Understanding options Greeks

E*TRADE from Morgan Stanley


An understanding of “the Greeks” can be useful to any options trader. In a nutshell, options Greeks are statistical values that measure different types of risk, such as time, volatility, and price movement. Though you don’t necessarily need to use the Greeks in order to trade options, they can be very helpful in measuring and understanding certain risks.

What is delta and how is it used?

Delta is a useful metric to help traders measure the impact that movement in an underlying security will have on the value of their option positions. Delta is not a static number—it fluctuates due to a number of factors including the price of the underlying security, time to expiration, and volatility.

The standard definition of delta is:

Change in the option price ÷ change in the stock price

Why is delta important?

  1. Measuring expected change in option price. Delta can be used to calculate how much an option’s premium is theoretically expected to change in response to a $1 move in the underlying security. For example, a call option with a delta of 0.50 would be expected to rise in value by about $0.50 if the underlying stock or ETF rises by $1.
  2. Calculating the percentage of price risk. Delta also represents the percentage of price risk of stock ownership that is currently represented in the option. So, a call option with a delta of 0.70 has 70% of the price risk versus owning the stock outright. If an investor wanted a greater or lesser amount of price risk, they could choose an option with higher or lower deltas.
  3. Determining the probability that an option will expire in the money. Finally, delta measures the approximate probability that at expiration the option will be in-the-money by at least $0.01 or more. Therefore, a call with a delta of 0.05 only has a 5% chance at that moment in time that the stock’s price will be higher than the option’s strike price at expiration.

What is gamma and how is it used?

Gamma is another widely used metric for options trading. It is most often used by traders with large positions, but grasping how it works can help any trader gain a better understanding of how options behave.

The standard definition of gamma is:

Change in the delta ÷ change in the stock price

Why is gamma important?

Gamma measures the rate at which an option’s delta changes as the underlying security moves. The gamma of an option reflects the change in the delta in response to a $1 move in the underlying security. For example, a call option with a gamma of 0.02 and a delta of 0.50 would be expected to change to a 0.52 delta if the underlying stock or ETF rises by $1.

What is theta and how is it used?

Theta measures the impact that the passage of time will have on an option’s price

The standard definition of theta is:

Change in the option price ÷ one day change in time

Theta represents how much an option’s premium is expected to decay per day with all other market factors and variables remaining the same. For example, a call option valued at $3 with a theta of $0.05 is expected to be worth about $2.95 tomorrow.

Theta can change as the options get closer to expiration. For example, options with a significant time premium (e.g., those with strike prices closest to the current underlying security price) tend to see theta growing larger as expiration approaches. Another thing to keep in mind: Theta is exponential, not linear. That means the time decay of an option accelerates more each day as it moves closer to expiration.

Why is theta important?

Time decay is an important concept in options trading. Theta is the metric that quantifies it, so that you can estimate how quickly you might make or lose money on an option strategy as time passes. However, remember that theta (like all the Greeks) is a theoretical estimate of what is expected to occur over time. On any given day, supply and demand in the market will determine whether an option’s price rises or falls.

What is vega and how is it used?

Vega measures the impact that changes in implied volatility will have on the price of an option contract. Volatility can have a major impact on your options trade, so vega can be important for assessing the risk-reward profile of a given strategy.

The standard definition of vega is:

Change in the option price ÷ percentage-point change in implied volatility

Specifically, vega represents the expected change in an option’s price for a one percentage point change in its implied volatility. For example, if implied volatility rises from 23% to 24%, a call option with a vega of 0.14 would be expected to rise in value by $0.14.

Why is vega important?

Vega plays a critical role in determining the risk-reward potential of a potential option trade. If traders believe an option to be overvalued or undervalued, they may look at vega to decide which options and/or options strategies have the most profit potential.

What is rho and how is it used?

Rho measures an option contract’s sensitivity to interest rate changes, and is expressed as the expected change in an option’s value given a one percentage point change in interest rates.

The standard definition of rho is:

Change in the option price ÷ percentage-point change in interest rates

How is rho used? For example, a call option with a rho of 0.02 would be expected to rise in value by $0.02 if interest rates rise from 2% to 3%. Rho can be positive or negative, but has the strongest impact on longer-term options and is often considered less important than the other Greeks by traders who focus on shorter-term options.

Why is rho important?

In a low-interest rate environment, rho has a less measurable impact on option prices compared to delta, vega, gamma, and theta. Still, it is another metric that can be used to help understand how options are influenced by interest rates and may have some bearing on longer-term options positions.

Volatility: An essential factor in options trading

In options trading, volatility measures the rate and magnitude of price changes in the underlying security, such as a stock or ETF. There are generally two types of volatility, and both are mathematically expressed as a percentage of the underlying security’s price:

  • Historical volatility: The actual volatility of a financial instrument over a given time period in the past.
  • Implied volatility: The expected future volatility of a security’s price, inferred from the current option prices.

Simply put, historical volatility measures the past price movement of a stock or ETF, and implied volatility measures the expected future price movement of a stock or ETF. When historical volatility and implied volatility are compared against each other, they can offer interesting insights. If implied volatility is greater than historical volatility, this signifies that the market expects the underlying stock or ETF to fluctuate in the upcoming time period, perhaps due to an upcoming event such as an earnings announcement. Discrepancies between historical and implied volatility could be completely justified in some cases, but in other cases could be an indication that options are over- or undervalued.

How do you use volatility in options trading?

Regardless of whether market volatility is high or low, options can be used to seize opportunities or avoid losses. A few options strategies that may be beneficial when there are large, significant moves in stock prices include:

  1. Protective puts: If you already own a stock or ETF and you’re worried about volatile conditions negatively impacting the price, buying puts can help protect your investment and limit any losses (up until the put’s expiration date).
  2. Straddles and strangles: These strategies consist of buying a call and a put simultaneously, which can help you profit from movement in a stock or ETF regardless of the direction (provided that it moves at least a certain amount), or if there is an increase in implied volatility.
  3. Call spreads and put spreads: These strategies can also be used to profit from high volatility; they have lower profit potential than long straddles or strangles, but also typically have a lower cost (and thus more limited losses if the stock or ETF does not move as much as you expect).

Market volatility, whether high or low, can be used in options trading to seize opportunities.

How to use theoretical models to help assess options values

Just as equity traders use analytical tools and fundamental indicators to help them try to assess a stock’s value versus its current price, experienced traders use theoretical pricing models to assess options. These models are based on inputs such as underlying price, strike price, days until expiration, implied volatility, and other factors that often change frequently, usually many times during a single trading session.

Popular among professional traders and investors, theoretical models—such as Black-Scholes and binomial—are designed to help monitor changing risks and accurately assess the value of options positions on an ongoing basis.


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