What does gamma measure?
Gamma is the rate of change of delta, or the derivative of delta. If delta is the first derivative of the option price, gamma is the second derivative of the option price is useful for the measuring the stability of an option's probability of success.

Expiration and Gamma
A high gamma implies a high rate of change of delta and therefore a high rate of change of the option's price. In order to ensure a successful outcome, as methodical traders we hope to maintain a high probability of success. Yet, with high gammas, the location of our option price is unpredictable. 

How to Avoid High Gammas: Rolling Options
As expiration approaches, there is less time for the option price to change. This causes for more fluctuation in delta as the contract approaches expiration, and therefore a higher gamma. In these instances, the options can be rolled in order to restore a longer DTE and therefore lower gamma. 

W What does delta measure?
Delta measures the rate of change of an option's price given a plus or minus change of $1 in the underlying price. Delta answers, "If the underlying increases or decreases by $1, by how much will the option price increase or decrease?". For us math nerds, delta can be thought of as the derivative of an option's price. 

Option Price Deltas
Option price deltas range form -1.0 to +1.0. If an option price has a delta from -1.0 to 0, it has a negative delta. If an option price has a delta from 0 to +1.0 it has a positive delta. Positive and negative deltas are important in assessing our directional assumptions regarding the options transactions. Let's take a look:

Options Transactions and Delta Signs

• Buy Call : Bullish, option price increases as underlying price increases -> Positive Delta
• Sell Call: Bearish, option price increases as underlying price decreases -> Negative Delta
• Buy Put: Bearish, option price increases as underlying price decreases -> Negative Delta
• Sell Put: Bullish, option price increases as underlying price increases -> Positive Delta

A positive or negative delta, as implied above signifies a directional assumption, and therefore risk. A positive delta, such as a in the case of buying calls or selling puts assumes a long market, whereas a negative delta like those of selling calling and buying puts assumes a short market. The sign of a delta assigns a directional risk to our overall positions. In order to reduce our risk, it is preferable to keep deltas neutral or as close to 0, so as to avoid the association of an underlying's direction to the fate of our positions. 

Delta Benefits 
An option's delta is equivalent to the probability of being ITM. As established earlier, sellers want the options they've sold to expire ITM in order to profit. Therefore, sellers can use deltas to assess the probability of ITM. Similarly, buyers can use deltas to assess the probability of the option expiring OTM (where they profit). For example, if we sell a + 50 delta call, there is 50% chance the option will be ITM, and a 50% the delta will be OTM. What if the delta is negative?  If we sell a -30% delta call, there is 30% of the option expiring OTM and therefore a 70% of the option expiring ITM. 

16 Delta
You might often hear of the mysterious "16 delta". What does this even mean? If we look at a one standard deviation move on the traditional bell curve, the distance from the mean is 34% on either ends. The width is approximately 68%, leaving 16% percent flaps near each tail end. If we sell a -16% delta call, this means we have an 84% (16% flap we mentioned earlier + 68%)  chance of the option expiring ITM (success!). This is usually the sweet spot we like to look for when trading. 

What does theta measure?
Theta is the rate of decay of an option's price, all else held equal (including the fluctation in stock price and volatility). As you may recall from the Extrinsic Value post, the extrinsic value of a stock is determined by time and volatility. Theta measures how the rate at which the time value of an option price changes (or the time value aspect of the option's extrinsic value). ​

Theta in Conjunction with Buying and Selling Options
Sellers love theta. When selling options, as we've established, sellers sell premium to the buyers for the right to buy stock for the strike price at or before expiration. As time progresses throughout the duration of the contract, the extrinsic value, and therefore time value, of the option decreases. The seller can now profit by buying an option, with a now lower option price as a result of time decay ("Sell high, buy low"). The opposite is true for buyers, will are at a disadvantage as a result of time decay. 

ATM, OTM, and ITM
The value of an option is always highest for ATM options, because here there is the most extrinsic value (0 intrinsic value). The curve of option prices slopes downwards as the underlying price goes further ITM and OTM because here there is more intrinsic value than extrinsic value. How does this principle relate to theta?
Because ATM options only have extrinsic value, theta decay increases faster than OTM/ITM options. When ITM or OTM, there is more intrinsic value, so there is not much left for the extrinsic to deecay by expiration. Contrastringly, when ATM, there is only extrinsic value so the option's theta decreases rapidly. 

How can we apply this? Example:
If we know that theta decays rapidly for ATM options, we can sell an ATM options in order to buy back the option for an even lower premium and profit!

Greeks? Although I wish I could say that a plate of piping spanokopita would endow you with unbounded option trading knowledge, I can assure that the Greeks we will discuss are a formidable asset. In the world of options trading, the "Greeks" are crucial to the understanding of option prices. The Greeks are derived from the option pricing model. Typically the price of an option changes with time, or direction or time till expiration, implied volatility etc. All these can be quantified and measured using the various 'Greeks'.  

The greeks provide very useful insight on how a specific options in your portfolio will affect the profitablity of your portfolio.  You'll typically hear of traders saying that they are 'long delta' or 'short delta' in terms of direction. Or you'll hear of them say that they have positive or negative theta. What all these mean would be a bit more clear once we dive into this a bit more deeper.

In the next four posts, we will discover the relevance of the various options greeks like theta, delta, gamma, rho and vega. 

Image Source: Options Playbook