Delta:
\(\Delta\) measures the sensitivity of an option price change in relation to the changes in the underlying stock price. $$ \Delta = \frac{\partial V}{\partial S} $$ , where \(V\) is the option price, and \(S\) is the underlying stock price. Call Delta range: \([0, 1]\). Put Delta range: \([-1, 0]\). The closer Delta is to +1 or -1, the more strongly that the option's premium responds to the change in the stock price.Gamma:
$$ \Gamma = \frac{\partial \Delta}{\partial S} = \frac{\partial^2 V}{\partial^2 S} $$ Gamma is the rate of change of an option’s Delta over its underlying stock price. High Gamma means a dramatic Delta change with even a small stock price change. Options have the greatest Gamma value when it is At-the-money.
Theta:
$$ \Theta = - \frac{\partial V}{\partial \tau} $$ Time decay.
Vega:
$$ \nu = \frac{\partial V}{\partial \sigma} $$ , where \(\sigma\) is the volatility of the underlying stock. Vega measures the option sensitivity to \(\sigma\).