Navigation skipped

Options Trading: Understanding Options Greeks

Dive into Options Greeks in this webinar. Learn how Delta, Gamma, Theta, Vega influence option prices.

Updated
56 min. read

David McGann (00:00:17):

Hello to all of our viewers, my name is David McGann, I'm a director here at BMO InvestorLine and I'm thrilled to be co-hosting today's webinar on Understanding Options Greeks, this comes to you as part of our webinar series that seeks to unpack Options trading. Be sure to check out our Education Hub to find other webinars in the series that may be of interest to you. And once again, today we'll be joined with our friends at OptionsPlay and I'm pleased to introduce Jessica Inskip.

(00:00:42):

Jessica is director of Education and Product at OptionsPlay, where she focuses on bridging the gap between education and complex financial products. Her work is featured in esteemed firms in exchanges, including Fidelity, Merrill, TD, and NASDAQ. She has held diverse roles in brokerage firms, including specializing in high-frequency trading, complex Options, and derivative strategies. So we're pleased to have Jessica here with us today to go through some great content on Understanding Options Greeks. And with that, Jessica, I'll hand things over to you.

Jessica Inskip (00:01:13):

Thank you so much, it's a pleasure to be here, really excited to talk about today's subject, Understanding Options Greeks. It's something that is certainly advanced territory for Options traders when we're talking about Options Greeks, however, it's something once you understand how the components of Greeks work, once you understand Options pricing and you put that puzzle together, it can be utilized in so many different ways and shapes and forms. Greeks can help us understand the impacts of that Options premium, so a lot to cover today, but a presentation that can help take your Options trading to the next level, but no, it always starts with understanding and financial literacy, so excited to dive in today.

(00:01:56):

Now, naturally before we get started, there are some disclaimers that I have to make you aware of. Options trading is complex and it's not necessarily for everyone, examples are for informational and educational purposes only. I do want to pause for a moment and just give our viewers a moment to read the screen through these disclosures and make sure that they're aware of the risks that are associated with Options, especially as we're covering the complexities and opening up our world today, utilizing the Options Greeks.

(00:02:23):

Let's talk about what we're going to discuss today. Naturally, this is the Greeks that we're going to go through, and we're specifically going to focus on delta, theta, gamma, and vega. And when we're talking about these Options altogether, we want to know what they are, how it's measured, and what it's used for. We want to bridge that understanding into practical application and know that the Greeks can certainly seem daunting, but this is designed to give you light bulb moments to understand how the Greeks work to expand your Options trading knowledge and ultimately enhance your entire process.

David McGann (00:02:59):

I'm going to jump in for a quick second if you don't mind.

Jessica Inskip (00:03:01):

Sure.

David McGann (00:03:02):

And so I love this slide because we're setting the agenda for what we're going to be getting into. And maybe for our audience, because Greeks can be complex, and so as we dive into the mechanics of each Greek to help our audience follow along even better, what should we put out there to help keep in mind what to focus on to simplify and demystify the complexity as you go through the content here?

Jessica Inskip (00:03:28):

Absolutely. What a wonderful question. Well, we want to focus on, one, understanding what the Greeks are, but then also the impacts that it has on an Options premium. So expanding on that, we'll review how an Option is priced, but we want to know the positive and negative factors that affect the Options price. And once we understand the positive and the negative, so that's what I would love our listeners to view or really focus on, is what has a good impact on my Option or potentially a negative impact on Options prices. And then we want to make sure that we amplify the positive and mitigate the negative. So that's the focus that I believe our viewers should really, really get our mind in the right spot when we're going through these complex topics. So great question, thank you.

(00:04:15):

Before we dive into the Greeks, it's important to do a little bit of a review because when we're dealing with individual Options, it's important that we know an Option is a derivative, which means it's derived from an underlying security. We add a layer of complexity, which is an expiration date, and the expiration date then drives different components of the Option, which means we need to understand not only how an Option is priced, which is derived from the underlying security and other pricing factors, which we'll dive to in a moment, but our goal with each individual Option. So this is something in our previous content that you can certainly look at to understand each individual leg, but this is the foundation in which we build the Greeks on.

(00:04:56):

If you've never seen this chart before, I always like to explain it, first and foremost, on the left-hand side we're going to have calls, and then on the right-hand side we have puts, and the intent of this T-chart, if you will, is to make you realize or wrap your head in the right way, the way that Options are comprised, everything is essentially a mirror. If you've never looked at Options before or you're understanding Options, we have to focus on long calls first because everything is a mirror, and I'll expand more on that.

(00:05:26):

We've got calls on the left-hand side, puts are on the right-hand side, and the key takeaway from all of this is when we have long Options, there is terms that we consistently put within our terminology that we like to bring out. So for example, long Options mean purchase Options, and when I purchase an Option, I own the execution rights, and since I own the execution rights, I want that Option contract to go up in value as much as possible. So when you have long in your mind, purchase execution rights, short is just the other end, when I'm short in Option, that means I sold those execution rates, which means I don't want it to go up in value, I would be obligated to fulfill the other side of that contract. And that's how we have those terminologies in our mind and then we can utilize this for our individual goals.

(00:06:11):

On the left-hand side, we've got long calls on the top quadrant, the bottom is going to be short calls, and what you'll notice, is one is containing the execution rights, the long, short is the obligation and corresponding goal associated with it. So when we have long Options, we are bullish, that's why we have bullish on the top there, we want the stock to go up in value as much as possible. We've purchased time when we have long Options, so that's something that's working against us, so these are the goals that we need to keep in mind. And then the inverse is true when we go to the other side of the equation with short calls, when we have a short call, we sold it for a premium, we receive that upfront premium and since we sold it, we potentially want to buy it back at a lower price, we purchase it back at a lower price, then that means time is working in our favor and we'll review time in a brief moment, but I have an obligation to fulfill the other side of the contract.

(00:07:01):

And then again, a mirror, if we flip it over to the put side, you'll see that everything is essentially the opposite, we've got the bullish side of puts, which is selling a put, we don't want the contract to go up in value. We do want the contract to go up in value, as in we want the underlying security to go up in value, that means the contract will not go down in value, that is why the bullish strategies are found on the top quadrant and at the bottom we have the long put. So as the security goes down, the long put collects value, as the security goes up, since the long put's not collecting value, that's why we are bullish on short puts, we don't want the contract to have any value. So it's important to keep in mind how does a contract have value and what impacts that value.

(00:07:43):

And whenever you're lost, especially on the Greeks, we build on this chart to bring you back to that moment as in, how does a contract contain value? What are the internal and external impacts? And then that helps us understand the Greeks. So today we're going to expand on that, I know that's a lot to bring upfront, but this is a review of really Options essentials one-on-one. But the key takeaways are, when I'm long in Option, I have time working against me because I've purchased it, I want the Option to go up in value as much as possible. When I'm short in Option, time is working for me, I'm not expecting a sharp directional move because I don't want the Option to have any value whatsoever. So those are the takeaways to keep in mind as we shift to the Greeks, but the prerequisite is understanding the goals associated with each individual Option leg.

(00:08:35):

Taking a step back, why would we study the Greeks? So first and foremost, and I touched on this, it's Options pricing, an Option is a layer of complexity because we've added an expiration date. So not only is the underlying security driving that Option's price, does it have value, but we also have other factors such as time and implied volatility, which we'll touch on. If we understand the impacts of those external and internal factors, that can help us understand a probabilistic approach of an Options price.

(00:09:06):

Second is strike selection, when we understand how the Option is going to move in response to these different events, then that can help us understand exactly what strike and expiration that we need to choose, and ultimately, that leads to position management. If we understand that, then that can help us define optimal entry and exit points, which is often overlooked. A lot of times when we're thinking about developing our investment thesis, we focus on our entry point, what does this stock or underlying security fit into that? But we also need to focus on our exit point because we're adding that layer of complexity, which is time. The Option contract will cease to exist at some point, we need to understand that impact and the Greeks help us understand the impacts of not only that but all other factors that affect the Options price.

(00:09:55):

With that, let's take a moment and understand Options pricing. So still a review, but we want to keep that focus of positive and negative factors. So first and foremost, I've got an example here, we've got ABC at $103 per share and we have got an ABC 100 strike 30 days until expiration call with a premium of $5. So the premium is comprised of two components, intrinsic value and extrinsic value, intrinsic value really means executable value, does this contract have any value whatsoever?

(00:10:31):

In this example, an ABC 100 strike 30 days until expiration call trading at a premium of $5, well, that represents the right to buy 100 shares of ABC at $100 per share at any time for the next 30 days. So if ABC is at $103 per share and I own the right to purchase at a $100 per share, that has to be worth at least $3 per share because I could execute upon the terms of that contract, go ahead and buy ABC at 100 and immediately sell it at the market price of 103. That contract, the strike price is more favorable than the market, which means it's in the money, has intrinsic value.

(00:11:09):

It's important to note that a Option can be out of the money or even at the money, it may not have intrinsic value, which is where it leads me to the second component of the Options premium, which is extrinsic value. An extrinsic value is comprised of two main components, so the third of the Options premium, the second of intrinsic and extrinsic, and that is time value and implied volatility. We touched on time value, time value is really the more time and Option has until expiration, the more likelihood it has to have that executable value, the more expensive it's going to be. It all comes back to what components are happening around this Option where it could have executable value, that's the time value component, is the time aspect.

(00:11:55):

And then that third component, second of extrinsic is implied volatility and a great example is binary events, which would be earnings or even macro events like the Fed and things we see often within the media. That means that there is a likelihood movement of the underlying security when there is amplified implied volatility, that's the definition of it. The market's anticipated movement of the underlying security. Now think about that for a moment, if I'm thinking about all these external factors and how it impacts the Options premium, the external factors are all focused on, will this contract have value or not?

(00:12:34):

Well, we know when earnings occur that the underlying security tends to move quite a bit, we don't know necessarily what direction, but we know that there's a date and there is an analyst consensus and then an earnings call that could even cause more movement hence the name volatility. Volatility means uncertainty, those two go hand in hand, when there is amplified uncertainty, there is increased implied volatility from the Options market, that makes the Options premium more expensive. But normally, once those binary events occur such as earnings, then implied volatility just subsides, we call that volatility crush and that's important to understand how the Options premium is comprised, which is, does it have executable value? What's that time value component? And is there any external events that would amplify or mitigate implied volatility? And then understanding that will help us understand those positive and negative factors. So extremely important to understand how an Option is priced.

(00:13:28):

I wanted to make sure for our viewers today that we covered the components of an Options price and even if you've seen it before, it's good to review it as we are going to bring this back to the Greeks. Now another view of this is events, what effects that Options premium? This is where I'm going to bring in those positive and negative factors, so we're going to say the same thing, we're just going to add positive and negative signs, take you back to math if you will. So first event, and we're looking at this versus a long call and a long put, so again, that terminology, when we hear the word long, I want you to think purchased and then call or put just tells me the right to buy or the right to sell. So a long call means I've purchased the right to buy, long put, I have purchased the right to sell, that simple.

(00:14:12):

The event if a stock moves above the strike price, well, if I've purchased the right to buy in a long call, that's going to be more valuable for the long call, positive event, it's a negative event for the long put. If the stock moves below the strike price, if I've purchased the right to buy, that's a negative event, so that's going to negatively affect my Option on the long call side. On the long put, however, that's going to positively affect it because it's moving more in my desired direction.

(00:14:39):

If we have the external factors, so see how this is comprising those internal and external factors that make up the premium intrinsic and extrinsic value. On the extrinsic value component, if we have less time until expiration, regardless if it's a call or a put because it's a purchased Option, that has a negative effect on the Options premium, it's going to decay, I purchased it, I want to be able to sell to close it at a higher price and time is something, as much as we would like, is always working against us.

(00:15:08):

And then the fourth which we touched on before is anticipated earnings event. Now this is important to wrap our head around the positive and negative because now we're bringing in some sentiment. If we've purchased a long call and we expect implied volatility to increase, so we're moving into an earnings event, then that has a positive effect because there's a more likelihood of a movement, we're not sure which direction, but a movement so that therefore makes the long call and the long put more valuable. So that is a good way to think about these events and the way that we like to frame it from positive and negative. So keep that in mind as we then really translate these events to the Greeks.

(00:15:51):

Let's talk about our first Greek, which is delta. Now delta by definition answers the question, how much does my Option premium move if the underlying moves by $1? Delta is just measuring the intrinsic value component, so does this contract have executable value or not? There's lots of terminology used here, intrinsic value and the money value, but all it means is, does it more favorable to utilize the terms of this contract versus the market? That's simply it. And what delta tells us, is if the underlying security, so the stock that this contract is derived from, if it moves by $1, how much will the Options premium move? Because there are other components, it doesn't necessarily move dollar for dollar.

(00:16:40):

For example, if SPY, which is an ETF that tracks CS and P 500, were to move up $1 and we have an SPY call with a 0.3 delta and an SPY call with a 0.6 delta, the SPY call with a 0.3 delta would move up 30 cents and the 0.6 would be 60 cents. Now it's important to know that this is all else equal, remember that Options premiums are comprised of more than just the underlying security. So just for this example only, we're assuming a snapshot in time where time doesn't move, implied volatility doesn't move, we just mean the underlying security moves by $1, that's what delta tells us, and you will see this moving quite a bit if you look at an Options chain.

(00:17:21):

How is it measured? This is important, bringing back those positive and negative factors. Delta is on a scale from negative one to positive one, the math behind that should click and there should be some logic here because if it's measuring by a dollar, we want to know, how is the Option going to move dollar for dollar with the stock. So this is literally in translated to dollars and cents, but $1 maximum. Calls have a positive skew, meaning the destination is one, so bullish strategies are going to lean towards a positive one delta and negative strategies towards a negative one delta. So what exactly does that mean?

(00:18:09):

If we have a contract that is an Options contract, speaking of a long call, right at zero, if it's a long call, as that Option moves deeper in the money, as in gets more value, the underlying security moves up, it's going to move closer to that positive one, whereas a put is going to move the other direction. And that's if you've ever heard that terminology, this Option is acting like a stock, that's what it means, but we're going to expand on that a little bit more in a moment. The takeaway from this is, the definition of delta simply means if the underlying security were to move a dollar, how would that affect my premium? And it's measured on a scale from negative one to positive one.

(00:18:51):

Expanding on that, let's bring it back to those events. If the stock were to move above my strike, the long call would be more valuable, the long put, less valuable. So what does that mean? So if we look at the measurement of delta and where it is on its scale, and remember we're moving, I like to think delta as its destination. When we're purchasing an Option, and again speaking to this in terms of long call because going back to that T chart, it really helps you wrap your mind around it, if I'm purchasing an Option, I want it to have as much value as possible because I own the rights in the case of a long call to purchase those shares at a lower price potentially in the market. And as the market goes up in value and I hold that lower price, that's better for me.

(00:19:39):

As it moves deeper in the money, it moves closer to one, and as soon as it gets to that or really close to the end of that spectrum, we call that delta magnifying, it begins to act like the stock. That's why we say a delta of one would represent being long or short 100 shares, the long or short would just be positive or negative. So if I have a long call, I'm positive delta, and if I have a long put, I'm negative delta because of where I move on the spectrum of how it's measured.

(00:20:09):

This all just helps set foundational measures on how to bring absolutely everything together. But for example purposes only, let's say I've got that long call where I have the right to purchase ABC at $100 per share and ABC is at 105, well, I've got that $5 worth of intrinsic value, executable value as ABC moves to 110, now I have $10, as it moves to one 112, now I have $12, this movement up is going to magnify the deltas and put me closer to acting like the stock. And that's also regardless of expiration, which we'll show in a couple of examples moving forward.

(00:20:51):

Let's look at that on an Options chain to really understand that. On this Options chain we're looking at Shopify, all of these are 30 days until expiration, so a 30 DTE call, and what I have here is a very deep in the money Option. So same expiration an at the money Option, and an at the money Option means that the strike price is relatively close if not equal to the market price. And then an out of the money Option means that the market price is more favorable than the strike price contains, so very far away.

(00:21:27):

What you'll notice and hopefully you see this when looking at an Options chain, and I certainly encourage this from just an understanding perspective when you're reviewing an Options chain, at the money Options tend to have a delta of 0.5, and that seems logical, we call it a coin toss because it has a probability of being in the money by 50% essentially. And logic should kick in there because if it moves by one penny, it's going to be in the money or out of the money, so it's generally around a 0.5 delta.

(00:21:56):

What you'll notice with the deep in the money delta, that's going to be magnified, so as the Shopify here, the deep in the money has a 66 strike call with Shopify around 71, that's got intrinsic value of about 530. So that means that there is a lot of value attached to that Option, there is more executable value that's there, so it has a magnified delta. The out of the money Option, so the right to buy Shopify at 77 when it's at 71, well, that means the market's more favorable because I can buy Shopify at 71 versus the contract turns of 77 that has a lower delta, it's not at its destination, if you will.

(00:22:40):

Now you'll notice on the other side of these examples, we have the intrinsic and the extrinsic value components, and there's some observations that I hope you keep in mind here. First and foremost, the deep in the money Option has the most intrinsic value as it should because it has the most executable value, it also has the least extrinsic value. So just an observation I'd like you to hold onto until we move on to the next ones, the at the money Option is going to have the highest extrinsic value, has no intrinsic value whatsoever and then the out of the money Option has a little less extrinsic value. But again, you can see the distribution here, it's just the observation I'd like you to make, but the key takeaway from this is, as an Option moves deeper in the money, these are all 30 days until expiration.

(00:23:26):

You can see how delta magnifies and it does start beginning to act like the stock, meaning that extrinsic value component dissipates regardless of expiration. And it's important observation to understand, but you need to know the other Greeks to understand actually how do we even use this and put it together. So let's talk about how it is used purely from a delta perspective. One is, we can understand our directional bias regardless of our overall portfolio or if we trade a lot of Options on a single security, Options will do what they do regardless of a name. So Options that have a positive net delta combined together are bullish, you have a bullish directional bias, and if we can mitigate or we can magnify those deltas, easy enough, right?

(00:24:18):

Bearish strategies inverse have a negative delta, put them all together, if it is bearish, it will have a negative delta. Combined can reveal altogether if your strategy is bullish or bearish, if you end up with a portfolio with a ton of long calls, even long stock, you would see that you have a very positive delta. But if you have covered calls, you'd reduce your deltas. Like this example here, we have long stock, say in your portfolio for example, you own 100 shares of SPY, that has a delta of one. If SPY moves $1, your underlying security is going to move dollar for dollar because you don't have that layer of complexity, your stock you could theoretically hold forever. Add the short call, we're creating an obligation to sell that stock at a strike price, so we're capping your unlimited gain potential of owning that underlying security, you're also reducing your deltas.

(00:25:14):

In this example, that short SPY call, you should click in your mind since it's showing a 0.3 delta in this example that that's probably farther away from the money, but I'm creating an obligation to sell. So this is telling me that I've reduced my deltas to 0.7, it doesn't move dollar for dollar, but as the underlying security moves up, together, my covered call would move 70 cents all else equal. So it's a great example of showing how we cap upwards potential in these type of strategies when we combine stock and create a covered call in this use case.

(00:25:55):

Let's talk about assessing directional risk. Options are often utilized for analysis in addition to creating a directional bias and trading off of them. Oftentimes, there is a strategy called a long straddle, and a long straddle will take a long put and a long call and understand the skew that's there. And there's this common misconception that happens with Options traders, well, they'll create a long straddle around binary events, for example, earnings once more where someone will purchase a long call and a long put that's at the money. So in this example, we've got a long SPY 100 call and a long SPY 100 put.

(00:26:39):

Assuming SPY is at $100 per share or relatively close to it, one, it's very difficult to get exactly at the money Options, which means you're going to create a directional bias of some way, shape, or form which is depicted by delta. So when we have these binary events, you're trying to understand market direction at-the-money straddle is often used, but it doesn't show true market neutrality unless we adjust the deltas. So here for example, the long call has a delta of 0.55, the long put has a delta of 0.45, since the long put is bearish, it's a negative delta, put those together. If I was looking for a true delta neutral strategy, which means I don't have a directional bias delta of zero, this actually has a slight directional bias to the upside because the long call is, in this case I can look at this and see that it might be slightly in the money. And that's one way that we can utilize this just thinking about Options from not only an analytical perspective but a trading perspective.

(00:27:46):

Delta, out of all the Options Greeks actually has the most use cases, so important to make a couple of notes here. And I hope that this perhaps clicked and there were some takeaways, one, it can give you your stock sensitivity. Back to that covered call example, we reduced our stock sensitivity because a delta of one means that my underlying security or that contract is going to move dollar for dollar with the underlying security. We're reducing our sensitivity when we structure and layer on different Options like the example of long stock capping our upward potential with a covered call. So you could see how it could help you choose your strike price and my sensitivity, where do I feel? How far do I think the stock's going to move? Do I want to benefit dollar for dollar? Am I okay capping that? So there's some examples that you can utilize the Option.

(00:28:35):

Again, just keep this in mind, because this helps you understand the other Greeks is, the Option can only get to a positive one or negative one delta. So in the case of the long call, all the way to that positive one, and then for the long put to the negative one then just keep that one in mind. And probably more commonly utilized delta is the probability of being in the money at expiration, so a higher delta means it's going to have a higher probability of being in the money at expiration. Perhaps this is because it's already in the money, so you can see that example when we were looking at the money Option that had a 0.5 delta, well, that's a 50% probability of being in the money or not, which logically makes sense because it just needs to move a penny to be in the money or out of the money. So the probabilities and the logic should coincide at this moment.

(00:29:22):

Long Options, because we want them to go up in value as much as possible, so purchased Options benefit from deltas growing, going to either end of that measurement scale. Whereas short Options don't want that to happen, we have a slight directional bias, they are neutral with a slight directional bias, so a short call is neutral to bearish, a short put is neutral to bullish, that's on an individual basis. And hopefully, that gave you a click as well because when we create a covered call, we flip our deltas positive because we've added long stock and so now we have a bullish bias. So that's really pulling everything together when utilizing delta in practical terms, if you will.

(00:30:08):

Let's bring that back to our T-chart and we'll add the Greeks. And keep in mind the reason why we build this out this way is so we can focus on, once again, you know long calls really well, you can utilize this as a tool to understand everything else. So on this chart, bullish strategies are on the top quadrant, you probably made an observation that anything that's bullish has a buy transaction associated with it. The long call is going to be the right to buy, I can execute upon them. The short put is the obligation to buy, but both of those are bullish strategies therefore have a positive delta, whereas the inverse is true on the bearish side. So we've got a short call and a long put, long benefits from a sharp directional move downwards, so therefore that has a negative delta, we want it to move closer to negative one.

(00:30:58):

Whereas a short call on an individual basis, so not including that covered call, so we're just saying individual benefits, it becomes worthless, which is the goal with the short Option, we want it to expire, that's how you realize your maximum profit potential. It benefits from the security moving downwards, moving to its directional bias, so therefore, it has a negative delta. So strategies, that we're going to utilize this in the positive, and negative sense is, what direction do I need the stock to go? Positive delta means up, negative delta, means down. Any questions here?

David McGann (00:31:32):

Well, Jessica, you went really deep on delta, which I think is phenomenal and lots of great content. You touched on this already a little bit in terms of just trying to summarize some of the key aspects to practically consider delta when it comes to Options trading. If you were to do that all in one minute, what would be the biggest way or the best way you would summarize that for our audience in terms of how to practically think about delta and use delta for Options trading?

 

Jessica Inskip (00:32:03):

Absolutely. And you're so right, delta has the most use cases out of any Options Greek, so I don't want to scare anyone who's made it this far. I spend the most time in delta because of its mass amount of uses, but in my opinion, the best use case is understanding my directional bias. So am I bullish, am I bearish? Which way do I need the stock to go in order to be profitable? That's the focus that I would have, and looking at delta on an individual basis. So delta was that intrinsic value component, now we're going to layer on an extrinsic value component.

(00:32:41):

Theta by definition tells us how much does my Option lose each day as it approaches expiration, so daily time decay is how we like to think about this. How does that mean and how is that essentially measured? Options, remember we're purchasing them and this is why we start with the goal, when we're purchasing something, we want to go up in value as much as possible. If theta is telling us that something is going down in value, that means it doesn't benefit us, so it's going to be negative for long Options regardless if it is a call or put, and it'll be positive for short Options regardless if it's a call or put. Because simply, if I sold something, I want to be able to buy it back at a lower price, purchase something I want to be able to sell it to close at a higher price.

(00:33:24):

Positive and negative factors that are there, which means theta is going to favor the seller and it hurts the buyer. So positive and negatives, external factors, things out of our control of the Options contract, but we can certainly be prepared. Now let's talk about those events, bringing it, again, same concept, just different visualization because Greeks can be daunting, so we'd like to bring this together. We have less time until expiration, that's less valuable for the long Options regardless if it's a color put, regardless if I purchased the right to buy or sell, it hurts me because it's losing value. If my premium is losing value and I purchased it, that's not going to be good for us.

(00:34:07):

However, theta in this case will increase, what does that mean? Well, theta is not linear and that means as time moves, I have more value that that Option needs to lose because an Option on the day of expiration is generally only worth its executable or in intrinsic value. That means it's generally only worth its executable or intrinsic value, it has to lose its external value. And so any external value that's there has a higher likelihood and needs to deplete as we get to expiration. So that's why theta increases, it gets bigger because there's more premium to take away as we get closer to expiration.

(00:34:51):

And again, it's not a straight line, actually, around about 14 to 21 days until expiration for at the money Options anyways, you'll see theta just completely drop off because there is some movement that has to be there. But we're going to expand on that when we look at theta on an Options chain. So again, we're going to look at Amazon here, Amazon is at 179 a share, we've got a very deep in the money Option, so the 150 Option and we have got a 180 which is our at the money and we've got a 205 which is out of the money. And again, we're looking at long calls in the terms of a long call because it's easier to understand these represent the 150 means I have the right to buy at 150, 180, right to buy at 180, 205, right to buy at 205 versus that market price of around 180, Amazon 179, in this example, in that snapshot at time.

(00:35:43):

What I hope you took away from this thinking about when we were talking about delta and the reason why we had intrinsic and extrinsic value, you'll notice that theta is the highest around at the money Options. So as you see, we've got a 0.14 theta for the at the money Option, so it's the close as we can be because Amazon's at 179.62, this one's at 180. This means that as time decays, and again these are all 30 days, it's going to lose 0.14 or 14 cents. Theta can be any value, especially Amazon I think is a lovely example, pre-split, it used to be about 2000 a share and you would even see theta around $40 because it had a lot of premium. So it literally means dollar premium that it's going to lose each day, all else equal.

(00:36:31):

And a great way to really visualize this and understand this, and this is why you have to know an Options premium, is separating it between intrinsic and extrinsic value. And hopefully, you made an observation once more, they'd vary deep in the money Option, so the right to buy at 150 when Amazon is at 179, that's about $29 worth of value there. So the mid-price there is 31.30, if that's about $29 worth of intrinsic value or 29.62 worth of intrinsic value, the excess of that mid-price is the extrinsic value, which is 168. And you'll notice that this is relatively low compared to the at the money Option, and the same occurs with the out of the money Option. So what that should visualize is that theta is centered around those at the money Options and theta is not just inclusive of the time value component, it's extrinsic value component. That's why we teach Options with intrinsic and extrinsic because it does not just mean the time value, it means premium and excess of executable value. That is what the extrinsic value means and that is the theta component.

(00:37:47):

The important observation with theta is that it's centered around at the money Options. So a very common misconception with theta, maybe because that they both began with T, is that it measures only a time value component, but it doesn't, it's the complete decay of extrinsic value because remember the Option is only going to be worth its intrinsic value at expiration. So if you'll notice with at the money Options that has the highest extrinsic value and therefore the highest theta value, which logically should make sense, the Option has more theta to decay as it gets higher to expiration or gets closer to expiration rather.

(00:38:29):

Let's talk about how theta is actually used. So first and foremost, we're going to access our extrinsic value exposure, long Options are going to have a negative theta, so that means that this decay and extrinsic value isn't good for me. Short Options are going to have a positive theta value because decay is good for me, I want to be able to buy it back at a lower price. So if we're looking at, for example purposes only, a bull call spread, a bull call spread caps our upwards potential, but it contains a positive and a negative theta example. So this is purely for analysis and understanding, if we have a long call with the one SPY, so the right to buy at 100 and then we create an obligation to sell at 110 by selling a call, one, we know that that is a bullish strategy, it's going to have a net positive delta, but this can have a positive or a negative theta because theta is centered around at the money Option.

(00:39:31):

It really depends on where my strike is to understand where this is going to be. And we need to think about our upward momentum, so you can see I can layer everything together with delta and theta, but this is an example of how it's actually used to see my extrinsic value exposure. In this case, due to the structure, the extrinsic value is higher on the long Option, you can see that it has a 0.05, it's still mitigated, but we really flattened it, we reduce our cost, which is the logic behind putting the strategy in place in the first place and that therefore reduces our extrinsic value exposure.

(00:40:07):

Here we can see that theta can be positive or negative and it really depends on our strategy selection, but the intent of strategies like this or structure is to mitigate or amplify, in this case it's mitigating my theta exposure or extrinsic value exposure because those words are synonymous. So let's put this all together and bring it to the positive and negative factors that are there, and then hopefully you got this one right away. Long Options are going to have a negative theta regardless if it's a call or put because they are purchased Options, and in purchased Options, I own executable rights, therefore I want those executable rights to have as much value as possible, hence the negative theta. Whereas short Options are going to have a positive theta because I don't want to fulfill the terms of those obligations, I have a slight directional bias, so therefore I want the underlying security to move just slightly, stay exactly where it is or move towards my directional bias so therefore they have a positive theta.

(00:41:10):

Putting that all together, we have a negative theta for purchase Options and we have a positive theta for short Options and to put it all in summation, it essentially means, if the Option extrinsic value component decays, does it benefit me or not? If it does, positive, if it does not, negative. Any questions there?

David McGann (00:41:32):

Yeah, so thank you, Jessica, for that double click into theta. So am I correct to say that theta measures the impact of extrinsic value of an Options premium and delta is the intrinsic value component? And if so, to bring it to bridge these things together, how would I use delta and theta to choose strike and expiration?

Jessica Inskip (00:41:58):

That's so wonderfully put, so I appreciate that. Delta is going to give us our directional bias, so that's going to give us an an insight rather into our strike price selection. Theta, we're looking at the extrinsic side, so now we're looking at our expiration selection, how far out do I need to go? What direction do I feel? So it really pulls our goals back in with the Options and that's why we started with your directional bias and does time work in your favor or not? So delta is going to give us our indication of our directional bias, then theta would help you answer or determine that question by when do I think the security is going to go where? And then we need to understand, do I need to perhaps go short or long? Meaning, am I positive in the time scenario or am I negative in the time scenario? So really bringing it back together, those positive and negatives help put that Options Greek puzzle together, if you will.

(00:43:00):

All right, so let's talk about Gamma. Gamma, I will say, is one of my favorite Options Greeks, and this one is a derivative of delta, but don't let that deter you, we've got some great analogies for this one. Gamma tells us all else equal, if delta were to change, what would be the new delta value? Meaning we have an underlying security move that delta tells us what the underlying security moves, gamma tells us the new delta value. This is just the domino effect, if you will, of the underlying security moving, so now we're moving back to the intrinsic value component, but we're adding another layer.

(00:43:39):

In real terms, what you would see on an Options chain, if we have gamma representing that change between delta, if the underlying security moves, if SPY, in our example, were to move up or down by a dollar and we had an SPY call with a 0.2 gamma and an SPY call with a 0.8 gamma, then that means the 0.2 gamma, so again, on the sense on that scale from one to negative one, it would move up by 20 cents if the SPY were to move up, so that means delta's new value would be increased by 20 cents. And then if it's a 0.08 gamma, then that means delta's new value would be increased by 8 cents by gamma.

(00:44:20):

Gamma just tells us new delta, think of it as domino effect, it tells us where delta is going to go. And think, again, about delta as that destination, as the security moves in our favor, delta magnifies, gamma is going to show us if that convexity is positive or negative. And so what that means, is gamma really benefits buyers because it's going to get us more to our destination and it's actually risk for sellers. Because remember when we're selling Options, regardless of what's call or put, we're neutral with a slight directional bias. So if we're expecting a sharp move, we're going to increase our convexity to delta, that could be risky because we could be unprofitable very quickly, especially as we get to expiration, but we'll expand on that and move a little further.

(00:45:14):

Let's look at the events once more. So if the stock were to move up and we have a long call, this is the same effects as delta, it's going to be more valuable. So think about in terms of delta and we're going to add on the layer of gamma, long put, less valuable, because it's not moving in my favor. Delta, it has a positive impact on the long call, if it has a positive impact on the long call, it has a positive impact on gamma because it's moving me towards my destination. Then the inverse is true, if it doesn't move in our directional bias, and these examples are just long call versus long put, again, we can use that T chart to put everything together.

(00:45:47):

And that means since it's measuring delta, it has to be on a scale from negative one to positive one. So if we have that ABC 100 strike call and ABC moves up to 110, and remember how delta on an Options chain as it got deeper into the money, it started losing its extrinsic value, that's because gamma is pushing delta higher. So that means that it's pushing us to act more like the stock, move dollar for dollar with the stock or if it doesn't move in our favor, gets to use that neutrality zone, which is zero. So a delta of zero means that I don't have a directional bias and the market altogether, so think about that with a sharp directional move. And that's why we say we expect a sharp directional move because a higher gamma subsequently in the domino effect will give you a higher delta.

(00:46:42):

And if we want to eventually end up with a magnified delta, so on a long call side, a delta of positive one or a long put a delta of negative one, that magnification helps us. That's why we say sharp directional move, and it's important to understand where gamma is on an Options chain to even put that to work, so let's pull that up. In this example we have Apple, Apple is at 168, around 169 a share, so 168.84 and we're looking at a deeper in the money Option and at the money Option and an out of the money Option. Our deeper in the money Option here is a 155m and these are all 14 days until expiration Option, so keep this in mind. Again, we've got our mid-price, so the difference between the bid and ask right in the middle and then we have the intrinsic and extrinsic value components of each subsequent Options contract within this example.

(00:47:33):

If we're looking at the at money Option, I hope you made an observation, which is the highest extrinsic value is comprised there, we already talked about that with theta. There also is a higher gamma value, gamma is also centered around at the money Options. And the logic there if you think about it, well, if it has a 50% probability of being in the money because of 0.5 delta at the money Option, it just needs to move by one penny in order to be in the money or out of the money, and if it does, then that acceleration suddenly kicks in. So I like to think of delta as a destination and then gamma is the acceleration, and that acceleration is higher with at the money Options and then it drifts away, so the curve looks like this, it's a good bell shaped curve when you go farther away, meaning I have a long call as delta on that long call is very close to one.

(00:48:25):

If that's a destination, gamma doesn't have any more work to do, gamma's job is to get to delta to one or zero at expiration. In other words, is the Option worth something or not? That's that simple. Sometimes we in finance like to add a lot of terminology and there's reasons for it, but that's all it means. Is this Option worth something or not? A delta of one, it's worth something, a delta of zero, it is worth nothing at expiration. Gamma, since at expiration we call this the gamma-theta trade-off, extrinsic value is going to completely deplete because it's only worth its intrinsic value. Gamma risk, this is where that word comes from, means an acceleration in either direction could make me very profitable or unprofitable, so that's why it is positive for those purchase Options and negative for those short Options and why we talk about gamma risk with short Options when I have my covered call. Because if I am on my max profit potential, a sharp movement could put me unprofitable really quickly because I've already experienced that theta or extrinsic value decay.

(00:49:26):

That hopefully puts a puzzle together of those Options premium components that we talk about quite often. But the observation I want you to make here is, extrinsic value is the lowest on the outside of the Options chain, the highest at the middle, and that's because that is where theta is centered, so extrinsic value, but it's also where gamma is centered. And think about that in terms of destination, if I'm purchasing a farther out of the money Option, I have a lower gamma, logically that makes sense because I have a long way to go before I get a delta of one, which is my destination.

(00:50:04):

Let's bring that again with how it's used and understand this is sensitivity. So long Options, positive gamma, short Options are going to be a negative gamma. Since this is centered around at the money Options, your gamma could be positive or negative depending on your strategy, and this really helps with strategy selection when we're moving into the world of multi-layered Options. But it's good to understand if you are just utilizing individual Options because we want to understand our acceleration, if you will. But from this example, we have a bull call spread, so purchasing the SPY 100 calls, selling the SPY 110 calls, and this type of strategy, the maximum profit potential is reached when SPY hits 110, they offset one another, we reduce our deltas and we are mitigating the extrinsic value component by selling an Option.

(00:50:56):

If we were to purchase this Option while SPY or this whole strategy while SPY is at 100, that means that SPY 100 call is going to be at the money, it's going to have the highest extrinsic value component, but it's also going to have the highest gamma because I need an acceleration to 110, that's my maximum profit potential. What will happen as the security moves up towards past my strike price to that 110 area, and this will happen with a covered call as well, same type of logic applies, gamma will actually flip negative and that should click and make some sense. So if my maximum profit potential occurs at 110, even in a covered call, this just means a capped scenario, any sharp directional movement could make me unprofitable. I can't make any more money because I created an obligation to sell at 110, there is no more while this contract exists.

(00:51:50):

And so that really helps with strike price selection in this case and understanding the magnification that I need if I'm looking for a sharp directional move, which is why we talk about the goals associated with each individual Option. So let's bring that back together with our chart and hopefully this one really clicked as well. Long Options, regardless if it's a call or put, since we expect a sharp directional move, that's what we want, positive gamma. Short Options, regardless if it's a call or put will have a negative gamma because any sharp directional move because they're neutral with a slight directional bias could equate to risk and that risk is amplified as you near expiration. So bringing that one together, do we have any questions on gamma?

David McGann (00:52:34):

Well, thank you Jessica, great job there as well. And so I'm going to do my best to try to link some of this together and then ask you how we layer gamma in. And so as I've been following along, and I think through the eyes of long Options holders, obviously the intent is for the contract to go up in value as much as possible. In other words, continue to move further in the money. And so when an Option moves deeper in the money, from what we've heard from you today, delta moves closer to one, and so since gamma measures delta's change, how would I use gamma to choose my strike price with this example in mind?

Jessica Inskip (00:53:15):

Absolutely wonderful question. And I've got a fun analogy for that one, I like to think of it as terms, like I said before, delta is our destination. So if we're purchasing Options, and we'll use that long call again because essentially it's a mirror, and our destination is one, gamma's job is to get delta to zero or one, once it's done its job, it's exited, if something changes, then it moves back into the equation. So if my destination we're on a journey with these Options, I want to know what motor do I have, what is the acceleration? That's what gamma tells us, so a very far out of the money Option has a long way to go until we get to our destination delta of one.

(00:53:54):

In the sense of an engine, you've got a bicycle, we're pedaling, we're not getting too far and it's going to take a while to get there. Whereas if you were looking at an at the money Option, since that's where gamma is centered, you have a Maserati, you've got a faster engine that will get you to where it needs to be, but once you've already reached your destination, you're back in that bicycle because you don't need to go anywhere, you're hanging out, and that's how it can end up in risk though. So as far as terms and practical use case, it's, do I have a sharp directional bias? If I do, let's make gamma work in my favor, let's get in the Maserati and go to our destination. Whereas if perhaps I was choosing a very far out of the money Option, I better have conviction and other terms for that to be profitable, otherwise, I'm not setting myself up necessarily for success depending on my strategy because I'm in terms of a bicycle of where I need to go. Hopefully, that helps make it make sense, one of my favorite analogies.

(00:54:51):

Let's move on to last, but certainly not least, is vega. Now vega answers that question, how much does volatility impact my Option? Remember, volatility goes hand in hand with uncertainty, I don't know if something's going to occur, there's a high likelihood of a movement and therefore implied volatility is amplified. Vega should not be confused with implied volatility, volatility and implied volatility are actually two different things. So vega measures the increase in an Options premium with a 1% point change in implied volatility, and implied volatility is a metrics that you can find on a lot of Options chain, and again, just tells us that likelihood movement of the underlying security, is it amplified or is it mitigated? So in terms of seeing this on an Options chain, if implied volatility were to move up by a percentage point, then an SPY call with a 0.17 vega will increase by 17 cents. Again, dollars here, this one could be any value, and an SPY call with a point in vega will increase by 10 cents.

(00:55:59):

In terms of buyers versus sellers or how we would look at this, think about an increase in implied volatility, that benefits purchased Options because it makes the Option more expensive. So all Options pricing comes down to, does it have an opportunity to have intrinsic value or not? If it does and it amplifies it, positive effect, if it mitigates it, negative effect. Since vega measures a change in implied volatility, that's going to make an increase in the Options premium, therefore it has a positive effect on buyers and a negative effect on sellers. But that measurement can help us understand exactly how it's practically used, but let's look at it an Options chain first.

(00:56:41):

Another observation here, again, we've got Apple and the same type of structure that we've utilized within these examples consistently, which is a deep in the money Option, a at the money Option, and an out of the money Option. Again, we have the intrinsic and extrinsic value components, hopefully right away you can see with all of these examples, extrinsic value is centered around at the money Options, that's because theta is higher, gamma is higher, and then you can see how it exits when we move away deep in the money and out of the money, so hopefully everything is clicking here.

(00:57:10):

In terms of vega, it is centered around at the money Options as well, and that's because of heightened implied volatility, lots of activity can occur there, but the market is certainly a function of supply and demand. And when that activity increases, volatility increases, implied volatility increases, implied volatility increases, we expect a likelihood movement because of that activity and uncertainty, that is why it's centered around at the money Option. So that's the takeaway here, is that is where it is centered and now we want to understand exactly how it is positioned.

(00:57:46):

How would we actually use that and positioning accordingly? Well, long Options are going to benefit from an exposure to an increase in implied volatility, whereas short Options not necessarily so much. And again, you can combine your strategy, you can combine your entire portfolio and understand, do I have positive or negative exposure to volatility? If there is an increase in volatility, is that good for me or is that bad for me? So you could think about how it's so important when you're trading in general, but it is elevated when we add the layer of complexity with Options because, again, it's derived not just from the underlying security, but all these external factors. So we need to keep in mind what occurs with these external factors. And if we feel that implied volatility is going to increase, well, perhaps it makes sense to have a long Option. If we feel like it's going to decrease, then perhaps a short Option, and that can help us understand and assess strategy implementation, if you will.

(00:58:48):

In this example, since the vega is centered around at the money Options, you can see where it's amplified and where it's mitigated and it could be positive or negative depending on your strategy selection. So the long call, in this case, for the same bull call spread, so SPY at 100, the buying side and the sell side at 110, the long calls driving the entire strategy, it's going to have the highest gamma, going to have the highest theta, it is also going to have the highest vega, and this is assuming we're purchasing at the money Option and then capping our upwards at 110. So purely for example purposes only, that tells me that this strategy is going to benefit from an increase in implied volatility.

(00:59:31):

Individually, a long call is going to benefit quite a bit from that, when I cap my gain potential, I'm mitigating my volatility exposure. So you can see the positive and negatives that come together when we start layering on multi-link Options, if you will, that happen later on in your journey. So bringing that all together, looking at vega, vega, hopefully this clicks as well, much like gamma is a derivative of a derivative because it tells us implied volatility movements is going to be positive for long Options and it's going to be negative for short Options, it doesn't matter if it's a color put, it just matters if I'm purchased or sold. And when we say purchased and sold in the Options world, that means net together or on an individual basis. So any questions on vega?

David McGann (01:00:17):

Thank you, Jessica. And so when we look back in all the Greeks that we've gone over so far, it seems that delta, theta and gamma, they aid in expiration and strike price selection. How would you then summarize how vega fits into the equation?

Jessica Inskip (01:00:37):

That's such a beautiful question. This is the last layer, and we worked in reverse when understanding the Greeks. So the delta and theta and gamma are going to help us understand our contracts, vega is going to help us understand our strategy. So if I have my directional bias and I know that I'm expecting a sharp directional move or I'm bullish, I probably look at a long call because those are the components and the characteristics that make up a long call.

(01:01:04):

However, if I expect a decrease in implied volatility, that may not make sense. And so a amplified volatility means higher premium, higher premium mixed with expectations will help me choose my strategy. Vega is primarily used, understanding positive and negative to decide if I'm going to sell or go long, it aids and strategy selection. And then the other Greeks help me construct that strategy with expiration and strike prices that we choose.

(01:01:36):

All right, well, that concludes the Greeks today, I hope that was certainly enlightening. The Greeks is a wonderful subject, it can be polarizing because it seems daunting, but once you understand an Options premium, how it's comprised, the Greeks just tell us the effect of all of those factors. How does it change my Options premium? And once we understand that, then we can really focus on graduating our Options trading experience and really understanding what moves in Options premium and that helps us be better Options traders all around. So thank you for spending the time today.

David McGann (01:02:12):

Thank you, Jessica, what a wonderful job. As I reflect on the slides, the content, and your delivery, I imagine our audience, we probably have a combination of some viewers that have very limited knowledge and exposure to Options Greeks, some that might be a little bit more advanced, I believe that based on what you went through, both groups would've tremendously valued a lot of what you shared today, so wonderful job.

(01:02:37):

The use of examples, of course, went a long way to help drive home some of the key points, and really the use cases for how we can use Options Greeks to help us with our trading decisions as it relates to Options and Option strategies. So really wonderful job, thank you very much and a big thank you to our viewers as well for tuning in, and we look forward to seeing you back at a future webinar where we will be going over exercise and assignments, which should be a very interesting topic as well. So thank you, Jessica, and thank you to all of our viewers.

Jessica Inskip (01:03:10):

Yeah, thank you so much.

Ready to start investing?

Start investing online with BMO InvestorLine Self-Directed.

Open an accountLearn more

Related articles

Options Trading: Single Legged Options

BMO InvestorLine Director, David McGann and Chief Strategist at OptionsPlay, Tony Zhang review single leg options trading, the fundamental building block of all options strategies.

Mastering Covered Calls in Options Trading

BMO InvestorLine Director, David McGann and Chief Strategist at OptionsPlay, Tony Zhang review the popular covered call options strategy, including what it is and how to use it.

Options Trading: What are Index Options?

Unlock the potential of index options in this introductory webinar. Minimize risk by trading on index market trends.