18 lines
1.2 KiB
Plaintext
18 lines
1.2 KiB
Plaintext
The Imprecision of Estimation
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It is important to notice that the P&(L) found by adding up the P&(L)’s
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from the greeks is slightly different from the actual P&(L). There are a
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couple of reasons for this. First, the change in delta resulting from gamma is
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only an estimate, because gamma changes as the stock price changes. For
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small moves in the underlying, the gamma change is less significant, but for
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larger moves, the rate of change of the gamma can be bigger, and it can be
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nonlinear. For example, as an option moves from being at-the-money
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(ATM) to being out-of-the-money (OTM), its gamma decreases. But as the
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option becomes more OTM, its gamma decreases at a slower rate.
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Another reason that the P&(L) from the greeks is different from the actual
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P&(L) is that the greeks are derived from the option-pricing model and are
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therefore theoretical values and do not include slippage.
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Furthermore, the volatility input in this example is rounded a bit for
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simplicity. For example, a volatility of 25 actually yielded a theoretical
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value of 2.796, while the call was bought at 2.80. Because some options
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trade at minimum price increments of a nickel, and none trade in fractions
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of a penny, IV is often rounded. |