Tools that measure how an option‘s price and risk are affected by the underlying parameter on which the value of the option depends. The most popular of these sensitivities are often symbolized by Greek letters, and hence the name the greeks. Each greek measures the sensitivity of an option or a portfolio of options to a small change in a specific underlying parameter, such as the price or volatility of an underlying asset, interest rates, etc. The most common greeks are the first-order greeks such as delta, vega, theta, lambda, and rho. Higher-order greeks encompass second-order and third-order greeks. Second-order greeks, which are based on the notion of stochastic volatility, include: vanna, vomma, and volga, vera, charm (delta decay), and gamma.

There are still yet higher order greeks, or third-order greeks, among which are: color (gamma decay), speed, ultima, and zomma. If the value of an option depends on two or more underlyings, as is the case with multi-asset options or rainbow options, its greeks are extended to account for any cross-effects between the underlyings. Examples of “cross greeks” include: cross gamma, cross vanna, cross volga, and correlation delta.

Investors and traders use option sensitivities to capture the risks of financial options/ derivatives.