The
“Greeks”
Options
are dynamic animals governed by a set of theoretical variables known as
“Greeks.” Together they assume the dynamics of the sensitivity of the option
with regards to a one point move in the underlying.
The most important of the “Greeks” are:
Delta
represents the rate of change in the price of an option in relation to a one
point move up or down in the underlying.
Gamma
represents the rate of change in the delta of the option itself. In essence the
rate of change in relation to the rate of change in relation to a one point
move up or down on the underlying.
Rho
represents
the sensitivity of an options price with regards to a change in interest rates.
Theta
represents
the option prices rate of decay price in relation to time until expiration.
Vega
represents
sensitivity of an options pricing to a change in implied volatility with
regards to the underlying.
Additional terms of note:
ITM in-the-money
ATM at-the-money
OTM out-of-the-money
Intrinsic
Value
Extrinsic
Value
The
above 5 “Greeks” are the most significant variables that go into the pricing of
an option when trying to determine what a positions inherent risk is with
regards to movement of the underlying and time left in an options life.
Delta
The
Delta of an option is used to identify the equivalency of the number of options
to the actual underlying shares. As time passes, the deltas rise or fall the
option in relation to the underlying, depending on the option in question, as
expiration nears.
Look at the following examples:
Delta Table
BRUN @ 75.00
Strike
August (16) September (51) December (142)
65
.91 .88 .80
70
.81 .72 .65
75
.42 .44 .47
80
.11 .19 .29
85
.02 .07 .17
In the above Table A notice that deltas increase on
the 65 and 70 strikes (ITM) where as they decrease on the 80 and 85(OTM)
strikes as expiration nears and stay relatively stable on the 75 strike
(ATM).
In-the-money options have little extrinsic values therefore
their Theta is low, but they have the risk of loss in value should the option
start to move to at-the-money or even out-of-the-money.
At-the-money options have the most Theta due to the
fact that they offer the closest relation to the underlying price they
typically have low to no intrinsic value associated with them.
Out-of-the-money options are comprised of only
extrinsic value.
Gamma
As the
price of the underlying moves up or down so does the delta in relation to
pricing of the option. A one point gain or loss means the underlying is either
closer or further from the strike, so the relation of the price of that option
changes accordingly as well. This is known as the gamma. As an option nears
expiration the gamma tends to increase as it becomes more sensitive to movement
in the underlying.
Gamma Table
BRUN @ 75.00
Strike
August (16) September (51) December (142)
65 .02 .03 .03
70 .06 .05
.03
75 .09 .06 .04
80 .04 .04 .03
85
.01 .02 .02
Notice in the above table that the most sensitive
options are again the august 75 strike, which again are the most sensitive to a
price change in the underlying.
Theta
Since
options have a defined life or set expiration date, Theta is one of the most
important of the variables. At expiration they will either expire worthless or
be converted to shares of stock. That is a given. Knowing how much time decay
an option will incur allows a trader to calculate his risk of owning or premium
capture if they were a seller of the option. The rate of decay increases
exponentially as the option gets closer to expiration. In the money options
have what is known as both intrinsic value which represents the amount of
premium in relation to the strike with regards to parity to the underlying.
Extrinsic is the amount of excess premium in relation to parity with regards to
the underlying.
Theta Table
BRUN @ 75.00
Strike August
(16) September (51) December (142)
65
-.03
-.01 -.01
70 -
.04 - .02 -.01
75 -
.05 -.02 -.01
80
-.03
-.02 -.01
85
-.01
-.01 -.01
In the
above table notice that the decay is greatest in the front month and on the 75
strike which represents the ATM options. This is due to the relation of premium
left in the option in relation to the amount of time left in the life of that
option. It is also worth noting that Theta is expressed as a negative value due
to the fact it represents decay. If Vega were to increase the value of the
options would also increase, but the decay would simply be greater.
Vega
Vega is
actually representing the value in relation to the underlying as volatility
increases so does the value of options. This occurs for a number of reasons. Traders
back off as sellers due to increased risk. They want to be paid for the
increased risk of selling that premium if you will. Buyers are also willing to
pay a higher premium as the chances of the option ending up ITM increase. It is
a constant ebb and flow and sets the pace for the rest of the “Greeks” to
follow suit.
Vega Table
BRUN @ 75.00
Strike
August (16) September (51) December (142)
65
.03 .05 .12
70
.06 .09 .17
75
.06 .11 .18
80
.03 .08 .16
85
.01 .04 .12
Rho
Though
at this point in time Rho has been rendered somewhat moot, it is important to
understand a couple of things with regards to options pricing. A rise in
interest rates causes puts to become cheaper due to the increased cost of carry
on stocks. Speculators would rather face premium decay as opposed to paying the
cost of carry. The at-the-money options in the furthest out months are the most
effected by the changes in interest rates.
*Disclaimer: This is not a recommendation. All
trading entails risk. Anyone employing any strategies and having limited
knowledge of options trading should consult with a FNRA licensed professional.