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Revisiting the Greeks of Investing

The “Greeks” is a wildly used terms when it comes to options investing/trading.  The term comes from the letters of the Greek alphabet being used something totally not related to the Greek language, or culture, but rather as a very specific term or formula as it relates to options risk and pricing.

Despite trading a lot of options contracts every month I have never built a strong foundation when it comes to understanding ‘The Greeks.’  The reasoning is probably because when it comes to options I am mainly self taught once a friend taught me about selling naked puts.  I taught myself by researching and writing posts on the different option strategies such as:

Defining The Greeks as it Relates to Options Investing

I am going to focus on the main Greek letters for now.


According to Investopedia Delta ,

measures an option’s price sensitivity relative to changes in the price of the underlying asset, and is the number of points that an option’s price is expected to move for each one-point change in the underlying. Delta is important because it provides an indication of how the option’s value will change with respect to price fluctuations in the underlying instrument, assuming all other variables remain the same. (emphasis added).

Remember, that an options contract value has two parts intrinsic value and extrinsic value.  Intrinsic value refers to the difference between the strike price and the actual value of the underlying equity.  Extrinsic is what the market is valuing on what could be.  Delta is trying to measure what the value of the options contract may do when the underlying equity changes in value.

Delta is typically shown as a numerical value between 0.0 and 1.0 for call options and 0.0 and -1.0 for put options. In other words, options Delta will always be positive for calls and negative for puts. Call options that are out-of-the-money will have Delta values approaching 0.0; in-the-money call options will have Delta values that are close to 1.0. It should be noted that Delta values can also be represented as whole numbers between 0.0 and 100 for call options and 0.0 to -100 for put options, rather than using decimals.

Using Delta When Options Trading

While the “idea” of delta is easy to grasp I had to do further research how this would actually be applied to trading.  While the Think or Swim explanation below makes theoretical sense, it seems that it isn’t applied to making a trade, but rather to grasp where your positions are at a given time,

You can add, subtract, and multiply deltas to calculate the delta of a position of options and stock. The position delta is a way to see the risk/reward characteristics of your position in terms of shares of stock, and it’s how thinkorswim presents it to you on the Position Statement on the Monitor page. The calculation is very straightforward. Position delta = option theoretical delta * quantity of option contracts * number of shares of stock per option contract. (The number of shares of stock per option contract in the U.S. is usually 100 shares. But it can be more or less, due to stock splits or mergers.) thinkorswim performs this calculation for each option in your position, then adds them together for each stock.

So, if you are long 5 of the XYZ Aug 50 calls, each with a delta of +.45, and short 100 shares of XYZ stock, you will have a position delta of +125. (Short 100 shares of stock = -100 deltas, long 5 calls with delta +.45, with 100 shares of stock per contract = +225. –100 + 225 = +125)

A way to interpret this delta is that if the price of XYZ rises $1, you will theoretically make $125. If XYZ falls $1, you will theoretically lose $125. IMPORTANT: These numbers are theoretical. In reality, delta is accurate for only very small changes in the stock price. Nevertheless, it is still a very useful tool for a $1.00 change, and is a good way to evaluate your risk.


Delta is sensitive to changes in volatility and time to expiration. The delta of ATM options is relatively immune to changes in time and volatility. This means an option with 120 days to expiration and an option with 20 days to expiration both have deltas close to .50. But the more ITM or OTM an option is, the more sensitive its delta is to changes in volatility or time to expiration. Fewer days to expiration or a decrease in volatility push the deltas of ITM calls closer to 1.00 (-1.00 for puts) and the deltas of OTM options closer to 0.00. So an ITM option with 120 days to expiration and a delta of .80 could see its delta grow to .99 with only a couple days to expiration without the stock moving at all.

The delta of an option depends largely on the price of the stock relative to the strike price. Therefore, when the stock price changes, the delta of the option changes. That’s why gamma is important. emphasis added.

So with that let’s talk Gamma


Gamma is an offshoot, or a derivative of delta.  According to Investopedia,

Since an option’s delta measure is only valid for short period of time, gamma gives traders a more precise picture of how the option’s delta will change over time as the underlying price changes. Delta is how much the option price changes in respect to a change in the underlying asset’s price.

As an analogy to physics, the delta of an option is its “speed,” while the gamma of an option is its “acceleration.”

Gamma decreases, approaching zero, as an option gets deeper in the money and delta approaches one. Gamma also approaches zero the deeper an option gets out of the money. Gamma is at its highest when the price is at the money.


A good way to think of Gamma is the measure of the stability of an option’s probability. If Delta represents the probability of being in-the-money at expiration, Gamma represents the stability of that probability over time. An option with a high Gamma and a 0.75 Delta may have less of a chance of expiring in-the-money than a low Gamma option with the same Delta.

Application of Gamma Information

According to TastyTrade, using Gamma data may be able to provide me with a deeper insight into the actual risk I am taking since I am usually an options seller,

Long Option Benefits of Gamma

Gamma is friendliest to long option holders. It accelerates profits for every $1.00 the underlying moves in our favor, and decelerates losses for every $1.00 the underlying moves against us. Since delta is the rate of change of an option’s price, and gamma increases an option’s delta as it moves closer to, or further in the money, in the example above the delta would just continue to increase. Every dollar the underlying increased would result in more and more efficient returns on the investor’s capital. This phenomena also decelerates losses, as it works in the opposite way for every $1.00 the underlying moves against us.

Short Option Risks of Gamma

Because it can be beneficial for option buyers, that must mean that it can be risky for option sellers. From the seller’s perspective, it can accelerate losses, and decelerate directional gains. It is just the opposite side of the coin from the example above.


Theta is my favorite Greek! Theta refers to the value of time decay.  Since I sell naked puts, I am giving someone the option to make me take their stock at a certain price, for a certain time period, and for that trade I get premium (dollars in my pocket).

If the stock price is above the strike price then there would be no reason to put the stock to me.  So, as time goes on, the value of that contract becomes less and less valuable because it becomes less and less likely that the stock will go below that strike price (with all things being equal of course).  It makes sense that this does not happen in a linear fashion,

But theta doesn’t reduce an option’s value in an even rate. Theta has much more impact on an option with fewer days to expiration than an option with more days to expiration. For example, the XYZ Oct 75 put is worth $3.00, has 20 days until expiration and has a theta of -.15. The XYZ Dec 75 put is worth $4.75, has 80 days until expiration and has a theta of -.03. If one day passes, and the price of XYZ stock doesn’t change, and there is no change in the implied volatility of either option, the value of the XYZ Oct 75 put will drop by $0.15 to $2.85, and the value of the XYZ Dec 75 put will drop by $0.03 to $4.72.

Theta is highest for ATM options, and is progressively lower as options are ITM and OTM. This makes sense because ATM options have the highest extrinsic value, so they have more extrinsic value to lose over time than an ITM or OTM option. The theta of options is higher when either volatility is lower or there are fewer days to expiration. If you think about gamma in relation to theta, a position of long options that has the highest positive gamma also has the highest negative theta. There is a trade-off between gamma and theta. Think of long gamma as the stuff that provides the power to a position to make money if the stock price starts to move big (think of a long straddle). But theta is the price you pay for all that power. The longer the stock price does not move big, the more theta will hurt your position.



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