Options can be terribly confusing for the trader
first encountering them. One of the most confusing concepts to understand is
the interplay of the three primal forces of options- price of the underlying
asset, time to expiration, and implied volatility.
of each of these three factors on any given option position can be measured
by its corresponding “Greek”. The “Greeks”
corresponding to each of these factors are: delta-price, theta-time,
and vega-implied volatility.
major Greek is gamma and represents the change in delta as
price of the underlying changes. Math majors among readers will recognize
that gamma is the second derivative of delta.
of data points available to the options trader can be overwhelming,
especially for the new trader first becoming familiar with these derivatives.
It is important not to get lost in the data available and to focus on the
decisions at hand. Consider the tremendous amount of information available on
the following small portion of the options montage for AAPL. For this article
I want to focus on delta and gamma exclusively.
Delta is a
measure of the correlation of price change of an option relative to the price
change of the underlying. It is a very dynamic attribute and can potentially
range from 0 to 1 for individual calls and 0 to -1 for individual puts. Delta
is always a positive number for calls and a negative number for puts.
option with a delta of 0.5 would move up 50¢ for the first dollar
increase in the price of the underlying. As an example, consider AAPL which
is trading at $605 / share.
605 call has a delta of 53.2 and would increase in value 53.2¢ as the
price of AAPL traded up to $606. To provide a point of reference for the
stock trader, each individual share of stock can be thought of to have a
delta of one.
that the delta of any individual option is not a constant value but increases
and decreases as price of the underlying changes. Gamma represents the rate
of change of delta as the strike price of an option moves closer to or farther
from the current market price of the underlying. The dynamic nature of delta
is a critical point of understanding for the successful options trader.
values for both puts and calls are positive. As an example, our August 605
AAPL call has a gamma of 0.93. As price moves from 605 to 606, delta will
increase from 53.2 to (53.2+0.93) = 54.13.
dynamic nature of delta has the net result of a positive gamma position
becoming increasingly long or short as price moves in the predicted
direction. Conversely, the trader holding a negative gamma position becomes
increasingly long or short inverse to the market’s direction.
practical use, delta has some exceedingly helpful characteristics and
provides several useful benchmarks for the trader. One particularly
interesting characteristic of delta is its relationship to our recent
probability discussion. The delta of any given option is a rough
approximation of the probability that it will expire
in-the-money. Therefore, our August AAPL 605 call with a delta of 53.2 has
around a 53.2% probability of being in the money at expiration.
correlation of the delta with the probability of expiring in the money has
great utility in selecting trades. For example, knowing this probability
relationship, the iron condor trader can easily select the strike with the
probability of success appropriate for his risk tolerance.
helpful and consistent observation is that the at-the-money strike always has
a delta of around 50 for calls and -50 for puts. In-the-money strikes always
have deltas with an absolute value greater than 50 and out of the money
strikes have deltas with absolute values less than 50.
infrequently discussed characteristic of delta is its behavior in relation to
time to expiration. Immediately before the moment of expiration, an
individual option must have a delta of either 0 or 100, and as it approaches
its point of expiration, the delta begins to rise or fall to meet that value.
articles we will tackle the issues of the other Greeks. At this point suffice
it to say that an intimate familiarity with the behavior of option positions
predicted by the metrics reflected in the Greeks will give you a significant
advantage in managing your option positions now and in the future.