of the at-the-money straddle on any future on any commodity —from optiontables published in the financial press. With the value of thestraddle determined, the implied volatility is also determined.PHANTOM OF THE OPTION 99
The complicated matrixes of option data, where every parameteris changing day to day, has been simplified into two familiarprice-time series—a strike independent at-the-money straddleversus time, and an implied volatility versus time. Figure 6-4illustrates in tabular form samples of these two data series forcrude oil. (Complete tabulations on this model for the 15 activelytraded futures comprising the data base can be found under"Volatility Profiles" at the back of the book.)
Precisely how information can best be extracted from thisdata base is the subject of the next chapter. Suffice it to say that,in terms of price sequences versus time, we now have as muchhistorical option data available as historical futures data. Thisdata can be used to determine basic option trading expectationsand to test different option trading strategies. Whether the database will be large enough to convince the reader of the validity ofany statistical inferences drawn from it, I cannot be sure. But ofone thing, I can be sure. As far as data collecting and data pro-cessing is concerned, this is as far as I could reasonably go andstill have a life.100 OPTION REALITY
CRUDE OIL April 1996 option and April 1996 future
Futures __ Closest strike Trading ImpliedDate price option max. option min. ATMSt days left volatilityJan 2 1884 73 54 125 53 18.26Jan 3 1890 68 58 125 52 18.36Jan 4 1893 67 60 126 51 18.70Jan 5 1928 73 57 129 50 18.86Jan 9 1896 65 61 126 48 19.13Jan 10 1878 73 51 122 47 18.93Jan 11 1805 65 60 125 46 20.35Jan 12 1774 78 53 129 45 21.60Jan 15 1779 74 53 125 44 21.18Jan 16 1743 72 65 136 43 23.87Jan 17 1779 81 56 135 42 23.34Jan 18 1796 70 68 138 4 23.97Jan 19 1781 73 57 129 40 22.82Jan 22 1774 81 56 135 39 24.29Jan 23 1767 78 56 132 38 24.22Jan 24 1788 71 59 129 37 23.71Jan 25 1737 74 60 133 36 25.47Jan 26 1736 75 60 134 35 26.03Jan 29 1716 78 62 139 34 27.69Jan 30 1724 81 57 136 33 27.40Jan 31 1737 74 61 134 32 27.24Feb1 1731 79 59 136 31 28.25Feb 2 1738 73 61 133 30 27.93Feb 5 1717 80 62 140 29 30.36Feb6 1730 78 58 134 28 29.30Feb7 1731 74 55 127 27 28.29Feb 8 1733 66 49 113 26 25.67Feb 9 1738 60 48 107 25 24.61Feb 12 1750 50 50 100 24 23.33Feb 13 1835 61 46 106 23 24.00Feb 14 1835 64 49 112 22 25.94Feb 15 1837 64 51 114 21 27.04Feb 16 1839 63 52 114 20 27.73Feb 20 1927 74 47 118 18 28.92Fab 21 1971 77 48 122 17 30.02Feb 22 1985 7 62 138 16 34.67Feb 23 1906 70 64 133 15 36.17Feb 26 1939 71 60 130 14 35.85Feb 27 1970 73 53 124 13 34.94Feb 28 1928 71 50 119 12 35.63Feb 29 1953 59 54 113 Ww 34.76Mar 4 1944 58 52 109 10 35.62Mar 4. 1920 9Mar 5 1953 8Mar 6 2019 7Mar 7 1981 6Mar 8 1961 5Mar 11 1991 4Mar 12 2046 3Mar 13 2058 2Mar 14 2116 1Mar 15 2199 April option expires
FIGURE 6-4. A sequence of at-the-money straddles and implied volatilities calcu-lated for April crude oil over a 2-month time interval. Note how the implied volatilityalmost doubles between January 2 and March 1, even though the absolute price of thefuture rises only by a small amount.
The column headed ATMS, is the "corrected at-the-money straddle price.CHAPTERSEVEN
THE PROMISEDLAND
Ape who has seriously tested a "system" for trading com-modity futures using historical price data knows that chanceplays a large part in the outcome of any one hypothetical trade.One system is long gold with a sell stop at 295; another systemis also long with a sell stop at 293. Gold comes down to 294,makes a bottom and immediately takes off on the upside. Thefirst system is stopped out of its long and goes short, the secondsystem stays long. The short-term performances for the two sys-tems are radically different, even though the result is clearly aPure fluke. Savvy researches are well aware of the sensitivity ofsystems to fluke occurrences and take precautionary steps toeliminate chance from invalidating any general conclusions theyare trying to draw.
First, they scrupulously avoid the temptation to start testingthe system at a favorable time. It is a powerful temptation andmay act even on a subliminal level. The way to avoid a bias of thiskind is to choose one's initial conditions in a way that is clearlyobjective. To that end, to eliminate as far as possible any selec-tivity in choosing a period, I have dealt with one specific calen-dar year, 1996 — beginningon the first trading day and ending onthe last trading day (1996 is the latest calendar year for whichdata were available when the study began).
Asecond precautionary line to take in preparing to test a trad-ing hypothesis is to broaden the scope of testing to cover as manydifferent markets as possible, to take as large samples as are prac-ticable, and to restrict one’s conclusions to the market as a
101102 OPTION REALITY
whole. To that end, I have selected 15 actively traded commod-ity futures markets with actively traded options, covering as widea range of market types as possible; the selected markets includegrains, meats, metals, tropical products, resources, and financialinstruments. The goal is not to come to any conclusions aboutparticular markets—the sample sizes cannot support this,but rather to come to particular conclusions about the market ingeneral.
*
Suppose it were possible to obtain for every option ever writ-ten its residual value at expiry. If these residual values could thenbe summed and compared with the sum of the premiumsreceived for writing them, it would be possible to answer, defini-tively, that most pressing of questions: Who has the edge in themarket, the writer of options or the buyer of options?
It is only practical to look at a very small sample from theentire universe of options ever written. But this can still be alarge absolute sample, and if made large enough should be rep-resentative of the universe of all options. How large is large? Thedata base available for testing here includes estimates of the trueat-the-money straddle values and implied volatilities for 15 com-modity contracts over 250 or so consecutive trading days—amounting to about 3750 observations in total.
Imagine that all 3750 of these at-the-money straddles wereactually written—15 per day, every day, for an entire year, andthat each straddle was held until it expired. Hold on, you say:How could these straddles possibly have been written? They haveimplied strike prices, not real strike prices. True enough. But,from a statistical perspective it makes no difference whether thestraddle price is taken at a theoretical strike price or at a truestrike price as long as the correction multiplier is properly applied.
Figure 7-1, an amplification of the information presented inFigure 6-4, lists the outcomes of writing phantom at-the-moneystraddles on the April 1996 crude oil futures contract over a42-day trading period commencing January 2. Assume one strad-dle is written each day, at the close of trading, at the correctedTHE PROMISED LAND 103
at-the-money straddle price. As each day passes, the times toexpiry of the straddles are continuously declining. The futuresprice is also continuously changing. The straddles are all boundto expire on the same date and be settled against the samefutures close, but, since the straddles are contracted at very dif-ferent prices and at very different times, as a group of hypothet-ical trades they are essentially independent and therefore whensummed and averaged can be considered representative of theaverage outcome of option writing or option buying during thetrading period in question.
Consider, for example, the statistics of Figure 7-1, beginningwith the first line of the table. The implied strike price onJanuary 2 is 1884. The option expires on March 15 with thefutures price at 2199, leaving the option with an expired residualvalue (the call side of the straddle) of 315 points. Since the strad-dle premium at the time the option is written on January 2 was125 points, this straddle transaction favors the buyer by theamount of 315 - 125, or 190 points.
Proceeding down the columns of Figure 7-1, it is evidentthat, in all 42 hypothetical straddle positions taken, the outcomefavors the straddle buyer. The reason, of course, is that the futuretakes off sharply to the upside close to option expiry. (Whenevera strong trend develops in a futures market, unprotected optionwriters can expect to suffer.)
During the test period of 42 days, the average premiumreceived by the writer of the straddle is 126 points, the averagevalue of the straddle at option expiry 377 points, and the averagegain to the buyer 251 points. How representative are these num-bers of the crude oil futures market during January and Februaryof 1996—as far as option writing and option buying are con-cemed? Pretty good, I think. A hypothetical straddle has beenwritten at every possible futures price close, ensuring that no onerogue observation at some extreme futures close can exert undueinfluence on the overall result.
The final column of Figure 7-1 lists the implied volatilities ofthe at-the-money options. Notice how the the implied volatilityincreases from 18.62 to 35.82 and how the straddle premium onJanuary 2 when there are 53 trading days to expiry is scarcely104 OPTION REALITY
CRUDE OIL April 1996 option and April 1996 future
May Change ‘Future at ATMSr ATMSt ATMSt Days ImpliedDate future (no sign) (as %) expiry expiry rec'd -ATMSr left volatility
 
 
Jan 2 1884 2199 315 125 -190 53 18.26Jan 3 1890 6 0.32 2199 309 125 +184 52 18.36Jan 4 1893 3 0.16 2199 306 126 -180 51 18.70Jan 5 1928 35 1.82 2199 271 129 1142 50 18.86Jan 9 1896 32 1.69 2199 303 126 177 48 19.13Jan 10 1878 18 0.96 2199 321 122 199 47 18.93Jan 11 1805 73 4.04 2199 394 125 -269 46 20.35Jan 12 1774 31 1.75 2199 425 129 -296 45 21.60Jan 15 1779 5 0.28 2199 420 125 -295 44 21.18Jan 16 1743 36 2.07 2199 456 136 320 043 23.87Jan 17 1779 36 2.02 2199 420 135 285 = 42 23.34Jan 18 1796 17 0.95 2199 403 138 265 41 23.97Jan 19 1781 15 0.84 2199 418 129 +289 «40 22.82Jan 22 1774 7 0.39 2199 425 135 -290 «39 24.29Jan 23 1767 7 0.40 2199 432 132 30038 24.22Jan 24 1788 21 1A7 2199 41 129 -282 37 23.71Jan 25 1737 51 2.94 2199 462 133 329 «(36 25.47Jan 26 1736 1 0.06 2199 463 134 32935 26.03Jan 29 1716 20 1.17 2199 483 139 3440034 27.69Jan 30 1724 8 0.46 2199 475 136 -339 033 27.40Jan 31 1737 13 0.75 2199 462 134 -328 32 27.24Feb 1 1731 6 0.35 2199 468 136 33200311 28.25Feb 2 1738 7 0.40 2199 461 133 -328 4-30 27.93Feb5 1717 21 1.22 2199 482 140 +342 29 30.36Feb6 1730 13 0.75 2199 469 134 -335 «28 29.30Feb7 1731 1 0.06 2199 468 127 -341 27 28.29Febs8 1733 2 0.12 2199 466 113 +353 26 25.67Feb 9 1738 5 0.29 2199 461 107 +354 25 24.61Feb 12 1750 12 0.69 2199 449 100 -349 24 23.33Feb 13 1835 85 4.63 2199 364 106 -258 «23 24.00Feb 14 1835 oO 0.00 2199 364 112 +252 22 25.94Feb 15 1837 2 0.11 2199 362 114 248 (21 27.04Feb 16 1839 2 0.11 2199 360 114 +246 0-20 27.73Feb 20 1927 88 4.57 2199 272 118 +154 18 28.92Feb 21 1971 44 2.23 2199 228 122 +106 17 30.02Feb 22 1985 14 0.71 2199 214 138 -76 16 34.67Feb 23 1906 79 4.14 2199 293 133 +160 16 36.17Feb 26 1939 33 1.70 2199 260 130 +130 14 35.85Feb 27 1970 31 1.57 2199 229 124 +105 13 34.94Feb 28 1928 42 2.18 2199 271 119 -152 12 35.63Feb 29 1953, 25 1.28 2199 246 113 -133 1 34.76Mar 1 1944 9 0.46 2199 255 109 7146 10 35.62Averages ——-B 23 1.26 377 126 -251 26.49
* On Mar 15, the Apr 96 option expired at 2199
FIGURE 7-1. The table above lists the outcomes of taking hypothetical at-the-money straddle positions on April crude oil on 42 consecutive trading days beginningJanuary 2, 1996. It is assumed that a straddle once written is held until option expiry.Since an at-the-money straddle has to pay off on one side for sure, the straddle mustend up having residual value, ATMS, (the difference between the phantom strike priceand the price of the future at option expiry). The writer's net gain is the differencebetween the straddle premium received, ATMS,, and the amount to be paid out,ATMS,.THE PROMISED LAND 105
more than the straddle premium on March 1 when there are only10 trading days till expiry.
As discussed in the chapters on option theory, the mostimportant determinant of option premium (or implied volatility)is the size of the typical daily price changes in the futures con-tract and not the direction of the futures market. Did the impliedvolatility of April crude oil rise in response to a sharp rise in themarket volatility of the future, as suggested by theory? To someextent, this is true, but visual inspection of the sequence of dailyprice changes does not suggest a doubling of market volatilitycorresponding to a doubling of implied volatility (daily pricechanges, and daily price changes expressed as percentages ofabsolute value are listed in the third and fourth columns ofFigure 7-1). Is it possible that writers of crude oil options rathersuddenly realized that the option market was underpriced forsome other reason, and for that reason raised their asking prices?An interesting conjecture; if true, it supports the hypothesis thatoption markets may not always be fairly priced and that suchconditions may persist for some considerable period.
In Figure 7-2, April crude oil numbers are replaced by thecorresponding May silver numbers from the same 2 calendarmonths. With silver straddles it is the writer who wins on everyhypothetical straddle, since on each occasion the straddle pre-mium collected exceeds the residual value of the straddle atoption expiry. The average premium received by the writer is 450points, the average value of the straddle at option expiry is 123points, and the average net gain to the writer 326 points. In con-trast to crude oil, where the implied volatility doubles over the 2-month period, the implied volatility of silver remains fairly steady,fluctuating between 20 percent and 26 percent.
The crude oil and silver markets during January and Februaryof 1996 represent polar extremes. In crude oil, the buyer wins allthe time, and in silver the writer wins all the time. Does this indi-cate that crude oil is an option buyer's market while silver is anoption writer's market? Hardly. The samples are much too smalland unlikely to be representative of future patterns. In other peri-ods, the outcomes could be completely different. Most of thetime, which side a market is favoring at any particular moment106
SILVER May1996 option and May 1996 future
OPTION REALITY
 
 
May —Change ‘Future at ATMSr ATMSt ATMSt Days ImpliedDate future (nosign) (as%) expiry expiry rec'd -ATMSr left volatility
Jan 2 5443 5618 75 505 430 73 21.74Jan 3 5440 3 0.06 5618 78 508 430 72 22.02Jan 4 5463 23 0.42 5618 55 504 449 71 21.91Jan 5 5603 140 2.50 5518 38s 526 441 70 22.46Jan 8 5603 Qo 0.00 5618 8s 526 441 69 22.62Jang 5610 7 0.12 5618 92 523 431 68 22.59Jan 10 5673 63 1.441 5618 155 564 409 67 24,29Jan 11 5583 90 1.61 5518 65 512 447 66 22.60Jan 12 5623 60 1.09 5618 5 508 503 65 22.83Jan 15 5498 25 0.45 5518 20 466 446 64 21.17Jan 16 5640 42 0.76 5518 22 457 435 63 20.78Jan 17 5568 28 0.50 5518 50 451 401 62 20.58Jan 18 5513 55 1,00 5518 5 445 440 61 20.69Jan 19 5523 10 0.18 5518 5 443 438 60 20.73Jan 22 5648 125 2.21 5518 130 495 365 59 22.82Jan 23 5628 20 0.36 5518 110 473 363 58 22.07Jan 24 5580 48 0.86 5518 62 470 408 57 22.33Jan 25 5638 58 1.03 5518 120 468 348 56 22.17Jan 26 5598 40 0.71 5518 80 464 384 55 22.36Jan 29 5598 o 0.00 5518 80 445 365 54 21.64Jan 30 5616 18 0.32 5518 98 459 361 §3 22.46Jan 31 5641 25 0.44 5518 123 462 339 4 22.73Feb1 5848 207 3.54 5518 330 531 201 51 25.43Feb2 §893 45 0.76 5518 375 539 164 50 25.85Feb5 5867 26 0.44 5518 349 516 167 49 25.11Feb 6 5829 38 0.65 5518 311 492 181 48 24.35Feb 7 5763 66 1.18 5518 245 460 215 47 23.28Febs 5780 17 0.29 5518 262 487 196 46 23.34Feb 9 §720 60 1.05 5518 202 447 245 45 23.32Feb 12 5723 3 0.05 5518 205 423 218 44 22.28Feb 13 §772 49 0.85 5518 254 393 139 43 20.76Feb 14 5790 18 0.31 5518 272 388 116 42 20.70Feb 15 5699 91 1,60 5518 181 392 211 41 21.46Feb 16 5776 7 1.33 5518 258 388 130 40 21.24Feb 20 5583 193 3.46 §518 65 368 302 38 21.36Feb 21 5633 50 0.89 §518 115 343 228 37 20.04Feb 22 5577 56 1.00 §518 59 352 293 36 21.01Feb 23 5504 73 1.33 §518 14 360 346 35 22.11Feb 26 5530 26 0.47 5518 12 352 340 34 21.82Feb 27 5504 26 0.47 5518 14 342 328 33 21.61Feb 28 5535 31 0.56 5518 17 341 324 32 21.78Feb 29 5545 10 0.18 5518 27 320 293 31 20.71Averages --——B 50 0.88 123 450 326
* On Apr 12, the May 96 option expired at 5518
FIGURE 7-2.
The table above lists the outcomes of taking hypothetical at-the-
money straddle positions on May silver on 42 consecutive trading days beginningJanuary 2, 1996. The outcomes are completely opposite to those for crude oil. Thestraddle writer is the clear winner; on every occasion, the premium collected exceedst