Options Trading: Greeks (Delta and Gamma)

Option Greeks

Delta (Δ)

• Measures the rate of change of the option's price with respect to the underlying asset's price
• Call option delta: 0 ≤ Δ ≤ 1, Put option delta: -1 ≤ Δ ≤ 0
• Interpretation:
  • Call option delta: The expected change in the option price for a $1 change in the underlying asset price
  • Put option delta: The negative of the expected change in the option price for a $1 change in the underlying asset price
• Delta-neutral strategy: A portfolio with a delta of zero, meaning the portfolio's value is not affected by changes in the underlying asset price

Gamma (Γ)

• Measures the rate of change of the option's delta with respect to the underlying asset's price
• Γ = Δ / (underlying asset price)
• Interpretation:
  • Large gamma: Option's delta changes rapidly, making it more sensitive to price changes
  • Small gamma: Option's delta changes slowly, making it less sensitive to price changes
• Gamma is highest for at-the-money options and decreases as the option becomes more in- or out-of-the-money

Theta (θ)

• Measures the rate of change of the option's price with respect to time
• Θ = - (option premium / time to expiration)
• Interpretation:
  • Options lose value over time, especially as expiration approaches
  • Theta is highest for at-the-money options and decreases as the option becomes more in- or out-of-the-money

Vega (ν)

• Measures the rate of change of the option's price with respect to volatility
• ν = ∂option price / ∂volatility
• Interpretation:
  • Increasing volatility increases the option's value
  • Vega is highest for at-the-money options and decreases as the option becomes more in- or out-of-the-money

Option Greeks

Delta (Δ)

• Measures the rate of change of the option's price with respect to the underlying asset's price
• Call option delta ranges from 0 to 1, while put option delta ranges from -1 to 0
• A call option delta represents the expected change in the option price for a $1 change in the underlying asset price
• A put option delta represents the negative of the expected change in the option price for a $1 change in the underlying asset price
• A delta-neutral strategy has a portfolio with a delta of zero, making it unaffected by changes in the underlying asset price

Gamma (Γ)

• Measures the rate of change of the option's delta with respect to the underlying asset's price
• Calculated as Γ = Δ / (underlying asset price)
• A large gamma indicates the option's delta changes rapidly, making it more sensitive to price changes
• A small gamma indicates the option's delta changes slowly, making it less sensitive to price changes
• Gamma is highest for at-the-money options and decreases as the option becomes more in- or out-of-the-money

Theta (θ)

• Measures the rate of change of the option's price with respect to time
• Calculated as Θ = - (option premium / time to expiration)
• Options lose value over time, especially as expiration approaches
• Theta is highest for at-the-money options and decreases as the option becomes more in- or out-of-the-money

Vega (ν)

• Measures the rate of change of the option's price with respect to volatility
• Calculated as ν = ∂option price / ∂volatility
• Increasing volatility increases the option's value
• Vega is highest for at-the-money options and decreases as the option becomes more in- or out-of-the-money

Understand the concepts of Delta and Gamma in options trading, including their interpretations and effects on option prices.