greeks

The greek letters used most commonly in finance are probably alpha and beta from the single-index model. However, the term 'greeks' colloquially refers to a different set of quantities, consisting of various derivatives (in the calculus sense) of the value of a financial contract (aka a financial 'derivative', not to be confused with the calculus concept).

The greeks measure the sensitivity of the value of an option or other financial derivative to changes in underlying parameters. There are names for second- and third-order partial derivatives, but the most important are the first-order derivatives:

• Delta is the derivative of an option's value (or the value of a portfolio of options) with respect to the underlying asset price ($\Delta = \partial V / \partial S$). It is close to 1 for deep-in-the-money options and close to 0 for far-out-of-the-money options. It is not actually equivalent to the probability that the option finishes in the money (this is the 'dual delta', which can be backed out as the derivative of option price wrt strike price), but it's sometimes used as a proxy for this.
  • Relatedly, $\lambda = \Omega = \partial V / \partial S \cdot S / V = \Delta \cdot S / V$ measures the percentage change in an option's value as a function of the percentage change in the underlying.
• Vega is the derivative of value with respect to (V)olatility of the underlying asset: $\nu = \partial V / \partial \tau$. This is always positive for options. Note that vega is a totally made-up Greek letter, which is wild. In practice it's often represented by $\nu$, which looks like a 'v'.
• Theta is the derivative of value with respect to (T)ime: $\Theta = \partial V / \partial \tau$, where the timestep $\partial \tau$ is conventionally measured in units of days. It is almost always negative for options.