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