The options greeks are a series of values that are collectively used to determine how closely an options or warrants contract will track its underlying market. The options greeks can be used in a variety of different ways, but they are usually associated with risk management. The most popular options greeks are delta, theta, vega, rho, and gamma, but depending upon the type of trade being made, some of the more obscure greeks can be very important.
First, Second, and Third Order Derivatives
The options greeks are divided into three categories based upon whether they are first, second, or third order derivatives (i.e. whether they are based upon a direct value such as price or volatility, or upon another options greek):
First Order Derivatives
- Delta (Δ)
- Theta (Θ)
- Vega (v, but not actually a greek letter)
- Rho (ρ)
Second Order Derivatives
- Gamma (Γ)
Third Order Derivatives
Using the Options Greeks
The options greeks are used either individually (e.g. using delta to choose an options contract) or collectively by options traders and by traders who use options and warrants to trade their underlying markets. The most often used options greeks are the first derivatives delta, theta, vega, and rho, and the second derivative gamma, as these are useful for the largest variety of trades. However, the remaining second derivatives, and the third derivatives can be very important depending upon the trade being made (e.g. delta and vega hedged trades, etc.).
For example, stock index or individual stock traders that use options or warrants to make their trades (which is preferable to trading the underlying stock directly), will need to use delta to choose the most efficient options or warrants contract (i.e. the contract which will most closely track the price of the underlying market). Options traders that trade options strategies such as straddles and strangles, will need to use delta, theta, vega, and possibly gamma to monitor their trades' reactions to changes in price, time, and volatility. Options traders that make exotic options trades will need to use most, if not all, of the options greeks, to make sure that they are pricing their options correctly.
Options Greeks Relationship Chart
The image shown above (view the image in full size) is a graphical chart showing the relationships between the options greeks, their underlying market, and each other. The chart is used to determine which options greeks are associated with which underlying market parameters, and with which other options greeks.
For example, if you want to know which of the first derivative options greeks tracks the relationship between the value of an options or warrants contract and the price of the underlying market, you would choose value on the vertical scale and price on the horizontal scale, and where they meet in the middle is the appropriate options greek, which in this case is delta. If you want to know which of the second derivative options greek tracks the relationship between the delta of an options or warrants contract and the passage of time, you would choose delta on the vertical scale and time on the horizontal scale, and where they meet in the middle is the appropriate options greek, which in this case is charm.