An article to understand the sensitivity indicators of Options prices: the Greeks.
Recently, due to tariffs and the earnings report season in the US stock market, the market has been highly volatile, and many Moo friends are seeking opportunities in Options. Especially some Moo friends who buy underlying stocks may also want to try their hand after seeing the kinds of multiple to dozens of times returns on Options in the Community. However, it is not that, although the basic Concepts of Options have been understood, the series of Greek letters in buying and selling Options prices can feel quite confusing.
As an investor hoping to reduce unnecessary risks through increased awareness, a summary has been prepared for all Moo friends, which can be referenced one by one while buying and selling Options.
1. Delta (Δ): Sensitivity of the symbol's price changes.
Definition: Delta measures the sensitivity of the Options price to changes in the symbol's asset price, meaning that when the symbol's stock price changes by $1, the Options price will change by how much.
For example:
If the Delta of a Call option is 0.6, it indicates that when the symbol's stock price rises by $1, the price of the option will increase by approximately $0.60.
If the Delta of a Call option is 0.6, it indicates that when the symbol's stock price rises by $1, the price of the option will increase by approximately $0.60.
We use this example of a Call Options for SVIX with a strike price of $14 that expires on June 6, 2025. Detal=0.3558, which means that if SVIX increases by $1, the price of this option will rise by approximately $0.3558.
For Call Options: Delta ranges between 0 and 1; for Put Options: Delta ranges between -1 and 0; At-the-money (ATM), Call Delta ≈ 0.5, Put Delta ≈ -0.5;
Uses: (Delta) controls directional risk, whether to go long or short? It determines whether the stance is "bullish" or "bearish." In general, Delta is used to assess directional exposure, exercise probability, and hedge ratios.
Used to construct a "Delta Neutral" strategy, such as buying Calls + selling the underlying stock to offset risk.
Determining exercise probability: The closer Delta is to 1 or -1, the more likely it is to be exercised at expiration.
Determining exercise probability: The closer Delta is to 1 or -1, the more likely it is to be exercised at expiration.
Note: Delta can also be interpreted as "how many units of the underlying stock a particular option is currently equivalent to," which can be elaborated on later.
For example:
You bought a Call with a Delta of 0.7, which means you effectively hold 0.7 shares of the underlying stock indirectly. If you do not want to bear such significant directional risk, you can sell 0.7 shares of the stock to hedge.
You bought a Call with a Delta of 0.7, which means you effectively hold 0.7 shares of the underlying stock indirectly. If you do not want to bear such significant directional risk, you can sell 0.7 shares of the stock to hedge.
2. Gamma (Γ): The rate of change of Delta.
Definition: Gamma measures how sensitive Delta is to changes in the underlying asset's price, i.e., the "second derivative": how much Delta changes if the stock price moves by $1.
Gamma is maximized at ATM Options,
When Deep ITM or OTM, Gamma approaches 0.
A high Gamma indicates that Delta will change rapidly → making risk more difficult to control.
Gamma is maximized at ATM Options,
When Deep ITM or OTM, Gamma approaches 0.
A high Gamma indicates that Delta will change rapidly → making risk more difficult to control.
For example:
Gamma = 0.1 means that when the stock price rises by $1, Delta will increase from 0.6 to 0.7.
Gamma = 0.1 means that when the stock price rises by $1, Delta will increase from 0.6 to 0.7.
Still using the previous example of the Options expiring on June 6, 2025, with a strike price of $14: Gamma = 0.2087, which means that if SVIX rises by $1, Delta will increase from 0.3558 to 0.5645.
Delta change (ΔDelta) = Gamma × change in symbol price = 0.2087 × 1 = 0.2087.
New Delta = Original Delta + ΔDelta = 0.3558 + 0.2087 = 0.5645
New Delta = Original Delta + ΔDelta = 0.3558 + 0.2087 = 0.5645
Usefulness: (Gamma) manage risk exposure during extreme fluctuations, used to assess whether your Delta will become uncontrollable during sudden surges and drops. Overall, Gamma: controls position sensitivity, manages risk in extreme market conditions, and high Gamma means frequent adjustments to positions are necessary to maintain a hedged state.
For example:
You sold an ATM Option with high Gamma. Once the stock price fluctuates sharply, your Delta will become quickly unbalanced, possibly shifting from balanced to significant loss. Therefore, close monitoring and timely re-hedging are essential.
You sold an ATM Option with high Gamma. Once the stock price fluctuates sharply, your Delta will become quickly unbalanced, possibly shifting from balanced to significant loss. Therefore, close monitoring and timely re-hedging are essential.
Supplement: Gamma is often used for risk management and dynamic hedging (delta-hedging), and will be discussed in detail later.
3. Theta (Θ): The impact of time passage on option prices.
Definition: Theta measures the sensitivity of option prices to the passage of time (time value decay). The unit is the value lost per day.
For buyers, Theta is negative, losing money every day. For sellers, Theta is positive, earning time value every day. As the expiration date approaches, the absolute value of Theta accelerates upward (especially at ATM). The part with the richest time value is ATM + options with longer remaining time.
Example:：
Example:：
Taking the example of the Options that expire on June 6, 2025, with a price of $14: Theta = -0.0122 indicates that due to the passage of time alone, the value of this option decreases by $0.0122 every day.
Use: (Theta) measures whether time is on your side, helping you determine whether you are 'earning time' or 'being consumed by time.'In general, Theta assesses the impact of time on strategy and helps determine the "decay speed" of Hold Positions.Sell strategies (such as selling Call or Put) particularly rely on positive Theta to make a profit.
Use: (Theta) measures whether time is on your side, helping you determine whether you are 'earning time' or 'being consumed by time.'In general, Theta assesses the impact of time on strategy and helps determine the "decay speed" of Hold Positions.Sell strategies (such as selling Call or Put) particularly rely on positive Theta to make a profit.
For example:
You Sell a Put Option that expires in two weeks and automatically earn $0.04 each day, that is, Theta = 0.04 as long as the stock price does not fluctuate drastically; time works in your favor every day.
You Sell a Put Option that expires in two weeks and automatically earn $0.04 each day, that is, Theta = 0.04 as long as the stock price does not fluctuate drastically; time works in your favor every day.
4.Vega (ν): The impact of volatility changes.
Definition:
Vega measures the sensitivity of the option price to changes in implied volatility (IV), that is, how much the option price changes when volatility changes by 1%.
Vega is largest for long-dated Options at the ATM. Buyers want volatility to rise (which increases the value of the Options), while sellers want the opposite.
Vega measures the sensitivity of the option price to changes in implied volatility (IV), that is, how much the option price changes when volatility changes by 1%.
Vega is largest for long-dated Options at the ATM. Buyers want volatility to rise (which increases the value of the Options), while sellers want the opposite.
For example:
Vega = 0.12, which means that when the implied volatility increases by 1 percentage point, the price of the option will increase by $0.12. If an option is bought, and the current implied volatility (IV) is 30%, while Vega = 0.12. Then if IV rises from 30% to 31%, the price of the option held will increase by $0.12, and if IV falls from 30% to 29%, the price of the option will decrease by $0.12.
Vega = 0.12, which means that when the implied volatility increases by 1 percentage point, the price of the option will increase by $0.12. If an option is bought, and the current implied volatility (IV) is 30%, while Vega = 0.12. Then if IV rises from 30% to 31%, the price of the option held will increase by $0.12, and if IV falls from 30% to 29%, the price of the option will decrease by $0.12.
Vega is not the market's "actual volatility"; it is the "market's expected future volatility". Therefore, it is possible for the symbol price to remain unchanged, but if a major event causes the implied volatility (IV) to rise, the price of bought Options will also increase.
Use: ((Vega) is mainly used to determine the direction and extent of the impact of changes in implied volatility (IV) on Options prices. You can think of it as a "volatility sensitivity indicator."
If you are a buyer, you want IV to rise because Options will be more valuable, and volatility is your friend.
If you are a seller, you want IV to decrease because Options will depreciate, and volatility is your enemy.
Capture opportunities in volatility IV:
Buy Options when IV is low, Vega will amplify your future gains from an increase in IV, commonly seen before major events (such as Earnings Reports or policy announcements).
Scenario 1: IV is currently very low, buy Options.
Meaning: The market is calm now, but you believe something significant will happen later (such as an Earnings Report).
• You bought an Option at a cheap price (because the IV was low, the price was low).
• Later, the market started to tighten, and the IV increased (for example, from 20% to 30%).
• At this point, you didn’t move, and the stock price didn’t change, but because the IV increased, your Option automatically increased in price.
• This is how Vega works: when IV increases by 1%, you earn money corresponding to the Vega.
→ • It's equivalent to correctly betting that "emotions have risen"; even if the direction is wrong, you can still make a profit.
Meaning: The market is calm now, but you believe something significant will happen later (such as an Earnings Report).
• You bought an Option at a cheap price (because the IV was low, the price was low).
• Later, the market started to tighten, and the IV increased (for example, from 20% to 30%).
• At this point, you didn’t move, and the stock price didn’t change, but because the IV increased, your Option automatically increased in price.
• This is how Vega works: when IV increases by 1%, you earn money corresponding to the Vega.
→ • It's equivalent to correctly betting that "emotions have risen"; even if the direction is wrong, you can still make a profit.
When IV is high, selling Options with Vega will help you profit when IV decreases (even if the price remains unchanged, you can still profit), such as "selling panic", and collecting premium by selling Put when the VIX is at a high level.
Scenario 2: IV is currently very high, sell Options.
Meaning: The market is currently very tense, and it is determined that it will return to calm.
• For example, if a company's stock price plummets and IV spikes to historical highs (panic).
• At this time, selling options (such as Put) is a strategy.
• Even if the stock price does not rebound significantly afterward, as long as IV decreases, the options you sold will also depreciate.
• You can buy back at a low price and earn the price difference.
→ This is equivalent to earning money from the "market returning from anxiety to calm."
Meaning: The market is currently very tense, and it is determined that it will return to calm.
• For example, if a company's stock price plummets and IV spikes to historical highs (panic).
• At this time, selling options (such as Put) is a strategy.
• Even if the stock price does not rebound significantly afterward, as long as IV decreases, the options you sold will also depreciate.
• You can buy back at a low price and earn the price difference.
→ This is equivalent to earning money from the "market returning from anxiety to calm."
Overall, Vega captures volatility opportunities and helps in constructing volatility-related strategies (essential for building volatility strategies such as Straddle, Strangle, Iron Condor, etc.).
For example:
If a significant market fluctuation is expected before the Earnings Reports, one can buy a Straddle (simultaneously buy Call + Put) to leverage Vega for the premium increase due to rising IV.
Supplement: Vega is not a true "Greek letter," but it is conventionally categorized under the Greeks system.
For example:
If a significant market fluctuation is expected before the Earnings Reports, one can buy a Straddle (simultaneously buy Call + Put) to leverage Vega for the premium increase due to rising IV.
Supplement: Vega is not a true "Greek letter," but it is conventionally categorized under the Greeks system.
5. Rho (ρ): Effects of interest rate changes.
Definition: Rho measures the sensitivity of the option price to changes in the risk-free interest rate, that is, how much the option price changes with a 1% change in interest rates.
For Call options, an increase in interest rates → value increases (Rho > 0).
For Put options, an increase in interest rates → value decreases (Rho < 0).
For Call options, an increase in interest rates → value increases (Rho > 0).
For Put options, an increase in interest rates → value decreases (Rho < 0).
When interest rates are extremely low or the option has a short expiration time, the effect of Rho can be ignored.
Example:：
Rho = 0.08, indicating that if interest rates rise by 1%, this option will increase by $0.08.
Rho = 0.08, indicating that if interest rates rise by 1%, this option will increase by $0.08.
Purpose: (Rho) A reference for the L strategy under changes in interest rates, considering the impact of Rho during periods of significant interest rate fluctuations (such as rate hikes/cuts). Rho must be evaluated when constructing a long-term options (LEAPS) portfolio. Overall, Rho should be considered for changes in returns in the context of rate hikes or long-term options strategies.
For example:
Planning to hold a Call that expires in two years. If the market expects interest rates to rise, this Call will increase in price due to the positive Rho, making a more favorable choice before opening a position.
Planning to hold a Call that expires in two years. If the market expects interest rates to rise, this Call will increase in price due to the positive Rho, making a more favorable choice before opening a position.
Supplement:Usually more important in long-term options (LEAPS).
This content is solely for the purpose of reviewing my trading records and strategies and does not constitute any recommendation or investment advice for financial products. The market involves risks, and investments should be made cautiously. This Account is not a licensed financial service provider and is only for learning and discussion reference.
This content is for educational and informational purposes only. It does not constitute financial advice or a recommendation to buy or sell any securities. I am not a licensed financial advisor. Investing involves risk, please conduct your own research.
Disclaimer: Community is offered by Moomoo Technologies Inc. and is for educational purposes only.
Read more
Comment
Sign in to post a comment
Griffo_au :![[undefined]](https://static.moomoo.com/nnq/emoji/static/image/default/default-black.png?imageMogr2/thumbnail/36x36 "undefined")
![[undefined]](https://static.moomoo.com/nnq/emoji/static/image/default/default-black.png?imageMogr2/thumbnail/36x36 "undefined")
![[undefined]](https://static.moomoo.com/nnq/emoji/static/image/default/default-black.png?imageMogr2/thumbnail/36x36 "undefined")
![[undefined]](https://static.moomoo.com/nnq/emoji/static/image/default/default-black.png?imageMogr2/thumbnail/36x36 "undefined")
Philip_AU : For beginners, which Greek would you suggest monitoring first when starting out?
0livia : This should be required reading!
0xdylan OP Philip_AU : First Delta, then Theta.
Jovi9488 : I don't really understand vega
0xdylan OP Jovi9488 : For example, if you Buy an Options contract and the current implied volatility (IV) is 30%, with Vega = 0.12. Therefore, if IV rises from 30% to 31%, the price of the Options you hold will increase by $0.12. If IV falls from 30% to 29%, the Options price will decrease by $0.12. Vega does not represent the market's 'actual volatility', but rather the 'market's expected future volatility', so it's possible that the symbol price remains unchanged, but due to significant events leading to an increase in IV, the price of Buy Options will also rise accordingly.
AC Loh : what cause delta change?
0xdylan OP AC Loh : Price, time, and volatility will be discussed in detail.
1. Price
When the symbol Stocks rises:
The Delta of Calls will increase (making it more likely to profit), while the Delta of Puts will decrease (making it more difficult to profit).
When the symbol Stocks falls:
The Delta of Calls will decrease (making it more difficult to profit), while the Delta of Puts will increase (making it more likely to profit).
Reason: The closer you are to 'in the money,' the closer Delta is to 1 (Call) or -1 (Put).
2. Time
The closer it is to expiration:
The Delta of in-the-money Options will quickly approach 1 or -1, while the Delta of out-of-the-money Options will quickly approach 0.
3. Changes in Implied Volatility (IV)
IV rises → Delta converges towards the middle (the Delta of Calls and Puts will be closer to 0.5 or -0.5), as the market believes "uncertainty increases, both rises and falls are possible."
IV falls → Delta moves towards both sides (approaching 0 or ±1), indicating that the market is becoming increasingly certain whether the Options are worthless or profitable.
sunwu79 :![[undefined]](https://static.moomoo.com/nnq/emoji/static/image/default/default-black.png?imageMogr2/thumbnail/36x36 "undefined")
104088143 : Is that true?
View more comments...