42 lines
2.0 KiB
Plaintext
42 lines
2.0 KiB
Plaintext
872 Part VI: Measuring and Trading Volatility
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shown in Table 40-9. However, since both options are sold, each sale places negative
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gamma in the position.
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The usefulness of calculating gamma is shown by this example. The initial posi
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tion is NET short only 100 shares of XYZ, a very small delta. In fact, a person who is
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a trader of small amounts of stock might actually be induced into believing that he
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could sell these 100 straddles, because that is equivalent to being short merely 100
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shares of the stock.
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TABLE 40-9.
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Position delta and gamma of straddle sale. XYZ = 88.
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Option Position Option Position
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Position Delto Delta Gamma Gamma
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Sell l 00 July 90 calls 0.505 -5,050 0.03 -300
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Sell 1 00 July 90 puts 0.495 +4,950 0.03 -300
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Total shares - 100 -600
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Calculating the gamma quickly dispels those notions. The gamma is large: 600
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shares of negative gamma. Hence, if the stock moves only 2 points lower, this trad
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er's straddle position can be expected to behave as if it were now long 1,100 shares
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(the original 100 shares short plus 1,200 that the gamma tells us we can expect to get
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long)! The position might look like this after the stock drops 2 points:
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XYZ: 86
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Position
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Sold 1 00 July 90 calls
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Sold 100 July 90 puts
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Option
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Delta
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0.44
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0.55
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Position
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Delta
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-4,400
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+5,500
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+ 1 , 100 shares
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Hence, a 2-point drop in the stock means that the position is already acquiring
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a "long" look. Further drops will cause the position to become even "longer." This is
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certainly not a position - being short 100 straddles - for a small trader to be in, even
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though it might have erroneously appeared that way when one observed only the
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delta of the position. Paying attention to gamma more fully discloses the real risks.
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In a similar manner, if the stock had risen 2 points to 90, the position would
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quickly have become delta short. In fact, one could expect it to be short 1,300 shares
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in that case: the original short 100 shares plus the 1,200 indicated by the negative
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gamma. A rise to 90, then, would make the position look like this: |