Common Option Indicators

(1) “Option break-even point”

The break-even point for US stock options refers to the specific level at which the price of the stock needs to reach at the expiration of the option, so that the investor holding the option neither makes a profit nor loses money. This price takes into account the premium paid when buying the option (the cost of the option). Understanding the break-even point is important for assessing the potential value and risk of options trading.
Break-even point of bullish options
For bullish options, the break-even point is calculated as follows:
Bullish option breakeven point = call-over price + option premium bullish option breakeven point = call-over price + option premium
This means that the market price of the stock needs to exceed this break-even price for the option holder to start making a profit. If the price of the stock is higher than this point, the intrinsic value of the option will increase with each increase, resulting in a profit.
Break-Even Point of Put Options
For put options, the break-even point is calculated as follows:
Put break-even point = call-over price − option premium Put break-even point = call-over price − option premium
In this case, the market price of the stock needs to be below the break-even price for the option holder to start making a profit. If the price of the stock falls below this point, the intrinsic value of the option increases with each drop, resulting in a profit.
example
Suppose an investor buys a bullish call-over option with a price of 100 dollars, pays a premium of 5 dollars, and its break-even point is: 100 + 5 = 105 dollars
This means that the stock price needs to reach at least 105 dollars at maturity for the investor to start making a profit and offset the premium paid.
Similarly, if an investor buys a call-over put option with a price of $100, the premium paid is $5, and the break-even point is: 100 − 5 = $95
This suggests that the stock price needs to be below 95 dollars at maturity for investors to start making a profit, offsetting the premium paid.
Understanding and calculating the break-even point of options is fundamental and critical for investors who trade options. This helps investors evaluate the risks and potential rewards of a trade and make more informed trading decisions.

(2) “Option premium rate”

The premium ratio for US stock options is the percentage of the additional cost of the option’s current price relative to its intrinsic value. This premium typically includes the time value of the option, as well as the volatility premium caused by the market’s expectations of future stock price fluctuations. Understanding the premium ratio is important for assessing whether an option is overvalued or undervalued and for determining a trading strategy.
The components of options
Option prices are mainly composed of two components:
Intrinsic value: This is the direct benefit of the option at call-over and only exists if the option is in-the-money. For bullish options, intrinsic value is calculated as the current price of the stock minus the option call-over price (if the outcome is positive). For put options, it is the option call-over price minus the current price of the stock (if the outcome is positive).
Time value: This is the portion of an option’s price other than its intrinsic value, based on the remaining expiration time, expected fluctuations in the stock price, risk-free interest rates, and other market factors. Time value decreases over time until the option reaches zero at expiration.
Calculate the premium rate
The premium rate is usually the ratio of the total option price (market price) to the premium portion of its intrinsic value. The formula is: premium rate (%) = (total option price − intrinsic value intrinsic value) × 100 premium rate (%) = (intrinsic value total option price − intrinsic value) × 100
If an option has no intrinsic value (i.e., it is flat or out-of-the-money), the premium rate can be very high because the entire option price is essentially a time-value and volatility premium.
Application of Option Premium Rate
The premium rate is a key metric used by options traders to determine whether an option is reasonably priced. A high premium rate may indicate that the option is overvalued relative to its intrinsic value, especially when market expectations are volatile or a major event is imminent. Conversely, a low premium rate may indicate that the option is undervalued or that the market has less uncertainty about the future of the stock.
example
Suppose the call-over price of a bullish option is 100 dollars, the current stock price is 105 dollars, and the option market price is 7 dollars. Then, the intrinsic value is 5 dollars (105 dollars - 100 dollars), and the time value of the option is 2 dollars (7 dollars - 5 dollars). Premium Rate = (25) × 100 = 40% Premium Rate = (52) × 100 = 40% This indicates that in addition to the intrinsic value, there is a 40% premium, which is mainly composed of the time value of the option and the market’s expectations for future fluctuations.
conclusion
The option premium rate provides insight into the relative cost of options and helps investors and traders make more informed investment and trading decisions. It is a useful tool for evaluating the value and time cost of options traded, especially in volatile market environments.

(3) "Option Implied Volatility"

The implied volatility of US stock options refers to the market’s expectation of the future volatility of the stock, and this indicator is reflected in the pricing of the option. Implied volatility is a very important concept because it affects the price of the option: the higher the volatility, the higher the value of the option is usually, because higher volatility means more uncertainty about the future of the stock price, which increases the likelihood that the option will reach a profitable state.
What is implied volatility?
Implied volatility is derived backwards from option pricing models such as the famous Black-Scholes model, which is calculated based on the current market price of the option. This volatility is not based on statistical calculations of the historical price of a stock, but on market predictions and expectations of future stock price fluctuations.
The significance of implied volatility
Option pricing: Implied volatility is a crucial variable in option pricing. Other things being equal, the higher the volatility, the higher the price of bullish and put options.
Indicator of market sentiment: Implied volatility is often seen as an indicator of market sentiment and expected uncertainty. For example, implied volatility in related options may increase before a company’s earnings announcement, reflecting market uncertainty about upcoming earnings results.
Trading strategy: Traders use implied volatility to evaluate whether an option is overvalued or undervalued. If an option’s implied volatility is much higher than the stock’s historical volatility, the option may be considered overvalued, and vice versa.
Application of Implied Volatility
Implied volatility is crucial for executing various options trading strategies, such as:
Volatility Trading: Investors can buy or sell options by comparing implied volatility with historical or expected volatility.
Arbitrage strategy: If the implied volatility of two similar assets is significantly different, a trader may attempt to arbitrage by simultaneously buying options on one asset and selling options on the other.
Volatility hedging: When using options hedging Spot Market risk, implied volatility helps determine the best time to buy or sell options.
Implied volatility is an extremely important concept in options trading. It not only helps traders understand the market expectations contained in the current option price, but also the basis for executing various option strategies. By analyzing the movement of implied volatility, traders can better grasp market dynamics and make more accurate trading decisions.

(4) “Intrinsic Value of Options”

The intrinsic value of a US stock option is a fundamental component of option pricing and represents the value of the option when it is immediately called-over. Specifically, intrinsic value is the non-negative part of the difference between the option’s exercise price and the underlying asset’s current market price. This means that an option has intrinsic value if it generates a profit immediately after call-over, and zero if it does not generate a profit after call-over.
Calculate intrinsic value
For bullish call options:
Intrinsic value = current stock price - call-over price of option
If the result is negative, then the intrinsic value is zero.
For put options:
Intrinsic value = call-over price of option - current stock price
If the result is negative, then the intrinsic value is zero.
The significance of intrinsic value
Measuring Option Value: Intrinsic value is a direct way to measure the actual value of an option. It reflects the actual value that an investor can get from the option if it is called-over immediately.
Non-speculative value: Intrinsic value does not depend on predictions or assumptions about the future, but simply reflects the actual situation under current market conditions.
The real value and out-of-the-money of options:
When the intrinsic value of an option is greater than zero, the option is called “In-the-money” (ITM).
When the intrinsic value of an option equals zero, if the exercise price of the option is equal to the current market price, the option is called “at-the-money” (ATM); if the call-over of the option immediately results in a loss, it is called “out-of-the-money” (OTM).
Intrinsic value and time value
Time value: In addition to intrinsic value, the total value of an option includes time value. Time value is based on the time remaining until the option expires and the market’s expectation of the underlying asset’s future volatility. Time value typically decreases as the term approaches until the option reaches zero at expiration.
Total Option Value = Intrinsic Value + Time Value
practical application
Investment decisions: Understanding intrinsic value can help investors identify and select options with higher potential profitability. In general, real-value options (options with intrinsic value) are less risky but can be more expensive.
Trading strategy: The concept of intrinsic value is the foundation for building a variety of options strategies (e.g. protective puts, covered bullish options, etc.), which helps investors manage risk and enhance their earning potential.
In conclusion, intrinsic value is a very important concept in options trading, which directly affects the pricing of options and the choice of trading strategies. Understanding and applying the concept of intrinsic value can help investors use options more effectively for investment and risk management.

(5) “Option time value”

The time value of US stock options is an important part of the option price, reflecting the potential value brought by the change of stock price during the remaining valid period of the option. The time value, together with the intrinsic value of the option, constitutes the total market value of the option. Time value is based on the remaining time before the expiration of the option and the market’s expectation of the future volatility of the underlying asset.
The Definition of Time Value
Time value is usually defined as the total price of an option minus its intrinsic value. If the option is out-of-the-money (i.e. has no intrinsic value), then its total value is entirely composed of time value. Time value can be seen as the additional amount that investors are willing to pay in exchange for the possibility of benefiting from stock price changes in the future.
Calculation of time value
Time Value = Total Option Value - Intrinsic Value Time Value = Total Option Value - Intrinsic Value If the option is out-of-the-money, the total option value equals the time value.
Factors affecting time value
Expiration time: The time value is closely related to the expiration time of the option. The longer the expiration time, the higher the time value of the option usually is, because a longer time increases the likelihood of the stock price reaching the expected level.
Volatility of underlying assets: The higher the volatility, the greater the potential for price changes in the underlying asset, and therefore the time value of options will also increase. Volatility is a key indicator for evaluating the uncertainty of future stock prices.
Risk-free rate: In theory, the higher the risk-free rate, the higher the opportunity cost of holding cash instead of investing in options, which increases the time value of options.
Stock dividends: For bullish options, the more expected stock dividends, the lower the time value usually is, because the stock price may decline during the dividend period. On the contrary, for put options, dividends may increase their time value.
Characteristics of time value
Time Decay (Theta): The value of time is not constant and will gradually decrease over time. This phenomenon is called time decay or Theta. Time decay usually accelerates before the option expires, especially in the last month.
Strategies for utilizing time value: Understanding time value is crucial for executing various option strategies, such as selling covered bullish options or conducting time value arbitrage. In these strategies, investors may use high time value to sell options to collect premiums, or use differences in time value by combining buying and selling options with different expiration dates.
Time value is a core component of option value, which is based on the potential economic value of underlying asset price changes during the option holding period. Effective management and utilization of time value can help investors improve the profitability and efficiency of option trading. Understanding the various factors that affect time value is the key to successful option trading.
Option delta
In options trading, Delta is a very important Greek alphabet indicator used to describe the sensitivity of the option price to changes in its underlying asset price. The Delta value represents the theoretical price change generated by each unit change in the option price relative to the underlying asset price of the option.
Delta in American
For options, Delta is the first derivative of the option value against the underlying stock price change, that is:
Delta of Bullish Options: When the price of the underlying stock rises, the value of the Bullish option also increases. The Delta value range of the Bullish option is from 0 to 1.
Delta of put options: When the price of the underlying stock decreases, the value of the put option will increase. The Delta value of a put option ranges from 0 to -1.
Delta value can be specifically explained as:
For bullish options, if Delta is 0.5, then for every $1 increase in the underlying asset price, the option value will theoretically increase by $0.5.
For a put option, if Delta is -0.5, then for every $1 decrease in the underlying asset price, the option value will theoretically increase by $0.5.
Application of Delta
Risk management and hedging: Delta is commonly used to manage the directional risk of option portfolios. For example, by adjusting the sum of Delta in the portfolio, investors can make their investment portfolio close to neutral and reduce the impact of market fluctuations on the portfolio.
Trading strategy: By understanding Delta, traders can choose options with specific risk exposure. For example, deep in-the-money options (Delta close to 1 or -1) respond sensitively to stock price changes like stocks, while out-of-the-money options (Delta close to 0) respond less to stock price changes.
Predicted probability: Delta value can also be interpreted as a rough estimate of the probability that the option will end up in the in-the-money state (i.e. valuable) at expiration. For example, a bullish option with a Delta of 0.25 means there is about a 25% chance that the option will be in-the-money at expiration.
Changes in Delta
Delta is not a fixed value, it changes with factors such as underlying asset prices, volatility, and expiration time. In addition, Delta has less variation for deep in-the-money and deep out-of-the-money options, while it has greater variation for at-the-money options. This variability of Delta is also known as Gamma, which measures the speed of Delta’s own changes. Delta is a key indicator for measuring the sensitivity of option prices to changes in underlying asset prices, and has important application value for option traders in risk management, trading strategy design, and predicting option behavior. Understanding and utilizing Delta can help investors more effectively execute and manage their options trading strategies.
Options gamma
In options trading, Gamma is another important Greek alphabet indicator that measures the rate of change of Delta (an indicator of the sensitivity of option prices to changes in underlying asset prices). Simply put, Gamma represents how the Delta value of an option will change when the price of the underlying asset changes.
Gamma in British
Gamma is the first derivative of Delta, reflecting the speed and magnitude of Delta’s changes with the underlying asset price. It provides a deeper understanding of the sensitivity of option Delta, especially when the underlying asset price is close to the call-over price of the option (i.e., the option with the value of “close”), Gamma will reach its maximum value.
Gamma for bullish and put options: Gamma is positive for bullish and put options, which means that whether it is bullish or put options, the increase in the underlying asset price will increase Delta (for put options, although Delta itself is negative, its absolute value decreases).
Application of Gamma
Adjusting Delta hedging strategy: When performing Delta hedging (especially dynamic hedging), Gamma provides information on how frequently hedging positions need to be adjusted. A high Gamma value means that small price changes in the underlying asset can cause significant changes in Delta, requiring more frequent position adjustments to maintain the effectiveness of hedging.
Risk Management: Options with high Gamma indicate that their prices are more sensitive to changes in the underlying asset prices. This type of option may bring higher risks and returns during market fluctuations, so managing the risks of this type of option is particularly important.
Strategy Selection: Understanding the Gamma of options can help investors choose trading strategies that suit their market views and risk preferences. For example, investors may choose options with higher Gamma values for short-term trading, taking advantage of small fluctuations in stock prices.
Characteristics of Gamma
Gamma usually increases as the option approaches expiration, especially for at-the-money options. This is because small price changes in the underlying asset become increasingly important for the option’s profitability as the expiration date approaches.
The impact of volatility: Although Gamma itself is not directly affected by volatility, large fluctuations in underlying asset prices in high volatility environments may cause Delta and Gamma to change more frequently.
Gamma is an advanced options Greek alphabet indicator that helps traders understand and predict changes in Delta, thereby more accurately adjusting risk management and hedging strategies. Understanding Gamma is particularly important in highly volatile market environments or near option expiration
Options theta
In US stock options trading, Theta is a key Greek alphabet indicator that measures the sensitivity of option prices to time, specifically the rate at which option value decays over time. Theta is known as “time decay” or “time erosion” because all options gradually lose value over time, especially as the expiration date approaches.
Theta in British
Theta represents the expected change in the value of an option over time, provided that other conditions remain unchanged (such as the underlying asset price and volatility). Theta is usually expressed as a negative number because the passage of time is unfavorable for option holders and the option value usually decreases.
Calculate Theta
The calculation of Theta involves option pricing models, such as the Black-Scholes model. It considers multiple factors, including the call-over price of the option, expiration time, current price of the underlying asset, risk-free interest rate, and implied volatility of the option. The specific value of Theta reflects the value of the remaining time of the option under current market conditions.
Application of Theta
Risk management and trading decisions: Understanding Theta is crucial for managing the time decay risk of option portfolios. Investors need to be aware that as the expiration date approaches, Theta will increase and the impact of time decay will intensify, especially for at-the-money and out-of-the-money options.
Selecting expiration date: Theta can help traders make decisions when choosing options with different expiration dates. If you want to reduce the impact of time decay, you may choose options with longer expiration dates; if you want to use time decay, such as collecting time value through selling option strategies, you may choose options with shorter expiration dates.
Optimizing Seller Strategy: Theta is particularly important for traders who execute seller strategies (such as writing (selling) bullish options or putting options), as they can use time decay to earn premiums. Understanding and managing Theta can help maximize the profit potential of this strategy.
Factors affecting Theta
Expiration time: As the option approaches expiration, Theta increases and time decay accelerates.
In-the-money status of options: At-the-money options usually have the highest Theta because their time value component is the largest. In-the-money or deep out-of-the-money options have lower Theta.
Volatility: The higher the volatility, the higher the overall price (including time value) of the option, so the Theta value may be larger in a high volatility environment.
Theta is a very important parameter in options trading, which helps traders quantify and manage the characteristics of option decay over time. Through reasonable strategy design and management, Theta can be effectively used to optimize the return of option investment, especially in high-frequency trading and short-term strategies. Understanding Theta is particularly important for option sellers who hope to profit from time decay.
Options vega
In options trading, Vega is a core Greek alphabet indicator that measures the sensitivity of option value to the implied volatility of the underlying asset. Specifically, Vega represents the expected change in option value when the implied volatility of the underlying asset changes by one percentage point.
Vega in American
Vega is not an actual Greek alphabet name, but it plays a key role in option pricing. It is a measure used to describe the impact of small changes in implied volatility on option prices. Since volatility represents the magnitude and speed of changes in the underlying asset price, it directly affects the time value of options.
Calculating Vegas
The value of Vega is calculated through option pricing models (such as the Black-Scholes model), which consider the call-over price of the option, remaining expiration time, current price of the underlying asset, risk-free interest rate, and current implied volatility. Typically, Vega decreases as the option expiration date approaches, as the decrease in time value reduces the impact of volatility.
Applications of Vega

1. Volatility trading: Understanding Vega is especially important for traders who focus on volatility as a trading strategy. By buying options with high Vega values (options are more sensitive to volatility changes) and/or selling options with low Vega values, traders can build investment portfolios based on predictions of future market volatility.
2. Risk management: Vega allows options investors to evaluate the sensitivity of their portfolio to volatility changes. This understanding helps investors take corresponding hedging measures when market volatility increases.
3. Strategy selection: Investors can use Vega to choose the best option strategy for different market views. For example, when market volatility is expected to increase, it may be more advantageous to buy options with high Vega.
   Factors affecting Vega

• Expiration time: Long-term options typically have a higher Vega because of greater market uncertainty and potential volatility over the long term, which increases the time value and volatility sensitivity of the option.
• The in-the-money/out-of-the-money status of options: Vega for at-the-money options is usually the highest because it is most sensitive to changes in volatility. Vega for in-the-money or deep out-of-the-money options is usually lower.
  Vega is an extremely important parameter in options trading, especially in evaluating and managing the sensitivity of options strategies to changes in implied volatility. Effective use of Vega can help traders optimize their options strategies, especially when market volatility is expected to change significantly. Understanding and applying Vega can greatly enhance the strategic and profitable nature of options trading
  Options rho
  In US stock options trading, Rho is an important “Greek value” that measures the sensitivity of option prices to changes in risk-free interest rates. Rho indicates how the theoretical price of options will change when the risk-free interest rate (such as US Treasury yields) changes by one percentage point.
  Rho in British
• For bullish options, if the risk-free interest rate rises, the value of the bullish option usually increases, so the Rho of the bullish option is usually positive.
• For put options, an increase in the risk-free rate usually leads to a decrease in the value of the put option, so the Rho of the put option is usually negative.
  The reason for this relationship is that in option pricing models (such as the Black-Scholes model), the theoretical value of options depends in part on the present value of future cash flows. The risk-free interest rate is a key variable in calculating the present value of these future cash flows.
  Calculation of Rho
  In the Black-Scholes model, the calculation of Rho involves complex mathematical formulas, which are basically partial derivatives of option value with respect to the risk-free rate. Typically, investors use option pricing software or trading platforms to obtain this indicator, rather than manually calculating it.
  Application of Rho

1. Investment decisions: Understanding Rho is especially important for long-term option holders, as interest rate changes have a greater impact on them. Investors can use Rho to evaluate and manage the latent risk of their option positions in the face of interest rate changes.
2. Risk management: By understanding the Rho of options, investors can better manage the interest rate risk of option portfolios. For example, in an environment where interest rates are expected to rise, increasing exposure to bullish options may help take advantage of this change.
3. Hedging strategy: Rho can help develop hedging strategies, especially in complex option strategies such as those that require hedging multiple Greek values.
   The practical importance of Rho
   Although Rho is an important option pricing factor in theory, it is usually not valued as much as Delta, Gamma, or Vega in actual trading. This is because in the short term, changes in interest rates usually have a smaller impact on option prices, especially for options with shorter expiration times. However, understanding and monitoring Rho is still very important when facing significant economic policy changes or changes in interest rate environments. In short, Rho is a useful tool for measuring the response of option prices to changes in interest rates, especially when evaluating and managing long-term options or option strategies in a changing interest rate environment.