# Delta, Gamma, Theta: What 'The Greeks' Are Telling Us About Apple

By
Schaeffer's Investment Research Feb 01, 2013 3:43 pm

## "The Greeks" help to quantify how much the price will increase/decrease based on changes in the equity, time, volatility, and interest rates. Here's what Apple's chart suggests.

As you approach the next level in your options trading, mastering the pricing characteristics of these derivatives is a necessity. A general knowledge of a group of variables known as "The Greeks" will help to clear some of the cloudiness surrounding the changes that option prices undergo.

The first Greek letter to introduce is delta, which is mathematically considered the first derivative of the price action. Delta is arguably the most important Greek symbol, and is the one that you should pay the most attention to. Delta is dependent on where the stock is trading relative to the strike price, and the time to expiration. Simply put, delta measures how much the option price will change relative to the equity-if you have a call option, with a delta of 0.70, and the equity moves 1 point ($1), that option premium will

Gamma, the second derivative of price action (and thus the first derivative of delta), is the next Greek symbol to get a hold on. Gamma measures how much delta will increase based on the move in the underlying asset-i.e. (going back to our previous example) with stock XYZ trading at $10 and focusing on an ATM call, let us assume the gamma is 0.15. If XYZ increases 1 point, and is now trading at $11, (option premium for the call thus increases $0.50), delta will now become 0.65-it increased 0.15 for this point move. Understand that gamma will be at its highest level for options that are ATM or near-the-money-you can expect the biggest moves for delta to take place during expiration week.

Before illustrating the Greeks in an option chain, I want to cover these final three variables quickly. If you are a premium buyer, time decay is your enemy as you will lose the extrinsic value in the option for each day that passes leading up to the option expiration date. Theta is the friend of the premium seller-if you are short premium you want that option to expire worthless (best case scenario) or to expire at a value less than what you collected in premium so that the trade was profitable. Vega measures an option's sensitivity to changes in the volatility of the underlying asset. Recently, I focused on volatility and how implosions in the implied volatility (IV) can lead to a dramatic decrease in the option's value. If Vega is 0.05, the option will decrease by $0.05 for each drop in IV. Finally, you have the last (and probably the least impactful) Greek letter known as Rho. Rho is the rate at which the price of a derivative will change relative to the risk-free interest rate. Changes in interest rates are likely to only effect longer-term options, as the more time that passes the more likely there are to be changes in treasury notes, bills, and bonds (risk-free rate). We only focus on short-term trading here at Schaeffer's and shy away from options that expire in a year or longer-LEAPS.

Putting all of this together-gloss over the below option chain for

Listed are calls on the left, puts on the right. The bid/ask, delta, gamma, theta, vega, and rho variables are also listed for each corresponding option. We'll zone-in on the ATM options-the 455-strike call to be exact. The delta is near .50 and gamma is highest for these options in comparison to the other strikes, and theta is relatively equal for most of the options within range of the (then) current market price of the shares-theta is listed as 0.781, and your option premium will lose $0.78 for each day that passes. Vega was 0.391-you would lose $0.39 for each decrease in the IV of the option. Rho is positive for calls, and is 0.105-a 1% move in the risk-free rate would increase your option by $.10. Not the most fascinating material, but important nonetheless.

Certainly the material covered in this writing will take some time to get used to, but the importance of utilizing "The Greeks" cannot be dismissed. Understanding delta will help to assess the amount of leverage that your option will experience-the higher the delta, the greater the leverage as you will control more of a "point for point" move in the option relative to the performance of the underlying security. Gamma helps to assess how delta will react to big moves, and theta will aid the option seller in their short premium position.

One final point that I cannot emphasize enough-Greeks do not determine the value of an option, they merely help to

The first Greek letter to introduce is delta, which is mathematically considered the first derivative of the price action. Delta is arguably the most important Greek symbol, and is the one that you should pay the most attention to. Delta is dependent on where the stock is trading relative to the strike price, and the time to expiration. Simply put, delta measures how much the option price will change relative to the equity-if you have a call option, with a delta of 0.70, and the equity moves 1 point ($1), that option premium will

*increase*$0.70. Puts have a negative delta (delta cannot be >+/-1), and move opposite from calls-if the underlying moves 1 point, and the delta is -.70, that put premium will*decrease*$0.70. Calls that are in-the-money (ITM) will approach a delta of 1 as the time to expiration approaches-puts that are ITM will approach a delta of -1. Want to determine the probability that your call/put finishes ITM? Simply take the absolute value of the delta of that option-if stock XYZ is trading at $10, and you are looking at a 10-strike call or put (an at-the-money (ATM) option), what do you think the probability is that this particular option will finish ITM? A 50% chance, as it can go only up or down-the delta will be 0.50.Gamma, the second derivative of price action (and thus the first derivative of delta), is the next Greek symbol to get a hold on. Gamma measures how much delta will increase based on the move in the underlying asset-i.e. (going back to our previous example) with stock XYZ trading at $10 and focusing on an ATM call, let us assume the gamma is 0.15. If XYZ increases 1 point, and is now trading at $11, (option premium for the call thus increases $0.50), delta will now become 0.65-it increased 0.15 for this point move. Understand that gamma will be at its highest level for options that are ATM or near-the-money-you can expect the biggest moves for delta to take place during expiration week.

Before illustrating the Greeks in an option chain, I want to cover these final three variables quickly. If you are a premium buyer, time decay is your enemy as you will lose the extrinsic value in the option for each day that passes leading up to the option expiration date. Theta is the friend of the premium seller-if you are short premium you want that option to expire worthless (best case scenario) or to expire at a value less than what you collected in premium so that the trade was profitable. Vega measures an option's sensitivity to changes in the volatility of the underlying asset. Recently, I focused on volatility and how implosions in the implied volatility (IV) can lead to a dramatic decrease in the option's value. If Vega is 0.05, the option will decrease by $0.05 for each drop in IV. Finally, you have the last (and probably the least impactful) Greek letter known as Rho. Rho is the rate at which the price of a derivative will change relative to the risk-free interest rate. Changes in interest rates are likely to only effect longer-term options, as the more time that passes the more likely there are to be changes in treasury notes, bills, and bonds (risk-free rate). We only focus on short-term trading here at Schaeffer's and shy away from options that expire in a year or longer-LEAPS.

Putting all of this together-gloss over the below option chain for

**Apple, Inc.**(NASDAQ:AAPL). To give you a reference point, this snapshot was taken on 1/30/13 at 1:20 p.m. with AAPL trading at $458.70-not that it is vitally important, but I wanted to give you some context. These options expire February 16, 2013.*Click to enlarge*Listed are calls on the left, puts on the right. The bid/ask, delta, gamma, theta, vega, and rho variables are also listed for each corresponding option. We'll zone-in on the ATM options-the 455-strike call to be exact. The delta is near .50 and gamma is highest for these options in comparison to the other strikes, and theta is relatively equal for most of the options within range of the (then) current market price of the shares-theta is listed as 0.781, and your option premium will lose $0.78 for each day that passes. Vega was 0.391-you would lose $0.39 for each decrease in the IV of the option. Rho is positive for calls, and is 0.105-a 1% move in the risk-free rate would increase your option by $.10. Not the most fascinating material, but important nonetheless.

Certainly the material covered in this writing will take some time to get used to, but the importance of utilizing "The Greeks" cannot be dismissed. Understanding delta will help to assess the amount of leverage that your option will experience-the higher the delta, the greater the leverage as you will control more of a "point for point" move in the option relative to the performance of the underlying security. Gamma helps to assess how delta will react to big moves, and theta will aid the option seller in their short premium position.

One final point that I cannot emphasize enough-Greeks do not determine the value of an option, they merely help to

*quantify*how much the price will increase/decrease based on changes in the equity, time, volatility, and interest rates. These are all important elements that should be analyzed when trading options and the better you understand them the better you will trade.*This article by Peter Bryans was originally published on Schaeffer's Investment Research.*

Below, find some more great content from Schaeffer's Investment Research:Below, find some more great content from Schaeffer's Investment Research:

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