Delta, Gamma, Theta, Vega, and Rho

Options Trading Greeks

1. Delta (Δ):

Definition: Delta measures the rate of change of the option price concerning changes in the underlying asset's price.

Calculation: Delta is calculated as the change in the option price divided by the change in the underlying asset's price.

Delta for call options: Ranges from 0 to +1

Delta for put options: Ranges from -1 to 0

Example: Consider a call option with a delta of 0.60. If the stock price increases by $1, the option price would theoretically increase by $0.60 (assuming all other factors remain constant).

2. Gamma (Γ):

Definition: Gamma measures the rate of change of Delta concerning changes in the underlying asset's price.

Calculation: Gamma is the rate of change of delta concerning changes in the underlying asset's price.

Example: If a call option has a delta of 0.60 and a gamma of 0.10, if the stock price changes, the delta will change by 0.10 for every $1 movement in the underlying stock.

3. Theta (Θ):

Definition: Theta measures the rate of time decay of an option's price as the expiration date approaches.

Calculation: Theta is usually expressed as a negative value. It represents the amount the option price decreases with the passage of one day.

Example: A theta of -0.05 means the option price will theoretically decrease by $0.05 per day, assuming all other factors remain constant.

4. Vega (ν):

Definition: Vega measures the sensitivity of an option's price concerning changes in implied volatility.

Calculation: Vega is the change in the option price for a 1% change in implied volatility.

Example: If a call option has a vega of 0.20, a 1% increase in implied volatility would theoretically increase the option price by $0.20.

5. Rho (ρ):

Definition: Rho measures the sensitivity of an option's price concerning changes in interest rates.

Calculation: Rho is the change in the option price for a 1% change in interest rates.

Example: If a call option has a rho of 0.03, a 1% increase in interest rates would theoretically increase the option price by $0.03.

The Greeks are derived from option pricing models such as the Black-Scholes model and are useful for traders and investors to assess the risks and potential price movements of options under different market conditions. They change dynamically with market movements, time decay, and changes in implied volatility.