The Effect of Moneyness on Vega
Like the other greeks, vega is a snapshot that is a function of multiple facets
of determinants influencing option value. The stock price’s relationship to
the strike price is a major determining factor of an option’s vega. IV affects
only the time value portion of an option. Because ATM options have the
greatest amount of time value, they will naturally have higher vegas. ITM
and OTM options have lower vega values than those of the ATM options.
Exhibit 2.13 shows an example of 186-day options on AT&T Inc. (T),
their time value, and the corresponding vegas.
EXHIBIT 2.13 AT&T theos and vegas (T at $30, 186 days to Expry, 20%
IV).
Note that the 30-strike calls and puts have the highest time values. This
strike boasts the highest vega value, at 0.085. The lower the time premium,
the lower the vega—therefore, the less incremental IV changes affect the
option. Since higher-priced stocks have higher time premium (in absolute
terms, not necessarily in percentage terms) they will have higher vega.
Incidentally, if this were a $300 stock instead of a $30 stock, the 186-day
ATMs would have a 0.850 vega, if all other model inputs remain the same.