29 lines
1.9 KiB
Plaintext
29 lines
1.9 KiB
Plaintext
Gamma
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The strike price is the only constant in the pricing model. When the stock
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price moves relative to this constant, the option in question becomes more
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in-the-money or out-of-the-money. This means the delta changes. This
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isolated change is measured by the option’s gamma, sometimes called
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curvature .
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Gamma (Γ) is the rate of change of an option’s delta given a change in
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the price of the underlying security . Gamma is conventionally stated in
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terms of deltas per dollar move. The simplified examples above under
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Definition 1 of delta, used to describe the effect of delta, had one important
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piece of the puzzle missing: gamma. As the stock price moved higher in
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those examples, the delta would not remain constant. It would change due
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to the effect of gamma. The following example shows how the delta would
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change given a 0.04 gamma attributed to the call option.
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The call in this example starts as a 0.50-delta option. When the stock
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price increases by $1, the delta increases by the amount of the gamma. In
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this example, delta increases from 0.50 to 0.54, adding 0.04 deltas. As the
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stock price continues to rise, the delta continues to move higher. At $62, the
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call’s delta is 0.58.
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This increase in delta will affect the value of the call. When the stock
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price first begins to rise from $60, the option value is increasing at a rate of
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50 percent—the call’s delta at that stock price. But by the time the stock is
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at $61, the option value is increasing at a rate of 54 percent of the stock
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price. To estimate the theoretical value of the call at $61, we must first
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estimate the average change in the delta between $60 and $61. The average
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delta between $60 and $61 is roughly 0.52. It’s difficult to calculate the
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average delta exactly because gamma is not constant; this is discussed in
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more detail later in the chapter. A more realistic example of call values in
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relation to the stock price would be as follows: |