224Exercise, 4-5, 224-225Exercise price, 1-4, 44-45, 46Ex-dividend, 48Expected return, 36-37, 40, 210Expiration, 1-4, 44-45, 46-47Exponential function, 446-449
oF &
Fence, 263-265
Figlewski, Stephen, 40n
Floor, 265
Forced liquidation, 227, 255
Forward price, 42
Front spread. See Ratio vertical spread
e GeGamma, 103, 105-106, 160, 360-361
Index
and adjustments, 196characteristics, 118-119dollar (S$gamma), 346effect of changing market conditions,106implied, 120of volatility spreads, 160-161tisk, 179, 353GARCH Model, 281Garman, Mark B., 66n, 433nGrabbe, J. Orlin, 433nGraphexpiration, 23-24theoretical, 358-363Guts, 143
H «
%“
Haircut, 9nHeath, David, 393nHedge ratio, 45, 82,101. See also DeltaHo, Thomas, 393nHorizontal spread. See Time spreadHull, John, 393noleIn-the-money. See Option, in-the-moneyIndex, 301capitalization weighted, 302divisor, 303implied value, 309options, early exercise of, 316-320price weighted, 302quoted price, 311replication, 304-305substitute, 322-326Interest rates, 38, 45, 47-48, 87, 116,129, 264-265, 388-389, 445effect on arbitrage, 223-224effect on early exercise, 241-242,245-246, 250neffect on index futures, 306Interest play, 252Investor's Business Daily, 31nIron butterfly, 158Index
%% J %
Jarrow, Robert, 393n
Jelly roll, 231-233, 254, 456-458Jump-diffusion process, 395, 397Jump process, 394-395
& K &Kappa. See VegaKlass, Michael J., 66nKohlhagen, Steven W., 433nKuberek, Robert C., 281nKurtosis, 402-404, 440-441, 443ol?Ladder. See Christmas treeLane, Morton, 275nLEAPS, 388Lee, Sang-Bin, 393nLeg, 181nLeverage value, 124Liquidity, 181, 196-197, 272Logarithmic function, 446-449London International Financial Futuresand Options Exchange (LIFFE}, 405Long, 11~12Long premium, 160Lot position. See Contract position*“M¢Margin, 9-10, 255Marketarbitrage-free, 42frictionless, 87, 386locked, 87, 386Mean, 56-57, 59, 60, 440-441Merton, Robert, 397nModel, 37-38ARCH {autoregressive conditional het-eroskedasticity}, 280, 281nbinomial. See Model, Cox-Ross-RubensteinBlack, 44, 353n, 432-433Black-Scholes, 43-44, 48, 81, 248,315, 352, 353n, 431-432, 446
467
assumptions in, 64, 385CEV (constant elasticity of variance),400Cox-Ross-Rubenstein, 248-249, 315,347n, 434-438GARCH (generalized autoregressiveconditional heteroskedasticity},281, 281nGarman-Kohthagen, 44, 48, 433jump-diffusion, 397quadratic. See Model, Whaleytheoretical pricing, 38, 40-41, 132Whaley, 248-249, 438-439Moments, 440Morton, Andrew, 393neN¢Naked positions, 199Natural long and short, 257Nelson, David B., 28