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The following show the sensitivity of European option prices to various inputs in a Black-Scholes world. The options are on an underlying priced at 25 that doesn't pay dividends, and annualized volatility is 20%. Formulas for Black-Scholes Greeks can be optained at wikipedia.
Delta is an option's sensitivity to changes in the underlying asset
Gamma is the second partial derivative of option price w.r.t. the underlying. It measures the sensitivity of delta to changes in the underlying. Gamma grows arbitrarily large as an at-the-money option approaches expiration (it grows like 1/sqrt(time to expiration) ), and puts and calls have the same gamma
Vega is an options sensitivity to changes in volatility over the remainder of its life. Calls and puts have the same Vega.
Theta measures an option's sensitivity to a decrease in time to expiration. That is, if option value decreases as expiration approaches, theta is negative.
Rho measures an options sensitivity to changes in the risk-free rate.