In mathematical finance, The Greeks are measurements of risk that are used to represent the sensitivity of the price of a derivative to underlying variables, such as timevalue decay and the implied volatility or price of the underlying asset.
Delta  The price sensitivity

Delta measures the rate of change of the derivative value, $V$, with respect to changes in the underlying asset's price, $S$.

$\mathrm{\Δ}\=\frac{\partial}{\partial S}V$
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Vega  The sensitivity to volatility

Vega measures the rate of change of the derivative value, $V$, with respect to the volatility, $\mathrm{\σ}$, of the underlying asset.

$\mathrm{\ν}\=\frac{\partial}{\partial \mathrm{sigma;}}V$



Theta  The time sensitivity

Theta measures the rate of change of the derivative value, $V$, and time, $\mathrm{\τ}$. This is also known as the "timevalue decay".

$\mathrm{\Θ}\=\frac{\partial}{\partial \mathrm{tau;}}V$



Rho  The sensitivity to the interest rate

Rho measures the rate of change of the derivative value, $V$, and the risk free interest rate, $r$.

$\mathrm{\ρ}\=\frac{\partial}{\partial r}V$



Gamma  The secondorder time price sensitivity

Gamma measures the rate of change of the delta of a derivative, $\mathrm{\Δ}$, with respect to changes in the underlying asset's price, $S$.

$\mathrm{\Γ}\=\frac{\partial}{\partial \mathrm{S}}\mathrm{Delta;}equals;\frac{{\partial}^{2}}{\partial {S}^{2}}V$


