Introduction to the Greeks
Last time I wrote about Delta, which is probably the best known of the Greeks. Wikipedia has a pretty good definition of these:
“The Greeks measure the sensitivity to change of the option price under a slight change of a single parameter while holding the other parameters fixed. Formally, they are partial derivatives of the option price with respect to the independent variables.”
In other words, each one of the Greeks tells us how much an option price should change when a specific thing happens.
The mathematical option pricing models, including Black Scholes and all the rest that have come after, assume that there are only four of these “independent variables” for any individual option, which has a given strike price and expiration date:
Underlying asset price
Time to expiration
Volatility
Interest rates
Each one of the Greeks tells us how much an option’s price should change when there is a small change in one of these four variables.
Here’s a quick rundown:
Delta: Sensitivity of option price to changes in underlying price. Shows expected option price change, in dollars per share, for the next one-point change in the underlying price.
Gamma: Rate of change of Delta with respect to underlying price change. Shows expected change in Delta, in percentage points, for the next one-point change in the underlying price. As you can see, both Gamma and Delta show aspects of the option price’s response to changes in the underlying’s price.
Theta: Sensitivity of option price to the passage of time. Shows expected option price change, in dollars per share, for the next one-day period of time.
Vega: Sensitivity of option price to changes in implied volatility. Shows expected option price change, in dollars per share, for the next one-percentage-point change in implied volatility.
(Interesting tidbit, or not:) Vega is not the name of any Greek letter. However, the glyph used is the Greek letter nu. Presumably the name vega was adopted because the Greek letter nu looks like the letter V, and vega was derived from vee by analogy with how beta, eta, and theta are pronounced in English.
