Using the Greeks

The Greeks aren't just friendly people with a great Mediterranean lifestyle and millenia of history in arts and literature. In finance, the Greeks are vital tools in risk management that describe the quantities representing the market sensitivities of Exchange Traded Options (ETO) or other derivatives.

Each Greek measures how the portfolio's market value should respond to a change in some variable such as the underlying security, implied volatility, interest rates or time. All of the quantities are named after letters in the Greek alphabet (with the exception of Vega, which is named after a star and had previously been known as Kappa) and therefore they are affectionately and collectively called the greeks;

• Delta
  The delta of an instrument is the derivative of the value function with respect to the underlying price, delta measures first order (linear) sensitivity to price. Its value will increase if the underlying security increases, and it will decrease if the underlying security decreases.

• Gamma
  The Gamma is the second derivative of the value function with respect to the underlying price, gamma measures second order (quadratic) sensitivity to price (the curvature of the Delta line).

• Vega
  The Vega is the derivative of the option value with respect to the volatility of the underlying, Vega measures sensitivity to implied volatility.

• Theta
  Theta is the derivative of the option value with respect to the amount of time to expiry of the option, theta measures sensitivity to the passage of time while the other four Greeks are risk metrics. Theta is not because the passage of time in certain�it involves no risk. Theta can be compared to the accrual of interest.

• Rho
  The Rho is the derivative of the option value with respect to the risk free rate, rho measures sensitivity to the applicable interest rate.

Less commonly used:

• Lambda
  The Lambda s the percentage change in option value per change in the underlying price.

As each of the above (with the exception of the theta) represents a specific measure of risk in owning an option, a desirable property of any model of a financial market is the ability to compute the Greeks. The Greeks in the Black-Scholes model are very easy to calculate and this is one reason for the model's continued popularity in the market.

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