The names 'color' and 'charm' presumably derive from the use of these terms for exotic properties of quarks in particle physics.įirst-order Greeks Delta ĭelta, Δ \Delta, measures the rate of change of the theoretical option value with respect to changes in the underlying asset's price.
Several names such as 'vega' and 'zomma' are invented, but sound similar to Greek letters. The use of Greek letter names is presumably by extension from the common finance terms alpha and beta, and the use of sigma (the standard deviation of logarithmic returns) and tau (time to expiry) in the Black–Scholes option pricing model. The remaining sensitivities in this list are common enough that they have common names, but this list is by no means exhaustive. The most common of the Greeks are the first order derivatives: delta, vega, theta and rho as well as gamma, a second-order derivative of the value function. Although rho is a primary input into the Black–Scholes model, the overall impact on the value of an option corresponding to changes in the risk-free interest rate is generally insignificant and therefore higher-order derivatives involving the risk-free interest rate are not common. For this reason, those Greeks which are particularly useful for hedging-such as delta, theta, and vega-are well-defined for measuring changes in Price, Time and Volatility. The Greeks in the Black–Scholes model are relatively easy to calculate, a desirable property of financial models, and are very useful for derivatives traders, especially those who seek to hedge their portfolios from adverse changes in market conditions. Each Greek measures the sensitivity of the value of a portfolio to a small change in a given underlying parameter, so that component risks may be treated in isolation, and the portfolio rebalanced accordingly to achieve a desired exposure see for example delta hedging.
The Greeks are vital tools in risk management. Three places in the table are not occupied, because the respective quantities have not yet been defined in the financial literature. Rho, lambda, epsilon, and vera are left out as they are not as important as the rest. Note that vanna, charm and veta appear twice, since partial cross derivatives are equal by Schwarz's theorem. First-order Greeks are in blue, second-order Greeks are in green, and third-order Greeks are in yellow. Use of the Greeks Underlyingĭefinition of Greeks as the sensitivity of an option's price and risk (in the first row) to the underlying parameter (in the first column). Collectively these have also been called the risk sensitivities, risk measures : 742 or hedge parameters. The name is used because the most common of these sensitivities are denoted by Greek letters (as are some other finance measures). In mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent.
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