Add training workflow, datasets, and runbook
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Dynamic Inputs
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Option deltas are not constants. They are calculated from the dynamic
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inputs of the pricing model—stock price, time to expiration, volatility, and
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so on. When these variables change, the changes affect the delta. These
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changes can be mathematically quantified—they are systematic.
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Understanding these patterns and other quirks as to how delta behaves can
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help traders use this tool more effectively. Let’s discuss a few observations
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about the characteristics of delta.
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First, call and put deltas are closely related. Exhibit 2.2 is a partial option
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chain of 70-day calls and puts in Rambus Incorporated (RMBS). The stock
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was trading at $21.30 when this table was created. In Exhibit 2.2 , the 20
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calls have a 0.66 delta.
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EXHIBIT 2.2 RMBS Option chain with deltas.
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Notice the deltas of the put-call pairs in this exhibit. As a general rule, the
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absolute value of the call delta plus the absolute value of the put delta add
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up to close to 1.00. The reason for this has to do with a mathematical
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relationship called put-call parity, which is briefly discussed later in this
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chapter and described in detail in Chapter 6. But with equity options, the
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put-call pair doesn’t always add up to exactly 1.00.
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Sometimes the difference is simply due to rounding. But sometimes there
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are other reasons. For example, the 30-strike calls and puts in Exhibit 2.2
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have deltas of 0.14 and −0.89, respectively. The absolute values of the
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deltas add up to 1.03. Because of the possibility of early exercise of
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American options, the put delta is a bit higher than the call delta would
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