Understanding The Greeks

Tony Zhang
May 26, 2022
12 minutes read
Understanding The Greeks


An option contract’s Greeks refers to the specific variables that, when combined, provide you with the value of expected changes in the option, which come because of changes in the underlying stock and the contract itself. In other words, the Greeks provide an insight into the possible future price movement of an options contract based on certain factors.

This article will briefly explore these Greeks to help readers understand how the Greeks can guide you in determining whether an options strategy is worth trading. Let’s get started!


Why Study the Greeks?

The Greeks can provide you with an insight into the various factors that may impact an options contract’s price. They can be beneficial to traders in developing their strategy and determining optimal strike points. Further, a strong understanding of the Greeks can also help you appropriately manage your position once you enter the contract. New traders must familiarize themselves with the Greeks before engaging in any serious options trading.


What impacts an options contract’s premium?

An options premium is the current market price of an options contract. A variety of factors can influence the price of these premiums. These factors include any price fluctuations in the price of the underlying asset, the length of time before the options contract expires, and any anticipated movements caused by catalysts such as earnings reports. To determine whether the cost of an options contract represents a good deal, traders often look to the option’s Greeks. Let’s look at those now.



The Delta is the most important of the four Greeks that we will discuss. This is because the Delta details the connection between the changes in the value of the underlying stock directly with changes in the option’s value. Although this may sound complex, it simply answers the question; if the underlying asset increases in value by X, how much does the options premium increase?

Delta values range from the following:

– Calls: 0 and 1.00 or 0 and 100.

  • Puts: 0 and -1.00 or 0 and -100.

Let’s assume that you have a $BMO $100 call option with the underlying price at $95 per share with a premium of $3.00 and a Delta of 0.30. In this example, the premium of the option would increase by $0.30 for every $1 the stock increased in value. Therefore, if the stock in our example rose to $96, the premium would increase to $3.30.


Apart from detailing the price movements of your options contract’s premium, you can also use Delta to measure the market’s expectation of the options contract expiring in the money. For example, if your options contract has a Delta of 80, this would mean that the market is pricing in an 80% chance of that contract expiring in the money. The lower the Delta, the lower the odds that the options contract will expire in the money.


How is Delta Used?

Assess traction (stock sensitivity)

  • A Delta of 1 is equivalent to being long stock (-1 to being short shares)
  • The closer an option is to-1 or +1 indicates when the option begins to act like the stock (time value is not priced in regardless of time left until expiration)

Assess Probability of In-the-money at Expiration

  • A higher Delta has a higher probability of expiring in the money at expiration
  • Long options benefit from greater Deltas
  • Short options benefit from shrinking Deltas



The Theta of an options contract refers to its time decay. Theta represents, in theory, how much an option’s premium may decay each day with all other factors remaining the same. For example, if an options contract had a Theta of 0.10, it would be expected to lose $0.10 of value every day. However, the depreciation is not linear. This means that Theta grows the closer the option gets to expiration. In other words, the time decay will accelerate. For example, if a 30-day $BMO $100 call option’s Theta is 0.10 (the call loses $0.10 per day), but Theta will increase closer to expiration. So if Theta increases by 0.01 per day for the first few days, the closer it gets to the end, each day Theta would increase by a higher increment. It is also important to note that only the extrinsic value of the option experiences time decay.



How is Theta Used?

Assess extrinsic value exposure

  • Long options have a negative Theta
  • Short options have a positive Theta
  • Combined contracts can reveal if a strategy or portfolio will benefit from Theta




In part 1 of Understanding the Greeks, we covered Delta, learning about how the connection between the changes in the value of the underlying stock can change the value of the option. We also saw how Theta relates to the time decay of an options contract. Now we will take a deep dive into the remaining Greeks of Gamma and Vega. Gamma represents the rate of change between an option’s Delta and the underlying asset’s price. The best way to understand this is in the context of an example. Let us assume that the same $BMO example detailed above maintains its Delta of 30 while having a Gamma of 0.05. When the price of that underlying security rises by $1, we know that the options premium will increase by $0.30 to $3.30.

However, what happens to the premium if the underlying stock price once again increases by $1? You simply need to add the Gamma and the Delta together to answer this. In our example, the second $1 increase in the underlying stock would increase the premium by $0.35. As a result, the new premium is $3.65. This is because a Gamma of 0.05 increases the Delta by 0.05 for every $1 move in the underlying.


How is Gamma Used?

Assess sensitivity to the underlying

  • Long options have a positive Gamma
  • Short options have a negative Gamma
  • Combined contracts can reveal if a strategy or portfolio will benefit from Gamma



Vega measures the increase or decrease in an option premium based on a 1%-point change in implied volatility. For example, if an options contract has a Vega of 0.02 and implied volatility increases by 1%, the premium of the option will be expected to rise by $0.02.

Implied volatility is a reasonably complex concept to grasp as there are several factors that could cause significant changes or spikes in the implied volatility of an options contract. These factors can include anything from political events to earnings announcements.

How is Vega Used?

Assess volatility exposure

  • Long options have a positive Vega
  • Short options have a negative Vega
  • Combined contracts can reveal if a strategy or portfolio has volatility exposure


Using OptionsPlay to Assess the Greeks

The OptionsPlay platform allows users to not only view the Greeks for each strategy, but also highlights and compares up to 3 different strategies against each other. The Strategy Explanation section provides an easy-to-understand guidance as to how the strategy can be impacted by the Greeks.


Adjust the sliders to see assess how each strategy will perform based on price targets, date targets and possible changes to implied volatility:



OptionsPlay provides the tools needed to effectively navigate the Greeks. Understanding the Greeks will aid you in analyzing whether the contract is a good value or not and can assist in the best-suited strategy depending on your directional view of the underlying.


Disclaimer: The strategies presented in this blog are for information and training purposes

only, and should not be interpreted as recommendations to buy or sell any security. As always, you should ensure that you are comfortable with the proposed scenarios and ready to assume all the risks before implementing an option strategy.

Copyright © 2022 Bourse de Montréal Inc. All rights reserved. Do not copy, distribute, sell or modify this document without Bourse de Montréal Inc.’s prior written consent. This information is provided for information purposes only. The views, opinions and advice provided in this article reflect those of the individual author. Neither TMX Group Limited nor any of its affiliated companies guarantees the completeness of the information contained in this publication, and we are not responsible for any errors or omissions in or your use of, or reliance on, the information. This publication is not intended to provide legal, accounting, tax, investment, financial, or other advice and should not be relied upon for such advice. The information provided is not an invitation to purchase securities listed on Montreal Exchange, Toronto Stock Exchange, and/or TSX Venture Exchange. TMX Group and its affiliated companies do not endorse or recommend any securities referenced in this publication. Montréal Exchange and MX are the trademarks of Bourse de Montréal Inc. TMX, the TMX design, The Future is Yours to See., and Voir le futur. Réaliser l’avenir. are the trademarks of TSX Inc. and are used under license.  All other trademarks used herein are the property of their respective owners.

Tony Zhang
Tony Zhang http://tmx.optionsplay.com

Head of Product Strategy for OptionsPlay


Tony Zhang is a specialist in the financial services industry with over a decade of experience spanning product development, research and market strategist roles across equities, foreign exchange and derivatives. As the current Head of Product Strategy for OptionsPlay, Tony leads the research and development of their OptionsPlay Ideas & Portfolio platform. He has leveraged his interest in financial technology and product development to provide innovative, reimagined solutions to clients and the users they seek to serve. Previously he spent 7 years at FOREX.com with a capital markets and research background as a market strategist specializing in equity and FX derivatives markets.

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