What are the common options metrics?

(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 refers to 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 market expectations of future stock price fluctuations. Understanding the premium ratio of options 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 assessing 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, thus increasing 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 expectations 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 the option minus its intrinsic value. If the option is out-of-the-money (i.e. has no intrinsic value), then its total value consists entirely of time value. Time value can be seen as the additional amount an investor is willing to pay in exchange for the possibility of benefiting from a stock price movement at some future period.

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 is equal to the time value.

Factors that affect the value of time

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, because the longer time increases the likelihood that the stock price will reach the desired level.

Volatility of the underlying asset: The higher the volatility, the greater the potential for price movement of the underlying asset, and therefore the time value of the option increases. Volatility is a key metric for assessing the uncertainty of the future price of a stock.

Risk-free rate: In theory, the higher the risk-free rate, the higher the opportunity cost of holding cash rather than investing in options, which increases the time value of options.

Stock dividends: For bullish options, the higher the expected stock dividend, the lower the time value, as the share price may decline during the dividend period. The opposite is true for put options, where dividends may increase their time value.

The characteristics of time value

Time decay (Theta): The value of time is not constant, it gradually decreases over time, a phenomenon called time decay or Theta. Time decay usually accelerates before the option expires, especially during the last month.

Strategies that capitalize on time value: Understanding time value is critical to executing a variety of option strategies, such as selling covered calls or performing time value arbitrage. In these strategies, investors may use high time value to sell options to collect premiums, or take advantage of differences in time value by combining the purchase and sale of options with different expiration dates.

Time value is a core component of option value, which is based on the underlying economic value of price changes in the underlying asset during the option holding period. Effective management and utilization of time value can help investors improve the profitability and efficiency of options trading. Understanding the various factors that affect time value is the key to conducting successful options trading.

(6) “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 the price of its underlying asset. The Delta value represents the theoretical price change of the option price relative to the price of the option’s underlying asset by one unit.

Delta in British

For an option, a Delta is the first derivative of the stock price movement against which the option value is based, namely:

Bullish option’s Delta: When the price of the underlying stock goes up, the value of the bullish option also goes up. The Delta value of the bullish option ranges from 0 to 1.

Delta for put options: The value of a put option increases when the price of the underlying stock decreases. The delta value of a put option ranges from 0 to -1.

The Delta value can be specifically interpreted as:

For bullish options, if the Delta is 0.5, then for every $1 increase in the underlying asset price, the option value theoretically increases by $0.5.

For a put option, if the Delta is -0.5, then for every $1 decrease in the underlying asset price, the option value theoretically increases by $0.5.

Application of Delta

Risk management and hedging: Deltas are often used to manage directional risk in a portfolio of options. For example, by adjusting the sum of deltas in a portfolio, investors can bring their portfolio close to neutral, reducing the impact of market volatility on the portfolio.

Trading Strategy: By understanding Delta, traders can choose options with specific risk exposures. For example, deep real options (Delta close to 1 or -1) react as sensitively to stock price changes as stocks, while out-of-the-money options (Delta close to 0) respond less to stock price changes.

Predictive probability: The delta value can also be read as a rough estimate of the probability that the option will end up in real value when it expires. For example, a bullish option with a delta of 0.25 means that there is approximately a 25% probability that the option will be in real value at expiration.

Changes in Delta

Delta is not a fixed value, it will change with the underlying asset price, volatility, expiration time and other factors. In addition, Delta options change less for deep real value and deep out-of-the-money options, but more for flat value options. This Delta variability is also known as Gamma, which measures the speed of movement of the Delta itself. Delta is a key indicator to measure the sensitivity of option prices to changes in the price of the underlying asset, and has important application value for option traders in risk management, trading strategy design, and predicting option behavior. Understanding and leveraging Delta can help investors execute and manage their options trading strategies more effectively.

(7) “Option gamma”

In options trading, Gamma is another important Greek alphabet indicator that measures the rate of change of the Delta (an indicator of the sensitivity of the option price to changes in the price of the underlying asset). In simple terms, Gamma represents how the option’s Delta value will change when the price of the underlying asset changes.

Gamma in British

Gamma is the first derivative of a Delta and reflects the speed and magnitude of the Delta’s change with the underlying asset price. It provides a deeper understanding of the option’s Delta sensitivity, especially when the underlying asset price approaches the option call-over price (i.e. the near-near value option), where Gamma reaches its maximum value.

Gamma for bullish and put options: Gamma is positive for bullish and put options, which means that an increase in the price of the underlying asset increases the delta, whether bullish or put (for put options, while delta itself is negative, its absolute value decreases).

Applications of Gamma

Adjust the Delta hedging strategy: When performing Delta hedging (especially dynamic hedging), Gamma provides information on how often hedging positions need to be adjusted. A high Gamma value means that small price changes in the underlying asset can cause significant changes in the Delta, requiring more frequent adjustments to positions to maintain the effectiveness of hedging.

Risk Management: Options with a high gamma indicate that their price is more sensitive to changes in the price of the underlying asset. This option may carry higher risk and reward when the market is volatile, so it is particularly important to manage the risk of this type of option.

Strategy Selection: Understanding the gamma of options can help investors choose a trading strategy that suits their market view and risk appetite. For example, investors may choose options with a higher gamma value for short-term trading, taking advantage of small fluctuations in stock prices.

Features of Gamma

Variation with expiration: Gamma usually increases near expiration, especially for flat options. This is because small price movements in the underlying asset become increasingly important to the option’s profitability near expiration.

The impact of volatility: Although Gamma itself is not directly affected by volatility, large fluctuations in the price of the underlying asset in a high-volatility environment may cause Delta and Gamma to change more frequently.

Gamma is an advanced options Greek alphabet indicator that helps traders understand and predict delta changes for more precise risk management and hedging strategy adjustments. Understanding Gamma is especially important in highly volatile market environments or near option expiration

(8) “Option theta”

In US stock options trading, Theta is a key Greek alphabet metric that measures the sensitivity of an option’s price to time, specifically the rate at which the option’s value decays over time. Theta is called “time decay” or “time erosion” because all options gradually lose value over time, especially as they approach their expiration date.

Theta in British

Theta represents the expected change in the value of an option over time over a day, all other things being equal (e.g. the underlying asset price, volatility, etc.). Theta is usually expressed as a negative number because the passage of time is unfavorable for the option holder and the option value usually decreases.

Calculate Theta

The calculation of Theta involves options pricing models such as the Black-Scholes model. It takes into account a number of factors, including the call-over price of the option, the expiration time, the current price of the underlying asset, the risk-free rate, and the implied volatility of the option. The specific value of Theta reflects the value of the remaining time of the option under current market conditions.

Applications of Theta

Risk management and trading decisions: Understanding Theta is critical to managing the time decay risk of an option portfolio. Investors need to be aware that as the expiration date approaches, Theta increases and the impact of time decay intensifies, especially for flat and out-of-the-money options.

Choose an 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 a longer expiration time; if you want to take advantage of time decay, such as through a sell option strategy to collect time value, you may choose options with a shorter expiration time.

Optimizing seller strategies: 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.

（9）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 appropriate 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 option’s time value and volatility sensitivity.
• In-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

（10）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.