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