期權希臘值計算器

分類： Uncategorized
- August 31, 2026
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Calculate and visualize option sensitivity metrics to help manage risk and optimize trading strategies

期權參數

期權類型
$
現時正股價格
$
期權行使價
Number of calendar days until expiry
%
年度無風險利率
%
Annual volatility of the underlying
%
年度股息率

期權希臘值

Δ
Delta
0.50
Rate of change in option price with respect to changes in the underlying asset's price
This option's price will change approximately $0.50 for every $1 change in the underlying.
Γ
Gamma
0.04
Rate of change in Delta with respect to changes in the underlying asset's price
For every $1 move in the underlying, Delta will change by approximately 0.04.
Θ
Theta
-0.12
Rate of change in option price with respect to the passage of time (time decay)
This option will lose approximately $0.12 in value each day, all else being equal.
V
Vega
0.25
Rate of change in option price with respect to changes in implied volatility
For each 1% change in implied volatility, this option's price will change by approximately $0.25.
ρ
Rho
0.10
Rate of change in option price with respect to changes in the risk-free interest rate
For each 1% change in interest rates, this option's price will change by approximately $0.10.
Lambda (Elasticity)
5.25
Percentage change in option price divided by the percentage change in the underlying price
Vanna
0.015
Rate of change in Delta with respect to changes in volatility
Charm
-0.008
Rate of change in Delta with respect to the passage of time
Vomma
0.036
Rate of change in Vega with respect to changes in volatility

Greeks Visualization

Option Statistics

期權價格
$5.10
Black-Scholes model price
內在價值
$0.00
In-the-money portion
時間值
$5.10
Extrinsic/time premium
Breakeven Price
$105.10
Stock price needed to breakeven at expiration
Put/Call Parity
$5.25
Theoretical price of the opposite option
Probability ITM
50.0%
Probability of being in-the-money at expiration

Trading Strategy Insights

Directional Exposure
看跌
看漲

This at-the-money call option has a Delta of 0.50, indicating a moderate bullish exposure. For every $1 increase in the stock price, the option will gain approximately $0.50 in value.

Volatility Exposure
Short Vol
Long Vol

With a Vega of 0.25, this option benefits from increasing volatility. A 1% increase in implied volatility will increase the option value by approximately $0.25, indicating a long volatility position.

Time Decay Impact
High Impact
Low Impact

With a Theta of -0.12, this option is losing approximately $0.12 per day due to time decay. As expiration approaches, this rate of decay will accelerate, particularly in the final month.

Recommended Strategies
  • Directional Trade: Suitable for traders with a moderately bullish outlook over the next 30 days.
  • Covered Call: Consider writing this call if you own the underlying and expect limited upside.
  • Spread Strategy: To mitigate time decay, consider a vertical spread strategy.
  • Risk Management: Set stop-loss at 50% of premium to manage potential losses.

Understanding Option Greeks

Option Greeks are a set of risk measures that describe the sensitivity of an option's price to various factors. They are named after Greek letters and are essential tools for options traders to understand and manage risk.

Primary Greeks

Δ Delta

Measures how much an option's price changes when the underlying asset's price changes by $1. Ranges from 0 to 1 for calls and -1 to 0 for puts. Also represents the approximate probability of finishing in-the-money.

Γ Gamma

Measures the rate of change in Delta for a $1 change in the underlying asset. High Gamma positions can see their Delta change rapidly, making them more risky and responsive to price movements.

Θ Theta

Measures the rate at which an option loses value as time passes (time decay). Typically negative for long options and expressed as the amount of value lost per day.

V Vega

Measures sensitivity to changes in implied volatility. Expressed as the change in option price for each 1% change in implied volatility. Higher for longer-term options.

ρ Rho

Measures sensitivity to changes in the risk-free interest rate. Typically has a smaller impact than other Greeks but becomes more significant for longer-term options.

Second-Order Greeks

Lambda (Elasticity)

A measure of leverage that represents the percentage change in an option's price divided by the percentage change in the underlying price.

Vanna

Represents how Delta changes with respect to changes in volatility, or equivalently, how Vega changes with respect to the underlying price.

Charm (Delta Decay)

Measures how Delta changes over time. Important for managing delta-hedged positions as expiration approaches.

Vomma (Volga)

Measures the rate of change in Vega with respect to changes in volatility. Important for volatility-focused strategies.

Trading Tips Using Greeks

Delta-Based Strategies
  • Use options with Delta near 0.50 (ATM) for balanced risk/reward and highest Gamma.
  • For directional plays with lower risk, use options with Delta around 0.70-0.80.
  • Adjust Delta exposure by using multiple contracts or delta-hedging with the underlying.
Managing Theta Decay
  • Avoid holding long options with high Theta in the last 30-45 days before expiration.
  • Consider selling options to benefit from time decay in flat market conditions.
  • Use calendar spreads to create positive Theta positions while maintaining directional exposure.
Volatility Trading
  • Long options (high Vega) benefit from volatility increases, while short options benefit from decreases.
  • Use straddles or strangles when expecting significant volatility but uncertain direction.
  • Compare historical and implied volatility to identify potential mispricing.
風險管理
  • Be aware of high Gamma positions which can rapidly change Delta exposure in volatile markets.
  • Monitor total portfolio Greeks, not just individual positions.
  • Use spreads to limit risk and reduce vulnerability to specific Greek exposures.

本工具計算什麼

計算 Delta、Gamma、Theta、Vega 及 Rho——期權的各項敏感度。

公式
delta = ∂C/∂S；gamma = ∂²C/∂S²；theta = ∂C/∂T；vega = ∂C/∂σ；rho = ∂C/∂r
計算示例
Delta 為 0.6，即正股每升 1.00，期權約升 0.60。Theta 為 −0.05，即每日時間值損耗 5 仙。
何時使用
了解期權持倉的價值每日實際由什麼驅動。
常見錯誤
希臘值屬瞬時數值。Delta 本身會隨正股波動而改變，這正是 Gamma 所衡量的，也是對沖會偏離的原因。