In mathematical finance, the quantities that represent the sensitivities 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 are referred to as the Greeks. This name is given to them due to the reason that most common of these sensitivities are usually denoted by Greek letters. Collectively these sensitivities have also been referred to as the risk sensitivities, risk measures or hedge parameters.
Use of the Greeks
There are more common sensitivities to the four primary inputs into the Black-Scholes model (spot price of the underlying security, time remaining until option expiration, volatility and the rate of return of a risk-free investment) and to the option’s value, such as delta, gamma, vega and vomma. Greeks which are a first-order derivative are indicated as blue, second-order derivatives are in green, and third-order derivatives are indicated by yellow color. Here you have to note that vanna is used, intentionally, in two places due to the reason that these two sensitivities are mathematically equivalent.
In risk management the Greeks are vital tools. The sensitivity of the value is measured by each Greek to a small change in a given underlying parameter, it is done so that component risks may be treated in isolation, and the portfolio could be rebalanced accordingly to achieve a desired exposure.
