### John Maynard Keynes

[The market] “can stay irrational far longer that you can remain solvent." Very true.

So, here is a summary of how to interpret the greeks of a stock option.

Delta is a number that measures how much the theoretical value of an option will change if the underlying stock moves up or down \$1.00. Positive delta means that the option position will rise in value if the stock price rises, and drop in value if the stock price falls. Negative delta means that the option position will theoretically rise in value if the stock price falls, and theoretically drop in value if the stock price rises.

Also, an ATM option has a delta close to .50. The more ITM an option is, the closer its delta is to 1.00 (for calls) or –1.00 (for puts). The more OTM and option is, the closer its delta is to 0.00.

The delta of a call can range from 0.00 to 1.00; the delta of a put can range from 0.00 to –1.00. Long calls have positive delta; short calls have negative delta. Long puts have negative delta; short puts have positive delta. Long stock has positive delta; short stock has negative delta. The closer an option’s delta is to 1.00 or –1.00, the more the price of the option responds like actual long or short stock when the stock price moves.

Example
Say, stock XYZ is at \$48.
XYZ Aug 50 call has a value = \$2.00, delta of +0.45.
If XYZ rises to \$49, XYZ Aug 50 call will theoretically rise to \$2.45.
If XYZ falls to \$47, XYZ Aug 50 call will theoretically drop to \$1.55.

XYZ Aug 50 put has a value = \$3.75, *delta of -0.55”
If XYZ rises to \$49, XYZ Aug 50 put will theoretically drop to \$3.20.
If XYZ falls to \$47, XYZ Aug 50 put will theoretically rise to \$4.30.

Summary: For every \$1 movement, the value of the option goes up (or down) by Delta.

Gamma is an estimate of how much the delta of an option changes when the price of the stock moves \$1.00. As a tool, gamma can tell you how “stable” your delta is. A big gamma means that your delta can start changing dramatically for even a small move in the stock price.

NOTE: The gamma of ATM options is higher when either volatility is lower or there are fewer days left to expiration.

What all this means to the option trader is that a position with positive gamma is relatively safe, that is, it will generate the deltas that benefit from an up or down move in the stock. But a position with negative gamma can be dangerous. It will generate deltas that will hurt you in an up or down move in the stock.

Summary: Gamma tells you how stable your Delta is. Negative gammas are dangerous.

From another site:
Why Gamma Is Important
Positive gamma means that the rate at which you profit will ACCELERATE as the stock price continues to move in your favor, while the rate at which you lose will DECELERATE as the stock price makes continued moves against you.

Conversely, negative gamma means price up -> profit decelerates; price down -> loss accelerates.

Special note: Gamma has an inverse relationship to Theta.

GAMMA is really only useful for those who trade Delta Neutral options – if Gamma is high, it means that the stability of your trade could change any time, and so you need to monitor your position closely.

Theta, a.k.a. time decay, is an estimate of how much the theoretical value of an option will decrease with each day passing AND there is NO move in either the stock price or volatility. Theta is used to estimate how much an option’s extrinsic value is whittled away by the (unrelenting and) constant passage of time. The theta for a call and put at the same strike price and the same expiration month are not equal. Without going into detail, the difference in theta between calls and puts depends on the cost of carry for the underlying stock. When the cost of carry for the stock is positive (i.e. dividend yield is less than the interest rate) theta for the call is higher than the put. When the cost of carry for the stock is negative (i.e. dividend yield is greater than the interest rate) theta for the call is lower than the put.

But theta doesn’t reduce an option’s value at 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 \$-0.15. The XYZ Dec 75 put is worth \$4.75, has 80 days until expiration and has a theta of \$-0.03. 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.

If you BUY calls or puts, THETA or TIME DECAY becomes your enemy. If THETA is high, you must plan to not hold on to the option for too long! TIME DECAY will eat up the premia paid (and/or profits made from an increase in the stock price).

Summary: Theta is a measure of how much your option premium will go down by with each passing day. The closer you are to option expiration, higher the Theta.

Let’s look at the XYZ Aug 50 call again. It has a value of \$2.00 and a vega of \$+0.20 with the volatility of XYZ stock at 30.00%. If the volatility of XYZ rises to 31.00%, the value of the XYZ Aug 50 call will rise to \$2.20. If the volatility of XYZ falls to 29.00%, the value of the XYZ Aug 50 call will drop to \$1.80.

Summary: In a way, this is a measure of volatility. IV or implied volatility can beat the bejasus out of your premia. Remember how with almost no price action, the premia drop in value on the day after earnings? That can kill you (with big option positions).

And just for completeness without going numb,

Rho is an estimate of how much the theoretical value of an option changes when interest rates move 1.00%. The rho for a call and put at the same strike price and the same expiration month are not equal. Rho is one of the least used greeks. When interest rates in an economy are relatively stable, the chance that the value of an option position will change dramatically because of a drop or rise in interest rates is pretty low. Nevertheless, we’ll describe it here for your edification.

Back to the XYZ Aug 50 calls. They have a value of \$2.00 and a rho of +.02 with XYZ at \$48.00 and interest rates at 5.00%. If interest rates increase to 6.00%, the value of the XYZ Aug 50 calls would increase to \$2.02. If interest rates decrease to 4.00%, the value of the XYZ Aug 50 calls would decrease to \$1.98.

Summary: Unless you are in a volatile interest environment, for e.g., if the long bond yields are about to shoot up (like in 2011), no need to worry about this.

Excerpted from thinkorswim.com