Options Trading: Greeks (Delta and Gamma)

Questions and Answers

The rate at which the option's delta changes with respect to time.

The value by which an option's price is expected to decrease over time.

The expected change in the option price for a $1 decrease in the underlying asset price.

The expected change in the option price for a $1 change in the underlying asset price. (correct)

The value of the option is primarily unaffected by changes in underlying volatility.

The option will lose significant value as expiration approaches.

The option's delta remains constant, making it less sensitive to price changes.

The option's delta changes rapidly, indicating greater sensitivity to price changes. (correct)

Negative, indicating that the portfolio will gain value as the underlying price increases.

High, indicating that the portfolio is likely to lose value with small movements in the underlying asset.

Equal to one, indicating strong sensitivity to the underlying asset price.

Zero, meaning the portfolio's value is unaffected by changes in the underlying asset price. (correct)

The rate of change of the option's price with respect to time. Signup and view all the answers

It indicates how the option price changes with respect to volatility. Signup and view all the answers

Theta increases, indicating a quicker loss in option value as expiration nears. Signup and view all the answers

Vega is highest for at-the-money options compared to others. Signup and view all the answers

Gamma affects how quickly an option's delta will change in response to the underlying asset price. Signup and view all the answers

Study Notes

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

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

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

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

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

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

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

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