A third-order greek is a third-order derivative of the option value with respect to some variable. Equivalently, it is the first-order derivative of an option’s second-order sensitivity with respect to some other variable. Third-order greeks measure the change of the second order greeks relative to an influencing variable.
Third-order greeks include: color (gamma decay or gamma bleed or DgammaDtime), speed, ultima, and zomma. The following table summarizes the main third-order greeks:
| Variable/ parameter | Symbol | Measures option’s sensitivity with respect to: |
|---|---|---|
| Color | – | Rate of change of gamma with respect to passage of time |
| Speed | – | Rate of change of gamma with respect to underlying price |
| Ultima | – | Sensitivity of vomma with respect to volatility |
| Zomma | – | Rate of change of gamma with respect to volatility |
For example, zomma is the third derivative of the option value, twice to underlying price and once to volatility. Similarly, color is the third derivative of the option value, twice to underlying price and once to time.
