“DELTA (D), GAMMA (G),
THETA(T), VEGA(V), RHO(R)
“It all sounds Greek to me”
• Delta is usually related to options in terms of
referring to the rate at which an option contract will
move in tandem with the underlying security.
• Delta was originally thought of as the hedge factor
in determining how many options were needed to
act exactly like the underlying investment.
• One of the biggest frustrations for an option trader
is having an option that is in the money move
maybe 1/2 to 3/4 for every point that the
underlying security moves. This is a major
frustration for traders, but most of this frustration is
due to a lack of understanding of how Delta works
and influences their option contracts.
Every option has a Delta value. They range from
0 to 100 in value. The put options have a value
from 0 to –100 in value.
• Example, if a option has a DELTA of 50, this
means that for every 1 point move in the
underlying security, the option contract would
move 50%, or in this case of an option priced at
$1.00, a 1/2 of a point.
• Usually options that are near the money have
Delta close to 50. In addition, as these options go
deeper into the money the Deltas on those
options tend to be closer to 70 or 80.
• The deeper in the money, the higher the Delta of
• Example: KLK is trading at 47 and the KLK
July 45 call is priced @ $4.50 with a Delta of 70.
• Simply translated: for every one point move in
KLK the July 45 call (with a Delta of 70) will
move .70 or 70%.
• So if KLK went from 47 to 49, then the July 45
call, which was trading at 4.50, will have gone
up to 5.90 (a 1.40 move, which is 70% of 2 or
• Add that 1.40 to the 4.50 and the option is
trading at 5.90.
• Let's take a look at a couple of situations so
you can see if you have it down.
• Please take note that this figure is strictly for
illustration purposes so that one can see how
generally Delta prices are figured.
• This is just a simple table to look over to get
a visual of how Delta is figured and let you
look at various examples
FIGURE 14-1: Look below to see how much the option will move
based on the following underlying Deltas.
• Delta is just one of the calculations that help one
understand why an option will move in the way it
does. However, Delta alone is not the only factor
that determines option movement. Delta is just the
most common due to the fact that large traders use it
to hedge their positions at all times. Understanding
why your options move as they do is an important
part of the overall understanding of option pricing
system. We will look at another important Greek term
called Gamma next.
• The Gamma of an option tells you how
much the Delta of an option changes as the
underlying stock or index changes. When
we examined Delta, we learned that every
option has a Delta, but we need to expand
on that knowledge to include the fact that :
• the value of that Delta changes as the stock
value changes. As the stock goes up or
down in value, the Delta also changes.
• Example: A call option, which is near the money
and has a Delta of 50, would see an increase or
decrease in that Delta as the price of the stock
rises or falls
• (e.g. If the hypothetical stock RRR was at 200
and went up 20 points and it RRR 200 call
increased 10 points, the Delta, which was at 50
may change and go up to a Delta of 60.
• The higher the stock goes, the greater the Delta
becomes of that option as it moves deeper into
• Gamma tells you the rate at which the option will increase or
decrease as the stock moves up or down.
• (i.e., If the RRR 200 call, had a Gamma
• this would mean that the Delta would
increase 3% for every point rise in the
• With the stock trading at 200, Let's
look at the example below.
• Delta Gamma
• RRR Jan 220 Call @ 4 50 4
• (The above option has a Delta of 50
• The above option has a Gamma of 4.)
• This would mean that if the stock goes
• the option that was at 4 would go to 6
(because of the Delta being 50, then the
Gamma of 4) would increase the Delta
to 52 because (4% increase of 50 is 2,
50+2 = 52 Delta).
STOCK GOES TO 210:
• If the stock goes up another 5 points to
210, the option would go up to 9 1/8,
and the Delta of 52 would now go up to
54 because of the Gamma of
See the Table Below
• RRR 200 205 210
• RRR JAN 220 Call 4 6 9 1/8
• Delta >>>>>>>>>> 50 52 54
• Gamma >>>>>>>>> 4 4 4
• Note: This is a hypothetical example of how Delta relates to the Gamma function.
• In the real world the Gamma would also change in relationship to the stock.
• Puts and calls have Gamma values,
and understanding Gamma will help
you to determine how much the Delta of
your option will change. By using
Gamma, you know how much the Delta
will change and Gamma will let you
know how quickly you must adjust your
• Please keep in mind that this would require
constant monitoring and a lot of time.
• Unless you are a trader who wants to
constantly monitor positions, this should just
be a lesson for you to become familiar with
how Gamma and Delta work together, and
give you a better understanding of their inner-
• Option Hedgers are always adjusting positions
attempting to keep these positions Delta NEUTRAL.
• Now, let's recall our definition of
Gamma, it defines the rate or the
speed or how much an option will
increase or decrease Delta points
as the underlying stock moves.
• The Delta on a call option increases with the increase
of the stock, but as a stock decreases, so does its
• Gamma just tells you how fast the change is taking
• (e.g. An option with a Gamma of 0.5 would tell us
that for every point rise in the stock, we would have a
1/2 point rise in the Delta of the option being traded.
If the Gamma were 2, the Delta would increase 2
points for every 1 point move in the stock.)
See example below:
The Real World
GAMMA, DELTA……Houston …we have a
• Unfortunately, just as Delta is not constant,
• Neither is Gamma.
• Gamma changes in value, just like Delta.
• The Gamma is highest when the option is at the
• The further out of the money the option is, the
greater decreases in the Gamma, meaning slower
and smaller changes of the Delta.
• Also, as it gets closer to expiration, Gamma will
Impact of GAMMA and DELTA
• Gamma is significant because it helps you manage
and measure how much risk you are taking.
• We learned that Delta was important because it
taught us that options move at varying amounts in
relationship to the stock
• and you might also need several options to get the
same result as the move of the underlying stock.
• If we know Delta , we can determine how many
options we need to equal the move of the underlying
Importance of GAMMA and DELTA
• Gamma becomes important because Delta is
always changing and as it changes we
learned that one may need to readjust one's
• Knowing Gamma helps to determine how
quickly the Delta is going to change and put
you in a position where you might need to
Traders use of Gamma
• Active traders use positions with
relatively low Gammas to reduce their risk.
• The reason is because they want their
Deltas to change less, so they don't have
to re-adjust their positions as much.
• Large Gamma positions are
usually considered riskier,
because you could be caught
long or short much quicker than
you would like to.
• JUST A NOTE IN CLOSING on
DELTA and GAMMA
• Gammas like Deltas have a
negative or positive
• Long Positions = Positive Gammas
• Short Positions = Negative Gammas
• Previously, we made references to how time
affects an option as it gets closer to its expiration
• We discussed that the value of that option will
decrease in price because of the reduction in the
time left until that option expires.
• We also learned that every option has time value
calculated in its premium,
• all out-of-the-money options are made up entirely
of time value.
• Theta is basically defined as the rate at which an
option losses its value as the option gets closer
• Theta, when calculated, is usually done by a
figure quoted in a certain number of points per
day that the option premium will decay.
• The unique thing that is inherent in Theta is that
the loss of value of the option premium because
of time decay is based on the assumption that
there is no change in the market price of the
option or the conditions in which the option is
• In other words, if you could isolate time
value and measure strictly an individual
• and assumed the price of the option did
not move, that would be a true measure of
how Theta functions.
• The reason all those other factors are not
considered is because they would
influence the price of the options and
• Example: volatility all of a sudden picks up in a
stock, or there are earnings rumors, buy-out
rumors, or various national economic news).
• All of these factors would affect Theta, and
that is why Theta, when analyzed, has to be
looked at as if these other market factors were
not in the equation.
• Theta works both ways in relationship to a
buyer or a seller. If you are a buyer of an
option, you want the option with a low Theta,
which has a very small erosion of premium as
time goes by.
• If you are a buyer of an option, you want
the option with a low Theta, which has a
very small erosion of premium as time
• On the other hand, if you are a seller of an
option, you want a rapid erosion of the
premium, giving the buyer less time to
make a profit.
• Theta is often most important in examining spreads.
• As you decide which spread to put on you could examine Theta
and make a determination whether the time value within the
spread is going to work for you or against you.
• By using Theta you can help better determine spreads that give
you the best time value disposition and
• which spreads would be better for you ultimately when it comes
down to making an educated decision as to which spread scenario
might be best, when you have several choices to choose from.
• This could be important, especially if you are a buyer or when
examining the long side of your spread, whether bullish or
• Vega has had various names associated
with it over time,
• such as Kappa or Omega.
• We will refer to it has Vega.
• Vega, in brief definition, is a value given
in points that measures change in
volatility. It measures a change in
theoretical value for each 1-point
variation in volatility.
• VEGA tells you how much an option will increase
based on an increase in the volatility of option and
the underlying stock issue.
• When you recall any number of your own personal
option trades, as the volatility increased in you
option, so did the premium and as volatility
decreased or slowed down, the premium of the
• The main use of Vega is to help and determine how
much risk you have from volatility increases and
• Remember, you may have only several days to go
on an option with little or no volatility, then all of a
• some market event, like a "surprise" earning report,
would could affect the volatility either positively or
negatively and exaggerate the price of the option,
even though there may be only a few days left
before its expiration.
• The net effect:
• The option being grossly overpriced due to
volatility from investor interest in that option.
• RHO is how an option reacts to changes in
• This Greek has a minor effect on pricing, but does have an
effect on premium, even if negligible.
• The Rho effect is similar to rises in interest rates.
• As interest rates go up, the option premium must increase
to keep the options in competition with other investment
vehicles. The premiums that the seller receives need to be
higher to compete with the other alternatives that an
investor has in the investment market place to choose from.
• Although Rho is part of the Greek family, its importance is
minimal at best.
The Real World
• The Greeks are used by many traders
to determine the various factors that
I related to in the above text.
• On the next slide you will find an
example of the Greeks we discussed
and how they look to traders and
followers of their use.
“IT ALL SOUNDS GREEK TO ME”
All the GREEKS
GREEKS – “The Bottom Line”
• As a trader, you can see there are many, many
trading tools that are available to attempt to give
traders any type of edge in their attempt to
maximize their trading profits.
• The use of Greeks are just one of the many tools
available to traders to help achieve that goal.
However, always remember, even the best financial
tools are not going to substitute for excellent
judgment, good risk/reward analysis and a sound
• As a trader, always try and expand your horizons
by examining new tools and philosophies that could
potentially serve to increase your bottom line