What are Options Greeks? See Examples


In the world of options trading, there are an important set of measurements known as options Greeks that consist primarily of delta, gammatheta, vega, and rho.

Options Greeks are the fundamental components of an option’s price. Understanding the Greeks Is critical to take advantage of opportunities in the options market.

Delta = Degree of Price Changes

Delta represents price change that an option contract has in regards to a $1.00 movement in the underlying asset.

Simply put, delta is the amount of price sensitivity a particular option contract has.

If an option has a delta of 0.30 it should theoretically move $0.30 for every $1.00 movement in the underlying asset.

For call options, delta ranges from 0.00 to 1.00. And for put options, delta ranges from -1.00 to 0.00.

The delta of an option contract can also be thought of as the amount of underlying asset that the option represents. For example, a call option with a delta of .30 represents roughly 30 shares of stock. Similarly, a put option with a delta of -0.30 represents 30 short shares of stock.

Deltas for at-the-money options, regardless of the amount of time until expiration, typically hover around 0.50 for calls and -0.50 for puts.

Another good way to think of delta is the probability that an option has of expiring in-the-money. For example, if a call option has a delta of 0.30, there is a 30% probability that the option will expire in-the-money.

Gamma = Rate of Change in Delta

Gamma represents the rate of change of an option’s delta.

In other words, gamma refers to how fast the price of an option can change.

For example, if a call option has a delta of 0.30, and the underlying increases by $1.00, the delta will no longer be 0.30. Let’s assume the delta is now 0.50.

The change in delta from 0.30 to 0.50 – 0.20 –  that is gamma.

Options that are very close to expiration will always have a high gamma, because the final outcome of an option at expiration has only two outcomes: in-the-money or out-of-the-money.

When an option expires in the money, it always has a delta of 1.00 for calls or -1.00 for puts, because 1 option contract represents 100 shares and remember, a delta of 1.00 equates to 100 shares.

Options with a high gamma are considered risky, for both buying and selling, because the value of the option is expected to change very rapidly within a short period of time. High gamma options mean the option’s delta has changed very rapidly. Since delta is, in essence, the price sensitivity of an option, options with high gamma are subjected to huge and wild changes in price.

Theta = Time Component

Theta is the time component of an option contract that is based on a one-day decrease in value as the option nears expiration.

In other words, theta is the amount of money that an option contract is going to lose every day until expiration. It is important to note that theta is always a negative value and gradually increases every day.

However, theta affects options differently. At-the-money options and out-of-the-money options will have greater theta values and lose more money than in-the-money options. This is because of the nature of options contracts. Theta is not as big of a pricing component for ITM options as it is for ATM and OTM options. ITM options are mostly comprised of intrinsic value, whereas OTM options have no intrinsic value and are comprised largely of theta. 

OTM options always have a possibility of expiring ITM and therefore having intrinsic value. This possibility is mainly reflected with the value of time premium built into the contract.

The concept is simple: on a longer time-horizon, there is more time for the underlying stock to move up or down, so there is more of a possibility of OTM options expiring ITM and therefore having value at expiration.

As expiration nears and the time-horizon shrinks, this possibility dwindles for options that have yet to make it ITM.

Vega = Sensitivity to Volatility

Vega, although it’s not even a real Greek letter, is a measure an option’s price per 1% change in implied volatility of the underlying stock.

In simpler terms, vega is the amount that an option will move based on changes in implied volatility of the underlying stock. 

Volatility is probably the most important component of an option’s price, so it is crucial for traders to be aware of vega. When implied volatility of the underlying stock increases, both puts and calls will typically increase in value as vega increases as well.

High levels of volatility are congruent with large downward moves in stocks, as fear and uncertainty tends to increase. Nevertheless, volatility increases don’t just make puts more expensive, they make calls richer as well. Subsequently, when volatility decreases, the prices of options decrease as well.

Rho = Sensitivity to Interest Rates

Rho is probably the least significant component of an option’s price in the short-term. Therefore, it’s easy to discount rho as an important option pricing variable, because it represents the expected change in an option’s price for a 1% change in the benchmark US Treasury-bill interest rate.

Rho represents the change in an option’s price according to changes in interest rates. 

Because interests rates, which are set by the Federal Reserve, don’t fluctuate that much on a short-term basis, rho is relatively unimportant for options expiring in the short-term.

For LEAP options, however, rho is a lot more important. If a LEAP option contract has several years before expiration, rising or declining interest rates can have a much more significant effect.

It is important to note that call options always have positive rho, and put options always have negative rho. As such, when interest rates increase, calls tend to increase. And when interest rates decrease, calls tend to decrease.

An Example

This is an option chain for SPY, the ETF that aims to track the S&P 500 index. Notice how gamma, theta, and vega are highest for at-the-money options, while delta essentially counts in order.

Option chain showing The Options Greeks.

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