Explaining the "Greeks"
Option traders look to make money by taking advantage of many different market forces; stock price changes, fluctuations in volatility, time to expiration etc. However, traders can also lose money if these factors move against their positions. So, traders need to understand all of these forces and be able to put a value on them to measure the risks/rewards.
Option Greeks are a group of calculations that help estimate the effect certain inputs have on the valuation of options. The Greek values most commonly referred to are Delta, Gamma, Vega and Theta. Other lesser known Greeks are Rho, Charm, Color, Speed and Weezu. Each of these Greeks help traders asses the risk of their option positions in order to place better trades, helping traders to answer questions such as:
- How will the value of the option change as the stock price changes? (Delta)
- What is the probability of the option expiring in-the-money/out-of-the-money? (Delta)
- How fast will the option lose value as it approaches expiration? (Theta)
- What effect will a change in the stock's volatility have on the option value? (Vega)
Here is a table that provides a brief definition of each option Greek:
Option Greek Definitions
| Greek | Measures the |
|---|---|
| Delta | Rate of change on the option price when the underlying price moves by 1 point. |
| Gamma | Rate of change of the Delta when the underlying price moves by 1 point. |
| Theta | Rate of change on the option price when 1 trading day passes. |
| Vega | Rate of change on the option price when the volatility changes by 1 percentage point. |
| Rho | Rate of change on the option price when interest rates change by 1 percentage point. |
| Charm | Rate of change on the Delta when 1 trading day passes. |
| Color | Rate of change on the Gamma when 1 trading day passes. |
| Speed | Rate of change on the Gamma when the underlying price changes by 1 point. |
| Weezu | Rate of change on the Vega when the volatility changes by 1 percentage point. |
Calculations
The Option Greeks are outputs from an option pricing model. There is a fair amount of math involved but you don't have to know the formulas to be able to use the Greeks.
Most broker terminals that facilitate options trading will provide support for option Greeks as part of their offering. Interactive Brokers supports many option calculations that you can use in your trading screen. However, if you don't have a broker account or you would like to simulate various option scenarios to test the effect of different input parameters, go ahead and download my option spreadsheet. You can enter and play around with various payoff scenarios and test the effects each has on the outputs.
Here is what all the option Greeks would look like, calculated across 3 different expirations for ITM, ATM and OTM options. I used the Black and Scholes Model with a spot price of 1,000, volatility of 35% and interest rates of 2.7%.
Call Option Example:
| Strike | Days | Price | Delta | Gamma | Theta | Vega | Rho | Charm | Color | Speed | Weezu |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 900 | 49 | 116.53 | 0.819 | 0.00205 | -0.397 | 0.963 | 0.945 | 0.00198 | 0.0000069 | -0.0000167 | 0.01973 |
| 1000 | 49 | 52.82 | 0.537 | 0.0031 | -0.558 | 1.456 | 0.652 | -0.00038 | 0.0000324 | -0.0000053 | -0.00014 |
| 1100 | 49 | 18.66 | 0.257 | 0.00252 | -0.441 | 1.182 | 0.322 | -0.00279 | 0.0000117 | 0.0000103 | 0.01716 |
| 900 | 140 | 147.57 | 0.74 | 0.0015 | -0.297 | 2.01 | 2.278 | 0.00038 | 0.0000042 | -0.0000059 | 0.01571 |
| 100 | 140 | 91.14 | 0.562 | 0.00182 | -0.341 | 2.441 | 1.817 | -0.00022 | 0.0000067 | -0.0000031 | -0.00066 |
| 1100 | 140 | 52.63 | 0.389 | 0.00177 | -0.323 | 2.374 | 1.299 | -0.00082 | 0.0000053 | 0.0000005 | 0.0096 |
| 900 | 232 | 172.24 | 0.719 | 0.00121 | -0.245 | 2.689 | 3.488 | 0.00013 | 0.0000024 | -0.0000037 | 0.0134 |
| 1000 | 232 | 111.67 | 0.555 | 0.00139 | -0.238 | 3.102 | 2.838 | -0.0001 | 0.0000032 | -0.0000022 | -0.0017 |
| 1100 | 232 | 79.42 | 0.445 | 0.00142 | -0.266 | 3.15 | 2.342 | -0.00047 | 0.0000028 | -0.0000007 | 0.00525 |
Put Option Example:
| Strike | Days | Price | Delta | Gamma | Theta | Vega | Rho | Charm | Color | Speed | Weezu |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 900 | 49 | 13.36 | -0.181 | 0.00205 | -0.33 | 0.963 | -0.258 | 0.00198 | 0.0000069 | -0.0000167 | 0.01973 |
| 1000 | 49 | 49.29 | -0.463 | 0.0031 | -0.484 | 1.456 | -0.685 | -0.00038 | 0.0000324 | -0.0000053 | -0.00014 |
| 1100 | 49 | 114.78 | -0.743 | 0.00252 | -0.359 | 1.182 | -1.148 | -0.00279 | 0.0000117 | 0.0000103 | 0.01716 |
| 900 | 140 | 38.23 | -0.26 | 0.0015 | -0.229 | 2.01 | -1.132 | 0.00038 | 0.0000042 | -0.0000059 | 0.01571 |
| 100 | 140 | 80.77 | -0.438 | 0.00182 | -0.266 | 2.441 | -1.972 | -0.00022 | 0.0000067 | -0.0000031 | -0.00066 |
| 1100 | 140 | 141.22 | -0.611 | 0.00177 | -0.24 | 2.374 | -2.869 | -0.00082 | 0.0000053 | 0.0000005 | 0.0096 |
| 900 | 232 | 56.64 | -0.281 | 0.00121 | -0.177 | 2.689 | -2.115 | 0.00013 | 0.0000024 | -0.0000037 | 0.0134 |
| 1000 | 232 | 106.96 | -0.432 | 0.00139 | -0.216 | 3.102 | -3.388 | -0.00016 | 0.0000032 | -0.0000022 | -0.0017 |
| 1100 | 232 | 160.34 | -0.555 | 0.00142 | -0.182 | 3.15 | -4.507 | -0.00047 | 0.0000028 | -0.0000007 | 0.00525 |
18 Comments
YEO January 4th, 2011 at 12:54am
How do we know if the option trading is under 'AMERICAN OPTION' or 'EUROPEAN OPTION' ?
Aft November 26th, 2010 at 2:24pm
Its a very good site, Especially for the newbees...Thnx..Aft
Peter August 8th, 2010 at 6:51am
Thanks Ritu!
Ritu August 8th, 2010 at 5:40am
Your's is the most exhaustive yet simple website in terms of information provided in layman terms.....
Trader Travis January 22nd, 2010 at 11:49pm
Your site is very nice and you have done an excellent job of explaining the greeks without confusing folks. New traders need to read your way of explaining it before they are guided down the wrong path.
Trader Travis
http://www.learn-stock-options-trading.com/
Mani Ghedia June 23rd, 2009 at 11:25pm
I agree the greeks are super important. Option Volatility and Pricing is a fantastic book - worth reading. Excellent website nonetheless! Cheers
Admin February 8th, 2009 at 3:38am
Thanks for the positive feedback and great suggestion! I will look to add greek explanations for all of the strategies soon.
pchaser87 February 7th, 2009 at 11:08am
This is an excellent site, but I think you could expand a bit on the greeks. They are very important in options trading and you could easily go into more deatail (with practical examples?) without making it sound very complicated. Great work other than that!
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