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 position’s 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

GILD @ 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 the 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 the movement in the underlying.

Gamma Table

GILD @ 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 the premium captured 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  intrinsic and extrinsic value. Intrinsic value represents the amount of premium in relation to the strike with regards to parity to the underlying. Extrinsic value is the amount of excess premium in relation to parity with regards to the underlying.   

Theta Table

GILD @ 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 and vice-versa. 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

GILD @ 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

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 carrying 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.

Ross Barnett Terry, Contributor