# What are Options Greeks?

March 27, 2023

Option greeks are a set of statistical measures used to determine the sensitivity of the price of an option to various factors such as the underlying asset price, volatility, and time to expiration. The main option greeks are delta, gamma, theta, vega, and rho.

There exist certain variables which help to assess the risk in the options market. These are better known as Greeks – so named because each is denoted by a Greek symbol. Option Greeks measure the sensitivity of the price of an option to its underlying asset. They are generally used to conduct a sensitivity analysis of a portfolio of options. Its importance lies in the fact that investors use these measures to make informed decisions for trading options.

#### The Need for Options Greeks

Traders find Greeks to be valuable tools as they help to assess the risk that is associated with different options. It is used to make new decisions regarding investments and to analyse the risk that exists in the portfolio that they are holding.

While Greeks use complicated mathematical formulae, they can also be obtained via a computerised solution. Brokers or brokerage firms may also be approached to run these formulae for you.

What needs to be remembered is that Greeks help to assess future prices, but there is no guarantee that they will be accurate every single time. They help remove some of the guesswork from options trading, but the final choice lies with the investor.

#### Types of Options Greeks

‍Types of options Greeks

Before analysing the various Greeks, which are classified into main and minor Greeks, below are some of the definitions that need to be known:

• Strike price – It is the price at which options can be converted into shares of the underlying asset
• Expiration date – The date which is an option’s end date
• Premium – It is the cost of value that is associated with an option. Its value is usually based on the pricing model, which, in turn, leads to price fluctuations.

#### Main Greeks

##### Delta

Delta (Δ) measures how sensitive an option’s price changes are as compared to the price changes of the underlying asset. In other words, if the underlying asset’s price goes up, the option’s price would also change by a certain amount.

Delta = ∂V/AS

Where:

∂ = first derivative

S = price of the underlying asset

V = price of the option

The value is generally a number which is in decimals and ranges from -1 to +1. Call options have a value between 0 to +1, and put options show a value of -1 to 0.

When finding out the delta of the entire portfolio of the options, it is taken to the weighted average of the deltas of all the options taken together. This is called a hedge ratio.

While calculating Delta values, it is good to remember that:

• The closer the option is to expiration for near or at-the-money, the value will rise.
• Delta values need to be evaluated using Gamma.
• Implied volatility changes can alter the Delta value.

Delta is usually used:

• When trying to find out how probable it is for a given option to be in-the-money at expiration. The assumption that is made here is that a log-normal distribution is followed by the prices.
• An investor can use Delta to measure a given option/option strategy’s directional risk. For example, a higher Delta value will be appropriate for a strategy that has higher-risk-higher-reward.
• To find out the directional risk – a positive delta is a long market assumption, and a negative delta is a short market assumption.
• When Delta is positive, it makes sense to buy a call option, as a positive value implies that the price will go up together with the price of the underlying asset.
##### Gamma

Gamma (Γ) is a measure of the relative change of the Delta’s in comparison to the change in the underlying asset’s price. This means that if the asset’s price changes, so would the delta, and this is measured by Gamma. So, Gamma measures Delta’s rate of change over a given period of time.

Gamma is the maximum when it is at the money. However, it is when an option is deep-in-the-money or out-the-money.

Gamma is used to assess an option’s Delta. Usually, a positive delta is shown by long options. For instance, if we take two options with the same Delta value, then it is good to find what their Gamma values are. The one which has the higher Gamma value will be the one that shows more volatile swings. Hence, this option will have a higher risk since there will be a greater impact on the underlying asset of this option in case of an unfavourable move. Gamma can, thus, be thought of as a measure which helps the investor to know how stable an option is. If Delta shows how probable it is for an option to be in-the-money at expiration, the Gamma represents how stable this probability will be over time.

##### Vega

Vega (ν) measures the sensitivity of the price of an option price as compared to the asset’s volatility. For example, if the asset’s volatility increases by one per cent, the price of the option will change. The amount that is changed by is the Vega amount. So, while Delta is a measure of the actual changes in price, Vega measures  how the expectations for future volatility changes.

Vega is expressed as money amount over the decimal number.

When vega increases, it means that the value of the option has increased. This is because, when volatility is higher, there is more chance of hitting the strike price at some point. This makes the options more expensive. When there is a rise in volatility, options buyers stand to benefit. This is why long options have a positive Vega value while short options have a negative value.

While calculating Vega values, it is good to remember that:

• It can increase/decrease even when there is no price change. This happens because the implied volatility changes.
• When there are reactions due to quick moves in the underlying asset then the Vega value can change.
• When options come near to their expiration the value of the Vega decreases.

##### Theta

With time, the probability of an option’s being profitable or being in-the-money falls. Theta (Θ) , also sometimes called time decay, measures how sensitive the price of an option is when compared to the time to maturity of the option. For example, if the time to maturity of an option falls by a day, the price of the option will change. The amount by which it changes is the Theta amount.

It is to be remembered that:

• Usually, the value of Theta, for long options, is in the negative. It depicts the greatest negative value when the option is at-the-money.
• Theta tends to accelerate as an option’s expiration date approaches. This is because there is less time available to make money from an option.

Theta is a useful measure. For example, using the Theta value buyers must decide whether it is worthwhile to exercise an options before its time runs out.

Over the long term, its value appears to be smooth and linear. However, as the expiration date for at-the-money options the slopes become steeper. The extrinsic value (that is, an option’s market price of an option and its intrinsic value or an asset’s worth) is very low near expiration for n- and out-of-the-money options. This is because the chance of the price reaching the strike price is low and thus, chances of profit is low. On the other hand, at-the-money options have the chance to reach these profits thereby earning a profit.

While calculating Theta values, it is good to remember that:

• If there is a lot of implied volatility for out-of-the-money options then the value of Theta will be high.
• At-the-money options have the highest Theta value because these take the least time to earn profits when the price moves in the underlying.
• As expiration nears, the time decay will go up, thus pushing up the Theta value. Due to this, especially if the volatility goes down during this time, the long option holder’s position can get undermined.
##### Rho

Rho (p) is a measure of how sensitive the price of the option is when compared to the increased rates. For example, if a benchmark interest rate rises by one per cent, then the price of the option will change. The amount by which it changes is the Rho amount. Thus, it ​​is a measure of sensitivity to interest rates.

Interest rates affect the cost of carrying the position over time. Hence, there is the possibility that interest rates will have an impact on an option’s value. The cost of capital should also be considered as it is applicable over time wherein longer term options  will be affected more.

Of all the Greeks, the Rho is usually regarded to be the least significant because the process of options are, in general, not as sensitive to changes in the interest rate as it is to other factors.

Usually, it is a positive Rho for call options and negative for put options. This is where its greatest use lies. When Rho is positive, calls are purchased as call premiums rise with higher interest rates.

#### Minor Greeks

##### Lambda

Lamda, also sometimes known as leverage factor or effective gearing, measures the amount of leverage that an option will provide when the underlying asset’s price changes by one per cent.

Lamda is represented as:

λ= (∂C/C)/(∂S/S)

Where:

∂ = first derivative

S = price of the underlying asset

C = price of option

It forms a part of the Minor Greeks because what it reveals can also be found out by using a combination of the other Greeks – when simplified, the calculation of Lamda can be represented as the product of Delta and the ratio of the price of the stock price divided by the price of the option.

However, its use lies in the fact that it tells an investor how much leverage he is employing while trading with his options portfolio.

It is good to note, here, that even though sometimes Lamda and Vega have been equated, they are not one and the same – their formulae are different. The confusion arises because Vega measures the influence of volatility on the option’s price, which is captured by Delta values, thus making Lamda and Vega pointing to the same/similar outcome when an option’s price changes.

##### Vomma

Vomma measures the rate at which an option’s Vega will react to the volatility in the market. It is a second-order derivative that measures the Vega’s convexity.

When the value of the Vomma is positive it means that when the volatility rises by one per cent, it will cause the option’s value to increase.

Together with the Vega, the Vomma is also used to understand how profitable a particular option trading will be. Together they provide information about the price of the option and option price’s sensitivity to market changes. Usually, investors who hold long options look for a high, positive Vomma value.

##### Zomma

Zomma, also called D-gamma, is not an easy concept to understand. It measures the degree to which the Gamma of an options is sensitive to changes in implied volatility. The higher the value of it, the larger the change in Gamma.

Zomma is a third-order derivative because it measures the change in Gamma, which, in turn, measures the change in Delta. Delta, in turn, is a measure of the sensitivity of change between the underlying asset and the derivative product.

Taking an example, if Zomma = 1.00, then a one per cent rise in volatility will increase Gamma by one unit. This will lead to an increase in the Delta. Thus the higher the Zomma, it will mean that small changes in volatility will lead the directional risk to change hugely.

Other than these, some other Minor Greeks that investors consider are:

• Epsilon – It is a measure of how sensitive an option’s value is when there is a change in the underlying stock’s dividend yield
• Vera – It is a measure of how sensitive Rho is to volatility
• Speed – It is a measure of how the underlying stock’s price changes affect the value of Gamma.
• Colour – It is a measure of how the passage of time affects the value of Gamma.
• Ultima – It is a measure of how changes in volatility affect the value of Vomma.

To Summarise,

Greeks are mathematical calculations encompassing many variables, which are used by investors to make more informed choices about options trading. Since these numbers can change over time, experienced traders usually calculate them daily to rebalance their portfolios. Even if they don’t look simple initially, their benefit is considerable and should be used by all who are in the options trading playing field.

Greeks are variables that help assess risk in the options market and measure the sensitivity of the price of an option to its underlying asset.

Greeks are used to make informed decisions for trading options and to analyze the risk that exists in the portfolio.

Greeks are classified into main and minor Greeks, with Delta, Gamma, and Vega being the main Greeks.

Delta measures how sensitive an option’s price changes are as compared to the price changes of the underlying asset.

Gamma is a measure of the relative change of the Delta’s in comparison to the change in the underlying asset’s price.

Vega measures the sensitivity of the price of an option price as compared to the asset’s volatility.

Greeks help remove some of the guesswork from options trading, but the final choice lies with the investor.

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