38 lines
2.6 KiB
Plaintext
38 lines
2.6 KiB
Plaintext
Chapter 40: Advanced Concepts 857
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delta will be more dramatic than it would be for a volatile stock. Out-of-the-money
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options are an entirely different story. Since the nonvolatile stock will have difficulty
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moving fast enough to reach an out-of-the-money striking price, the delta of the out
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of-the-money option is small and it will not change quickly (that is, the gamma is
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small also).
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These concepts are summarized in Figure 40-5 (see Table 40-5), which depicts
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the gammas for similar options on stocks with differing volatilities. For the purposes
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of these graphs, XYZ is equal to 50 and there are three months remaining until expi
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ration.
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Notice that for a very volatile stock, the gamma is quite stable over nearly all
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striking prices when there are 3 months remaining until expiration. This means that
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the deltas of all options on such a volatile stock will be changing quite a bit for even
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a 1-point move in the underlying stock. This is an important point for neutral strate
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gists to note, because a position that starts out as delta neutral may quickly change if
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the underlying stock is very volatile. As this table implies, the deltas of the options in
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that "neutral" spread may be altered quickly, thereby rendering the spread quite un
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neutral. This concept will be discussed in greater detail later in this chapter.
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As delta was used to construct the equivalent stock position of an entire option
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position or portfolio, gamma can be used in a similar manner. An example of this fol
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lows, using the same securities from the preceding example on the delta of a posi
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tion. An important point to note is that the gamma of the underlying security itself is
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zero. This is true because the delta of the underlying security (which is always 1.0)
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never changes - hence the gamma is zero. The gamma is measuring the amount of
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change of the delta; if the delta of the underlying security never changes, the gamma
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of the underlying security must be zero.
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Example: The following position exists when XYZ is at 31.75. Recall that it resem
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bles a long straddle ( or backspread) in that there is increased profit potential in either
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direction if the stock moves far enough by expiration. In addition to the delta previ
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ously listed, the gamma is now shown as well. Note that since gamma is a small
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absolute number, it is sometimes calculated out to three or four decimal places.
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Option Position Option Position
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Position Delta Delta Gamma Gamma
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Short 4,500 XYZ 1.00 - 4,500 0.0000 0
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Short l 00 XYZ April 25 calls 0.89 - 8,900 0.0100 -100
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Long 50 XYZ April 30 calls 0.76 + 3,800 0.0300 +150
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Long 139 XYZ July 30 calls 0.74 +10,286 0.0200 +278
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Totals: + 686 +328 |