Effect of Volatility on Delta
The level of volatility affects option deltas as well. We’ll discuss volatility
in more detail in future chapters, but it’s important to address it here as it
relates to the concept of delta. Exhibit 2.4 shows how changing the
volatility percentage (explained further in Chapter 3), as opposed to the
time to expiration, affects option deltas. In this table, the delta of a call with
91 days until expiration is studied.
EXHIBIT 2.4 Estimated delta of 50-strike call—impact of volatility.
Notice the effect that volatility has on the deltas of this option with the
underlying stock at various prices. In this table, at a low volatility with the
call deep in- or out-of-the-money, the delta is very large or very small,
respectively. At 10 percent volatility with the stock at $58 a share, the delta
is 1.00. At that same volatility level with the stock at $42 a share, the delta
is 0.
But at higher volatility levels, the deltas change. With the stock at $58, a
45 percent volatility gives the 50-strike call a 0.79 delta—much smaller
than it was at the low volatility level. With the stock at $42, a 45-percent
volatility returns a 0.30 delta for the call. Generally speaking, ITM option
deltas are smaller given a higher volatility assumption, and OTM option
deltas are bigger with a higher volatility.