The Greeks are primarily indicators of risks taken by those involved in the buying and selling of options. They detail the risks by origin: the price of the underlying, implied volatility, time and interest rates. They will therefore help manage each of these settings, whether in trading, or the level of services in risk control structures where they exist.
The Greeks are essential tools in the field of risk management, they take into consideration the reactivity of the value of a portfolio to minor variations in a particular underlying parameter, such that component risks are exclusively dealt with. Thereby, allowing the restructuring of the portfolio to accomplish an intended exposure.
The Greeks in the Black-Scholes model are significantly simple to compute, and are valuable for derivatives traders, particularly in relation to the hedging of portfolios. Particularly the Greeks that are helpful for hedging delta, gamma and vega are substantially outlined for evaluating variations in time, volatility and price.
‘Rho’ represents the derivative of the option value in reference to the risk free rate. Even though, rho constitutes a primary input into the Black-Scholes model, its effect on the value of an option in line with variations of the risk-free interest rate, is actually trivial which translates to low popularity of the higher-order derivatives.
In principle, the value of an option is has the lowest reactivity to alterations in the risk-free-interest rates, making rho the least prominent of all first-order Greeks.
Gamma represents the convexity of the price of an option depending on the course of the underlying. It indicates whether the option price tends to move faster or slower than the price of the underlying. By analogy, it is possible to compare the speed of the delta and gamma acceleration.
Another reading is the meaning of gamma delta evolution based on the price of the underlying. A positive gamma indicates that prices of the underlying and delta change in the same direction, while a negative gamma indicates otherwise.
A buyer of a put or call is long gamma, or gamma portfolio will be positive, and that a seller will be short, gamma-gamma or negative. All things being equal, the gamma is highest when the option is the currency (ie when the delta is equal to 0.5).
A portfolio consisting of long positions and short options with different exercise prices (on the same underlying) will therefore see the value of the gamma change, even change sign, depending on variations in the price of the underlying. Ideally, the gamma of a portfolio of options is the sum of the gamma of each option within it, gamma is a decreasing function of maturity.