37 lines
2.6 KiB
Plaintext
37 lines
2.6 KiB
Plaintext
764 Part VI: Measuring and Trading VolatiRty
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It's a little unfair to say that, because it's conceivable (although unlikely) that volatil
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ity could jump by a large enough margin to become a greater factor than delta for
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one day's move in the option. Furthermore, since this option is composed mostly of
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excess value, these more dominant forces influence the excess value more than time
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decay does.
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There is a direct relationship between vega and excess value. That is, if implied
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volatility increases, the excess value portion of the option will increase and, if implied
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volatility decreases, so will excess value.
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The relationship between delta and excess value is not so straightforward. The
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farther the stock moves away from the strike, the more this will have the effect of
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shrinking the excess value. If the call is in-the-money (as in the above example), then
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an increase in stock price will result in a decrease of excess value. That is, a deeply in
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the-money option is composed primarily of intrinsic value, while excess value is quite
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small. However, when the call is out-of-the-money, the effect is just the opposite:
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Then, an increase in call price will result in an increase in excess value, because the
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stock price increase is bringing the stock closer to the option's striking price.
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For some readers, the following may help to conceptualize this concept. The
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part of the delta that addresses excess value is this:
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Out-of-the-money call: 100% of the delta affects the excess value.
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In-the-money call: "1.00 minus delta" affects the excess value. (So, if a call is very
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deeply in-the-money and has a delta of 0.95, then the delta only has 1.00 - 0.95,
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or 0.05, room to increase. Hence it has little effect on what small amount of
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excess value remains in this deeply in-the-money call.)
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These relationships are not static, of course. Suppose, for example, that in the
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same situation of the stock trading at 82 and the January 80 call trading at 8, there is
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only week remaining until expiration! Then the implied volatility would be 155%
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(high, but not unheard of in volatile times). The greeks would bear a significantly dif
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ferent relationship to each other in this case, though:
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Delta: 0.59
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Vega: 0.044
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Theta: -0 .5 1
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This very short-term option has about the same delta as its counterpart in the previ
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ous example (the delta of an at-the-money option is generally slightly above 0.50).
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Meanwhile, vega has shrunk. The effect of a change in volatility on such a short-term
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option is actually about a third of what it was in the previous example. However, time
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decay in this example is huge, amounting to half a point per day in this option. |