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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.

## Option Deltas

Delta is an option's sensitivity to changes in the underlying asset

#### Call Delta

#### Put Delta

## Option Gammas

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

#### Call Gamma

#### Put Gamma

## Option Vega

Vega is an options sensitivity to changes in volatility over the remainder of its life. Calls and puts have the same Vega.

#### Call Vega

#### Put Vega

## Option Theta

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.

#### Call Theta

#### Put Theta

## Option Rho

Rho measures an options sensitivity to changes in the risk-free rate.

#### Call Rho

#### Put Rho