OPTION TALK: Understanding Our Greek Friends
Posted on March 16, 2007 at 15:30 PM EDT

In options trading there are four variables, termed the "greeks." They consist of Delta, Gamma, Theta and Vega. The greeks tell the astute options trader how a change in the underlying stock price, time to expiration or implied volatility will affect a position(s). In this article, I am going to explain how the four greeks can be used to give the trader a better understanding of how their position will change in value, with the change itself as one of the key variables.

Greek #1: Delta
Definition: The change in the price of an option relative to the change in price of the underlying security.

In plain English, Delta answers the question of how much can we expect our position to make/lose for a one point move in the underlying. Long call options have a positive Delta (0 to 1) whilst long put options have a negative Delta (0 to -1).

For example, if a US long call option (each contract = 100) has a Delta of 0.25, a \$1 move up in the stock would lead to the option position gaining \$25 in value (\$1 x 0.25 x 100).  If we had two contracts our position would increase in value by \$50 (\$1 x 0.25 x 200).

Should the stock go down by \$1 then the opposite would apply. For each long call option held the position would decrease in value by \$25.
The deeper a long call is In-The-Money [ITM] the closer the Delta value is to 1. Similarly, the deeper a long put option is ITM the closer the Delta will approach to the value of -1.

Greek #2: Gamma
Definition: The change in the Delta of an option with respect to the change in price of its underlying security. Gamma helps you gauge the change in an option's Delta when the underlying asset moves.

In simple terms, Gamma answers the question: what will the new Delta be if there is a \$1 movement in the stock price. Gamma is commonly labeled the Delta of Delta. In the above example, we used a Delta of 0.25. Let's have a Gamma of 0.05. If the underlying stock increased in value by \$1 then the Delta of the long call option would increase by 0.05 to 0.30.

Options that are At-The-Money [ATM] have the highest gamma value. This means the option will gain value at the fastest rate and thus provide the best return on investment [ROI]. However, be warned because this is a double-edged sword. If the underlying makes an unfavourable move and you are trading ATM options, the position will lose value at the fastest rate and hence produce the poorest ROI!

Greek #3: Theta
Definition: The change in the value of an option, relative to the change in its time to expiration.

Theta tells us how much our position will change in price for each passing day. With long options, Theta is working against us, whilst with short options Theta is on our side. Let's use an example to illustrate this:

We are long an option (call or put) priced at \$1.00 and it has a Theta value of -0.05. Ceteris paribus (holding all other variables constant) tomorrow we can expect the option to be priced at \$0.95 (1.00 - 0.05). Our position has lost \$0.05 of its value.

If we were short the option, our position would have gained \$0.05 in value. This is because we have sold an option for \$1.00 and now can buy it back for \$0.95.
The impact of Theta on your account value will vary depending on whether you are trading options in Australia or the USA. In Australia, one contract typically controls 1000 shares, whilst in the USA, one contract controls 100 shares. Using the above example which had a Theta value of -0.05, as one day passes:

In Australia one day would result in a change in your account of \$50.
In USA one day would result in a change in your account of \$5.

Greek #4: Vega
Definition: the change in price of the option relative to the change in its volatility.

Vega answers the question: How much does my position change with a one-point increase/decrease in volatility? If you are long an option and the IV (Implied Volatility) increases, then the position will gain value. If you are short, the position will lose value. The opposite applies for a decrease in IV.

Let's use an example of an option priced at \$2.00 with a Vega of \$0.06. If the IV increases by 1% the new option price will be \$2.06 (2.00 + 0.06). If the IV was to drop by 1% the option would be priced at \$1.94 (2.00 â 0.06)It depends on whether you are long or short as to how your position will be affected. If you are long, an IV increase (rush) is beneficial and a decrease (crush) has an adverse affect. The opposite applies for a short position, that is, an IV rush hurts you whilst a crush helps you.

Understanding the greeks allows traders to map out various scenarios and how they will impact their position if there is a change in one or more of the key variables. If you are still unsure of what they are telling you then do some further study as understanding them will make you a better trader.

Make it happen!

Guy Halpin

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