Understanding the option Greeks 

Delta

Delta represents the sensitivity of an option’s price to changes in the price of the underlying security. In other words, how much the option’s price will change as the security’s price changes. For purchased options, as opposed to shorted options, Delta is between 0 and 1.00 for calls and 0 and -1.00 for puts. Delta can only be calculated for a given moment in time and must be recalculated as the underlying security’s price, implied volatility and time to expiry change. To get a complete picture, option traders often study Delta in conjunction with Gamma and Theta, discussed later in this article.

Delta is sometimes used to estimate the percentage probability that an option will close in-the-money at expiry. A deep-in-the-money option has a much larger Delta, that is, a much higher probability of expiring in-the-money. The Delta of a far-out-of-the-money option will likely be small and may give you some idea of how likely it is to have value at expiry. An option with less than a 0.10 Delta can be seen as estimating less than 10% probability of being in-the-money at expiry. This option needs a strong move from the underlying stock to have value at expiry.

Time remaining until expiry will also have an effect on Delta. An in-the-money call with longer time until expiry will have a lower Delta than the same strike call with less time until expiry. It's the opposite for out-of-the-money calls; the call with a longer amount of time until expiry will have a higher Delta than the option with less time.

As expiry approaches, in-the-money call Deltas increase toward 1.00, at-the-money call Deltas remain around .50 and out-of-the-money call Deltas fall toward 0, all else being equal.

Low implied volatility stocks will tend to have higher Deltas for the in-the-money options and lower Deltas for out-of-the-money options.

It’s important to remember that Delta is constantly changing, even during the trading day. Typically, Delta won’t accurately predict the exact change in an option’s premium. However, it can be used as a general indicator and to compare one option choice with another.

Gamma

Gamma represents how much an option’s Delta will change as the value of the underlying security changes. As mentioned, the Delta value changes as the underlying security price fluctuates and Gamma helps determine the forecast magnitude of that change. In other words, will an option’s Delta value change a lot as the underlying security price fluctuates. This aspect of Delta is not evident by looking at the Delta value by itself and Gamma helps to understand how stable the Delta value is.

Gamma is a positive value for long positions and a negative value for short positions — regardless if the option is a call or a put. Gamma will be a number anywhere from 0 to 1.00.

As an example, imagine that an option's Delta is +0.40 and its Gamma is 0.10. A $1 increase in the underlying stock price would result in that option's Delta becoming +0.50. This is calculated as:

Theta

Theta represents the rate of time decay of an option. Specifically, it describes how much the value of an option changes each day as expiry approaches. An example of this is an option with a Theta of -0.50. This means this option’s value will decrease by an average of 50 cents every day until expiry if all other factors remain the same.

Remember that options will constantly lose time value until expiry, with time value erosion happening faster as expiry draws nearer. It makes sense that Theta is usually a negative number because time erosion decreases the value of the option. The value of Theta is also likely to increase faster near expiry, as time value erosion accelerates as expiry draws closer.

Vega

Vega represents an option’s sensitivity to volatility. It measures the rate of change of an option’s value relative to the security’s volatility. More specifically, it measures how much the price of an option changes based on a 1% change in the volatility of the underlying security. A decrease in Vega usually represents a decrease in the value of both call options and put options and, conversely, an increase in Vega usually represents an increase in the value of both.

There may be times when you choose an option because you believe a stock’s volatility will increase — for example, before an earnings announcement or when you anticipate an overall increase in market volatility. Looking at the option’s Vega value can help you gauge the potential opportunity of holding that particular option if your scenario plays out as you forecast.

Rho

Rho represents how sensitive the price of an option is relative to interest rates. It measures the rate of change in an option’s value based on a 1% change in the interest rate. The interest rate used in this calculation is the risk-free interest rate — typically, the annualized rate on a short-term security with a high credit rating, such as U.S. Treasury bills.

If an option has a Rho of 0.50, then the value of the option would increase or decrease by an average of 50 cents when the interest rate increases or decreases by 1%. Note that call options have positive Rho while put options have negative Rho. Rho is often less significant than the other factors we’ve discussed, since interest rates don’t usually affect option values as much as other factors. However, Rho becomes more relevant in periods where interest rates are changing or expected to change.