guided by objectivity rather thanby emotion. They also must have the discipline to implement a trading technique consistently.
T
• 343 •
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INDEX
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rhos of, 115–118thetas of, 108–112vegas of, 104–108
AAccount equity, 17Account value, 17Adjusting stock trades:bid-ask prices, 284–290in delta-neutral trading, 247for long-volatility delta-neutraltrades, 250–251for short-volatility delta-neutraltrades, 258–259American pricing formula, 34Arbitrage, 163–164Arbitrage pricing relationship, 164Arbitrage strategies, 163–204box spreads, 188conversions, 165–178long box spreads, 188–196pin risk, 167–168and put-call parity, 60reverse conversions, 178–188short box spreads, 196–203Ask price (ask), 12 (See also Bid-askprices)Assignment, 5, 7At-the-money options, 8calls, time decay and, 62,63, 65deltas of, 94–97gammas of, 100–104Greeks of, 89–91
BBear call spreads, 27, 318Bid price (bid), 11Bid-ask prices, 279–310limit on adjusting, 288–290need to adjust, 284–285process of adjusting, 285–287proﬁt and loss calculation for, 287real-world factors for, 283and theory of bid-ask spread,280–283as volatility changes, 290–292in volatility terms, 292–294when buying calls delta-neutral,296–298when creating butterﬂy spread inthree trades, 298–302when creating long box spread intwo trades, 306–309when creating reverse conversion intwo trades, 302–305Binomial option-pricing models, 53Black, Fisher, 53Black-Scholes option-pricing model,53, 54Book value, 224
• 347 •
348 • Index
Box spreads, 188long, 188–196, 306–309relative pricing and, 195–196short, 196–203Bull call spreads, 26, 318, 323–327Butterﬂy spread, bid-ask prices increating, 298–302Buy long, 3Buy to close, 4Buy to cover, 3Buy to open, 4Buyer, 6
CCalendar days, trading days vs.,220–222Call options, 1, 5exercising, 6in, at, and out of the money, 8Call values:delta of, 79–80and dividends, 69and extreme volatility, 71gamma of, 82–83and interest rates, 68put values relative to, 59–60rho of, 87–89and stock prices, 54–56theta of, 85–87vega of, 84Cash accounts, 16Cash-settled options, 7Competition:and conversions, 172–173and reverse conversions, 184–185Conversions, 165–178and competition, 172–173deﬁned, 165outcomes at expiration, 166–167pin risk, 167–168pricing, 168–172pricing, by strike price, 176–177
pricing, with dividends, 173–176and relative pricing, 177–178reverse, 178–188Cost of carry:for conversions, 165, 166and interest rates, 88Cox, J. C., 53Credit, 122
DDaily returns:calculating, 208comparing absolute values of,210–212comparing daily closing prices and,210, 211frequency of, 213–214Debit, 120, 335Debt-to-equity, 224Delta, 78–80of call values, 79–80changes in, 92–99 (See alsoGamma)deﬁned, 59, 77position, 120–123of put values, 80using theta with, 111Delta-neutral trading, 241–278bid-ask prices in, 296–298consistency of units in, 245–246deﬁned, 242with long calls and short stock,242–244with long puts and long stock, 245long volatility example of, 248–256market makers’ opportunities andrisks with, 275–277multiple-part positions in, 246position Greeks in, 327–329risk limits in, 337–340with short calls and long stock, 244with short puts and short stock, 245
Index • 349
short volatility example of, 256–262simulated “real” examples of,263–272speculators’ opportunities and riskswith, 272–275steps in, 247theory of, 247Directional positions, 339Directional risk, managing, 314–320Disclosures and disclaimers (Op-EvalPro), 33–34Discounted present value (DPV):for conversions, 168, 170, 173, 176,177for long box spreads, 193, 194for reverse conversions, 185, 187for short box spreads, 199, 200Distribution screen (Op-Eval Pro), 46,47, 218–220Dividends:deﬁned, 173and option values, 69pricing conversions with, 173–176pricing reverse conversions with,185–187in synthetic relationships, 156–160DPV (see Discounted present value)Dynamic markets, price behavior in,71–72
EEffective stock price, 136, 155–156for synthetic long call, 143for synthetic long put, 147–148for synthetic long stock, 138–139for synthetic short call, 145–146for synthetic short put, 150–151for synthetic short stock, 141Equity pricing formula, 34, 35European pricing formula, 34, 35Ex-dividend date, 175–176Exercise price, 2
Exercising an option, 6, 7Expected volatility, 230–231Expiration date, 2conversion outcomes at, 166–167long box spreads outcomes at,190–192and option values, 62–67reverse conversions outcomes at,179–180short box spreads outcomes at,197–199(See also Time to expiration)Extreme volatility, 71
FFloor brokers, 10Forecast volatility, 231 (See alsoExpected volatility)Frequency of daily returns, 213–214Future volatility, 216, 231 (See alsoRealized volatility)
GGamma, 80–81changes in, 99–104deﬁned, 77–78negative, 339position, 122–126Gap opening, 273–274Graphing, in Op-Eval Pro, 42–44The Greeks, 77–134changes in, 89–118delta, 78–80, 92–99, 120–123of delta-neutral positions,327–329of directional trades, 339–340gamma, 80–81, 99–104, 122–126position, 118–133rho, 87–89, 111, 113–118,129–131theta, 85–87, 108–112, 127–130vega, 83–85, 104–108, 126–128
350 • Index
HHedge funds, 13Hedging trades (hedges), 275, 280Historic volatility, 206–216changes in, 226–227and daily returns, 210–214Hull, J., 53
IImplied volatility, 222–230changes in, 225–230and insurance analogy, 228–229in Op-Eval Pro, 39, 42role of supply and demand in,223–225Increments of change, 290Index pricing formula, 34–35Initial margin, 17Insurance, options compared to,49–53, 229–230Interest income, from short stockrebate, 18–19Interest rates:and option values, 67–69positive, neutralizing Greeks with,333–337sensitivity to (see Rho)in synthetic relationships,156–160In-the-money options, 8calls, time decay and, 62, 63, 65deltas of, 94–97gammas of, 100–104Greeks of, 89–91rhos of, 115–118thetas of, 108–112vegas of, 104–108Intrinsic value, 9
LLeverage, 16Long, 6
Long box spreads, 188–196bid-ask prices in creating, 306–309double pin risk with, 192outcomes at expiration, 190–192pricing, 193–195Long call butterﬂy spreads:creating, 298proﬁt and loss diagrams for, 27Long call positions:deltas of, 120–123gammas of, 122–124proﬁt and loss diagrams for, 20rhos of, 129–131synthetic, 141–144for synthetic long put, 146–148for synthetic long stock, 137–139thetas of, 128, 130vegas of, 126–127Long call vertical spreads:position risk with, 318, 319proﬁt and loss diagrams for, 26Long condor spreads, proﬁt and lossdiagrams for, 27–29Long options, risk of vertical spreadsvs., 320–321Long put positions:gammas of, 122, 124proﬁt and loss diagrams for, 21, 22rhos of, 129, 130, 132synthetic, 146–148for synthetic long call, 141–144for synthetic short stock, 139–141thetas of, 128, 130vegas of, 126–127Long stock positions:synthetic, 137–139for synthetic long call, 141–144for synthetic short put, 148–157Long straddles, proﬁt and lossdiagrams for, 23Long strangles, proﬁt and loss diagramsfor, 24–26
Index • 351
Long-volatility delta-neutral trades,248–256adjusting trades, 250–251closing the remaining position,252–253opening the position, 250proﬁt and loss calculation, 252–255recapping trades, 255–256speculative risks of, 273
MMaintenance margin, 17–18Managing position risk, 311–341calculating position risks, 312–314directional risk with delta, 314–320establishing risk limits, 337–340Greeks of delta-neutral positions,327–329neutralizing Greeks when interestrates are positive, 333–337neutralizing position Greeks,329–333vertical spreads vs. outright longoptions, 320–327Margin accounts, 16–18Margin call, 17Margin debt, 17Margin deposit (margin), 4, 16Marginable transactions, 16–18Market:as exchanges, 10–11as prices at which buyers and sellerswant to trade, 11Market inefﬁciencies, 60Market makers, 13, 343buying calls delta-neutral, 296–298creating butterﬂy spread in threetrades, 298–302creating long box spread in twotrades, 306–309creating reverse conversion in twotrades, 302–305
delta-neutral trading opportunitiesand risks for, 275–277response to pin risk by, 168trading techniques of, 294–295Market orders, 276Minimum margin, 17Minus signs (see Position Greeks)
NNational best bid and best offer(NBBO), 13–16NC (net credit required per share),200Negative gamma, 339Net credit required per share (NC),200Net investment per share, forconversions, 169–170New York Stock Exchange, 10Normal distribution, 215
OOCC (see Options ClearingCorporation)Offer price (offer), 12Open outcry trading, 10, 12Op-Eval Pro software, 31–48American pricing formula, 34disclosures and disclaimers, 33–34Distribution screen, 46, 47,218–220equity pricing formula, 34, 35European pricing formula, 34, 35ﬁnding deltas in, 80index pricing formula, 34–35installing, 32–34option-pricing formulas, 34–35,53–54Portfolio screen, 45–46previewing, printing, and saving in,47program features, 31–32
352 • Index
Single Option Calculator screen,36–39Spread Positions screen, 39–42Theoretical Graph screen, 42–44Theoretical Price table, 44–45Option prices, volatility and, 98–99,222–238Option trades:essentials topics for, xv–xvistock trades vs., 2–5Option values:over- vs. undervalued, 232–233volatility and, 69–71Option volatility, deﬁned, 231 (Seealso Implied volatility)Option-pricing formulas, 34–35, 53–54Options, 1Options Clearing Corporation (OCC),7, 13OTC market (see Over-the-countermarket)Out-of-the-money options, 8calls, time decay and, 62, 63, 65deltas of, 94–97gammas of, 100–104Greeks of, 89–91rhos of, 115–118thetas of, 108–112vegas of, 104–108Over-the-counter (OTC) market, 10–11Over-the-Counter Put and Call BrokerDealer Association, 11Over-the-weekend risk, 167Overvalued options, 232–233Owner, 6
PParity:put-call (see Put-call parity)trading at, 10Past volatility, 231 (See also Historicvolatility)
Percent volatility, 209, 216–217Physical-delivery options, 7Pin risk:with conversions, 167–168with long box spreads, 192with reverse conversions, 180–181“Pinned to the strike,” 167Plus signs (see Position Greeks)Portfolio screen (Op-Eval Pro), 45–46Position Greeks, 118–133delta, 120–123in delta-neutral trading, 327–329gamma, 122–126neutralizing, 329–337rho, 129–131in risk management, 322–327theta, 127–130vega, 126–128Position risk:calculating, 312–314managing (see Managing positionrisk)tracking changes in, 318–320Predicted volatility, 231 (See alsoExpected volatility)Premium sellers, 67Premiums, 5–6Price behavior, 49–76call values and stock prices, 54–56call values relative to put values,59–60compared to insurance, 49–53delta, 59dividends and option values, 69in dynamic markets, 71–72extreme volatility, 71interest rates and option values,67–69intrinsic value and time value in,9–10option-pricing formulas, 53–54put values and stock prices, 56–58
Index • 353
strike price and option values, 60–62three-part forecasts, 72time to expiration and option values,62–67trading scenarios, 72–75volatility and option values, 69–71Price-earnings ratio, 224Price-to-sales, 224Pricing formulas, in Op-Eval Pro,34–35Pricing relationship, arbitrage, 164Proﬁt and loss diagrams, 19–29for long butterﬂy spread with calls,27for long call strategy, 20for long call vertical spread, 26for long condor spread, 27–29for long put strategy, 21, 22for long straddles, 23for long strangles, 24–26for short call strategy, 20–21for short call vertical spread, 27for short put strategy, 21, 22for short straddles, 23–24for short strangles, 24–26for straddles, 21, 23–24for strangles, 24–26Public traders, 12–13Put options, 2, 5exercising, 6in, at, and out of the money, 8Put values:call values relative to, 59–60delta of, 80and dividends, 69and extreme volatility, 71gamma of, 82–83and interest rates, 68rho of, 87–89and stock prices, 56–58theta of, 85–87vega of, 84
Put-call parity, 60and deltas of calls and puts withsame strike, 94and equality of call and putgammas, 100and rho, 88and synthetic positions, 135(See also Synthetic relationships)and vega, 84Put-call parity equation, 153–155
RRealized volatility, 216Record date, 175Regional stock exchanges, 10Regulation T, 13Relative pricing:and box spreads, 195–196and conversions, 177–178Retail investors, 13Reverse conversions, 178–188bid-ask prices in creating,302–305and competition, 184–185outcomes at expiration, 179–180pin risk with, 180–181pricing, 181–184pricing, by strike price, 187–188pricing, with dividends, 185–187Rho, 87–89changes in, 111, 113–118deﬁned, 78position, 129–131Risks:in arbitrage, 164in delta-neutral trading, 272–277directional, 314–320establishing limits for, 337–340over-the-weekend, 167pin, 167–168position, 312–314 (See alsoManaging position risk)
354 • Index
Risks: (Cont.)of short options, 314supporting equity to cover, 202–203Ross, S. A., 53Rubenstein, M., 53
SScaling in/out, 284Scholes, Myron, 53Sell long, 3Sell short, 3Sell to close, 4Sell to open, 4Seller, 6Selling stock short, 16Settlement date, 175–176Short, 6Short box spreads, 196–203motivations for establishing, 202–203outcomes at expiration, 197–199pricing, 199–202Short call positions:gammas of, 125–126proﬁt and loss diagrams for, 20–21rhos of, 129, 132synthetic, 144–146for synthetic short put, 148–157for synthetic short stock, 139–141thetas of, 128, 129vegas of, 127, 128Short call vertical spreads:position risk with, 318proﬁt and loss diagrams for, 27Short options, risk of, 314Short put positions:deltas of, 120–123gammas of, 125–126proﬁt and loss diagrams for, 21, 22rhos of, 129, 131synthetic, 148–151for synthetic long stock, 137–139
for synthetic short call, 144–146thetas of, 128, 129vegas of, 127, 128Short stock positions:synthetic, 139–141for synthetic long put, 146–148for synthetic short call, 144–146Short stock rebate, 18–19Short straddles, proﬁt and lossdiagrams for, 23–24Short strangles, proﬁt and lossdiagrams for, 24–26Short-volatility delta-neutral trades,256–262adjusting trades, 258–259closing the remaining position, 259opening the position, 258proﬁt and loss calculation, 259–262recapping trades, 262speculative risks of, 273–274Single Option Calculator screen (OpEval Pro), 36–39Size of the bid (size), 11Skew, volatility, 234–238Speculators, delta-neutral tradingopportunities and risks for,272–275Spread Positions screen (Op-Eval Pro),39–42Standard deviation, 206–208, 217–218Stock exchanges, 10–11Stock prices:and call values, 54–56changes in, 89, 90deltas and, 92, 93effective (see Effective stock price)and put values, 56–58rhos and, 113–114three-part price forecasts of, 72unequal to strike price, 151–153volatility of, 206–222
Index • 355
Stock splits, 61, 62Stock trades, option trades vs., 2–5Stop-loss points, 339Straddles, proﬁt and loss diagrams for,21, 23–24Strangles, proﬁt and loss diagrams for,24–26Strike prices, 2, 6choosing, 231–232deltas and, 92, 94and option values, 60–62pricing conversions by, 176–177pricing reverse conversions by,187–188unequal to stock price, 151–153vegas and, 108Supply and demand, options pricesand, 223–225Synthetic positions, 135–136Synthetic relationships, 135–161effective stock price concept,155–156interest rates and dividends in,156–160long call, 141–144long put, 146–148long stock, 137–139put-call parity equation, 153–155short call, 144–146short put, 148–151short stock, 139–141when stock price does not equalstrike price, 151–153
TTheoretical Graph screen (Op-EvalPro), 42–44Theoretical Price table (Op-Eval Pro),44–45Theta, 85–87changes in, 108–112
deﬁned, 78position, 127–130units of time for, 62, 64(See also Time decay)30-percent volatility, 216–217Three-part price forecasts, 72Time decay, 62–67 (See also Theta)Time premium (time value), 9of calls vs. puts, 159and put-call parity, 154–155and trading of synthetic vs. realstock, 159Time to expiration:changes in, 89, 90deltas and, 93–95and option values, 62–67rhos and, 115, 116thetas and, 109–111vegas and, 104–106Time value (see Time premium)Trades, planning, 231–232Trading at parity, 10Trading days, calendar days vs.,220–222Trading options, 6Transaction date, 175Treasury bills, 168
UUnderlying instrument (underlying), 2and call values, 54–56changes in price of, 89, 90delta and changes in price of, 77(See also Delta)gamma and changes in price of,77–78 (See also Gamma)and put values, 56–58Undervalued options, 232–233Units:for delta-neutral trading, 245–246of time, 86
356 • Index
VVega:changes in, 104–108deﬁned, 78position, 126–128Vertical spreads:long call, 26, 318, 319position risk with, 318–327short call, 27, 318Volatility, 205–239and bid-ask prices, 290–294calendar days vs. trading days,220–222changes in, 89, 91converting annual volatility todifferent time periods, 217–220and daily returns, 213–214deﬁned, 205, 206deltas and, 94, 96–98expected, 230–231extreme, 71forecast, 231future, 216gammas and, 102–104
historic, 206–216implied, 222–230nondirectional nature of, 206, 217and option prices, 98–99, 222–238and option values, 69–71and over- vs. undervalued options,232–233in planning trades and choosingstrike prices, 231–232realized, 216rhos and, 115, 117–118sensitivity to (see Vega)of stock prices, 206–222terms for, 231thetas and, 111, 11230-percent, 216–217and time decay, 64–67trading scenarios with changes in,72–75vegas and, 105, 107Volatility skew, 234–238
WWriter, 6
ABOUT THE AUTHORJames Bittman began his trading career in 1980 as a market maker inequity options at the Chicago Board Options Exchange. From 1983to 1994, he was a Commodity Options Member of the Chicago Boardof Trade where he traded options on ﬁnancial futures and agriculturalfutures.His afﬁliation with The Options Institute at The Chicago BoardOptions Exchange began in 1987 as a part-time instructor, and he hasbeen a full-time senior instructor since 1995. Mr. Bittman’s responsibilities at The Options Institute include teaching courses for individual and institutional investors, for stockbrokers, and for governmentregulators. He has also presented custom courses on market makingin the U.S. and around the world.In addition to Trading Options as a Professional, Mr. Bittman is theauthor of three books, Options for the Stock Investor, 2nd ed., (2005),Trading Index Options (1998), and Trading and Hedging with Agricultural Futures and Options (2003), all published by McGraw-Hill.He