Greeks (finance) - Use of The Greeks

Use of The Greeks

Spot
Price (S)
Volatility
Time to
Expiry
Value (V) Delta Vega Theta
Delta Gamma Vanna Charm
Vega Vanna Vomma DvegaDtime
Gamma Speed Zomma Color
Vomma Ultima Totto
Definition of Greeks as the sensitivity of an option's price and risk (in the first column) to the underlying parameter (in the first row). First-order Greeks are in blue, second-order Greeks are in green, and third-order Greeks are in yellow. Note that vanna appears twice as it should, and rho is left out as it is not as important as the rest.

The Greeks are vital tools in risk management. 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 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. For this reason, those Greeks which are particularly useful for hedging delta, theta, and vega are well-defined for measuring changes in Price, Time and Volatility. 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.

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. The remaining sensitivities in this list are common enough that they have common names, but this list is by no means exhaustive.

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