The Effects of Volatility and Time on
Theta
Stock price is not the only factor that affects theta values. Volatility and
time to expiration come into play here as well. The volatility input to the
pricing model has a direct relationship to option values. The higher the
volatility, the higher the value of the option. Higher-valued options decay at
a faster rate than lower-valued options—they have to; their time values will
both be zero at expiration. All else held constant, the higher the volatility
assumption, the higher the theta.
The days to expiration have a direct relationship to option values as well.
As the number of days to expiration decreases, the rate at which an option
decays may change, depending on the relationship of the stock price to the
strike price. ATM options tend to decay at a nonlinear rate—that is, they
lose value faster as expiration approaches—whereas the time values of ITM
and OTM options decay at a steadier rate.
Consider a hypothetical stock trading at $70 a share. Exhibit 2.11 shows
how the theoretical values of the 75-strike call and the 70-strike call decline
with the passage of time, holding all other parameters constant.
EXHIBIT 2.11 Rate of decay: ATM vs. OTM.