The Greeks are financial metrics that measure the sensitivity of an option’s price to various factors, such as changes in the underlying asset price, time, volatility, and interest rates. They help traders understand and manage the risks associated with options positions. Below are the key Greeks in options trading:
1. Delta (Δ)
• Definition: Measures the sensitivity of an option’s price to changes in the price of the underlying asset.
• Range:
• For calls: Between 0 and 1.
• For puts: Between -1 and 0.
• Interpretation:
• A delta of 0.5 means the option price will change by $0.50 if the underlying price moves by $1.
• ATM options typically have a delta of ~0.5 for calls and ~-0.5 for puts.
• Use:
• Hedging: Delta tells how many units of the underlying are needed to hedge the position.
• Directional Trading: Higher delta options respond more to price moves.
2. Gamma (Γ)
• Definition: Measures the rate of change of delta with respect to changes in the price of the underlying asset.
• Range: Always positive for both calls and puts.
• Interpretation:
• High gamma indicates that delta will change rapidly as the underlying price moves.
• ATM options have the highest gamma.
• Use:
• Risk Management: Helps in understanding how delta will change if the underlying moves, especially for large price moves.
• Gamma is particularly important for dynamic hedging strategies.
3. Theta (Θ)
• Definition: Measures the sensitivity of an option’s price to the passage of time (time decay).
• Range: Negative for long options and positive for short options.
• Interpretation:
• A theta of -0.05 means the option price will lose $0.05 per day due to time decay.
• Time decay accelerates as expiration approaches, especially for ATM options.
• Use:
• Buyers: Theta works against long positions since time decay reduces the option’s value.
• Sellers: Theta benefits short positions as they gain from time decay.
4. Vega (ν or V)
• Definition: Measures the sensitivity of an option’s price to changes in implied volatility.
• Range: Always positive for both calls and puts.
• Interpretation:
• A vega of 0.10 means the option price will change by $0.10 if IV changes by 1%.
• Longer-dated options have higher vega, as volatility affects their price more.
• Use:
• Volatility Trading: Use vega to predict how changes in IV will impact options.
• Hedging: Manage exposure to volatility changes.
5. Rho (ρ)
• Definition: Measures the sensitivity of an option’s price to changes in interest rates.
• Range:
• Positive for calls, negative for puts.
• Interpretation:
• A rho of 0.05 means the option price will change by $0.05 if interest rates increase by 1%.
• Rho has a more significant effect on longer-dated options.
• Use:
• Less important for short-dated options but crucial for longer maturities or interest rate-sensitive markets.
6. Secondary Greeks (Advanced)
• Vomma: Sensitivity of vega to changes in IV.
• Charm: Rate of change of delta with respect to time.
• Vanna: Sensitivity of delta to changes in IV.
• Zomma: Sensitivity of gamma to changes in the underlying price.
Greeks in Practice
• Delta-Neutral Hedging:
• A delta-neutral portfolio has an overall delta of 0, meaning it is protected from small price changes in the underlying.
• Gamma Scalping:
• Use gamma to dynamically adjust hedges to profit from underlying price movements.
• Theta Strategies:
• Option sellers, such as in credit spreads, benefit from positive theta.
• Vega Plays:
• Buy options when IV is low (expecting IV to increase).
• Sell options when IV is high (expecting IV to decrease).
Example: Applying the Greeks
Imagine a call option with:
• Delta: 0.6
• Gamma: 0.05
• Theta: -0.02
• Vega: 0.15
• Rho: 0.01
If:
1. The underlying price increases by $1, the option price increases by $0.60 (from delta).
2. If the underlying moves further, delta increases (by gamma) to 0.65.
3. The option loses $0.02 per day due to time decay (theta).
4. If IV rises by 1%, the option gains $0.15 (vega).
5. If interest rates rise by 1%, the option gains $0.01 (rho).
By understanding and combining these Greeks, traders can better manage their risk and optimize their strategies.