1. Options Greeks: Introduction
  2. Options Greeks: Options and Risk Parameters
  3. Options Greeks: Delta Risk and Reward
  4. Options Greeks: Vega Risk and Reward
  5. Options Greeks: Theta Risk and Reward
  6. Options Greeks: Gamma Risk and Reward
  7. Options Greeks: Position Greeks
  8. Options Greeks: Inter-Greeks Behavior
  9. Options Greeks: Conclusion

The best way to start learning anything new is to skim to table of contents and get a basic idea of what’s going to be involved before diving in on a deeper level. This way, you know what to expect and already have a basic understanding of how all of the pieces fit together.

In this section, we will take a high-level look at the five essential Greeks and a sixth that’s used by more advanced traders before diving deeper into each of the Greeks, how they work together, and other important considerations later in the tutorial.

Delta: Changes in Underlying Asset Prices

Delta values measure the risk from a move in the price of an underlying asset. Call options have a Delta that ranges between 0 and 1.0 (with 1.0 being the equivalent of long position in the underlying asset) and put options have a Delta that ranges between -1.0 and 0 (with -1.0 being the equivalent of a short position in the underlying asset).

For example, if you buy an at-the-money call or put option, it will have a Delta of about 0.5, which means that if the underlying stock price moves 1 point, the option price will change by 0.5 points, assuming that everything else remains the same. If the price of the asset increases, the call option would increase by 0.5 points and the put option would decrease by 0.5 points.

Vega: Changes in Implied Volatility

Vega measures the risk of changes in implied volatility – or the forward-looking expected volatility of the underlying asset price. While Delta measures actual price changes, Vega is focused on changes in expectations for future volatility. Higher volatility makes options more expensive since there’s a greater likelihood of hitting the strike price at some point.

For example, a put that is purchased is long volatility with a positive Vega since it increases when the price falls and decreases when the price rises. A naked put is short volatility with a negative Vega since it loses value if the volatility increases over time. A combination of options could produce a position Vega that could be negative or positive.

Theta: Changes in Time Decay

Theta measures the rate of time premium decay and it’s always negative for a single option since time moves in the same direction. As soon as an option is purchased by a trader, the clock starts ticking and the value of the option immediately begins to diminish until it expires worthless at the predefined expiration date.

For example, a call option with a price of $1.00 and a Theta of -0.05 will experience a price drop of $0.05 the next day, assuming everything else is equal. The Theta value tends to become increasingly negative for long option positions as the expiration date nears since there’s a greater rate of decay in the time remaining.

Gamma: Changes in Delta

Gamma measures the rate of changes in Delta over time. Since Delta values are constantly changing with the underlying asset’s price, Gamma is used to measure the rate of change and provide traders with an idea of what to expect in the future. Gamma values are highest for at-the-money options and smallest for those deep in- or out-of-the-money.

While Delta changes based on the underlying asset price, Gamma is a constant that represents the rate of change of Delta. This makes Gamma useful for determining the stability of the Delta, which can be used to determine the likelihood of an option reaching the strike price at expiration.

Rho: Changes in Interest Rates

Rho measures the impact of changes in interest rates on an option’s price. Since interest rates don’t change very frequently, we will not cover it in this tutorial, but they are frequently used in assessing arbitrage opportunities and with long-term options (e.g. long-term equity anticipation securities – or LEAPS) that may be influenced by interest rates over time.

For example, an arbitrage trader may pay more for call options and less for put options when interest rates rise because they can hedge the positions and earn interest on any free capital at the risk-free rate. A LEAPS investor may also pay attention to Rho when determining the impact of rising or falling interest rates over the years.

Using Greeks in Practice

You can use these Greeks to help determine potential changes in option valuations.

Position Greeks

If Positive Value (+)

If Negative Value (-)


Long the Underlying

Short the Underlying


Long Volatility

Short Volatility


Gains from Time Decay

Loses from Time Decay


Net Long Puts/Calls

Net Short Puts/Calls


Calls Increase with Interest Rates

Puts Decrease with Interest Rates

When looking at an option position (multiple options), a strategy can have a positive or negative value. The table above shows the essential characteristics of the Greeks in terms of potential changes in option valuations. For instance, a long Vega position will experience gains from a rise in volatility and a short Delta position will benefit from a decline in the underlying asset, assuming that everything else remains the same.

Looking Ahead

In the next section, we will look at Delta in greater detail and how it can be used to analyze options and option strategies.

Options Greeks: Delta Risk and Reward
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