A second-order Greek is a second-order derivative of the option value with respect to some variable. Equivalently, it is the first order derivative of an option’s sensitivity with respect to some other variable or sensitivity. Second-order Greeks measure the change of the first order Greeks relative to an influencing variable.
Second-order greeks include: gamma, vomma, vanna, charm, vera, and DvegaDtime. The following table summarizes the main second-order greeks:
| Variable / parameter | Symbol | Measures option’s sensitivity with respect to: |
|---|---|---|
| Gamma | Đ“ | Rate of change of delta with respect to underlying price |
| Vomma/ volga | – | Second order sensitivity to volatility |
| Vanna | – | Sensitivity of delta relative to volatility |
| Charm/ delta decay | – | Instantaneous rate of change of delta with passage of time |
| Vera/ rhova | – | Rate of change in rho with respect to volatility |
| DvegaDtime | – | Rate of change in vega with respect to passage of time |
For example, vanna is the second order derivative of the option value, once to the underlying price and once to volatility. Also, charm (or delta decay) is the second-order derivative of the option value, once to price and once to the passage of time.
During times of high volatility, second order Greeks become more important, especially for investors willing to determine the effect of volatility on their portfolios.
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