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No Math, No Problem: Learning Options Greeks through Metaphors

Episode 139

No Math, No Problem: Learning Options Greeks through Metaphors

Posted February 23, 2024
Mathew Cashman
Interactive Brokers

Mat Cashman, Principal of Investor Education at the OCC, Joins IBKR’s Jeff Praissman to explain the option Greeks without math. It’s an easy and clear way of thinking about the Greeks for even the most math averse person.

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Summary – IBKR Podcasts Ep. 139

The following is a summary of a live audio recording and may contain errors in spelling or grammar. Although IBKR has edited for clarity no material changes have been made.

Jeff Praissman 

Hi everyone. Welcome to IBKR podcast. I’m your host, Jeff Praissman, and it’s my pleasure to welcome back to the IBKR podcast studio, Mat Cashman, Principal of Investor Education at the Option Clearing Corporation, or OCC. Mat, welcome back. It’s always great to have you in the studio. 

Mat Cashman 

Thanks, Jeff. It’s great to be here. I always love being on these podcasts. 

Jeff Praissman 

You just finished up the great webinar on ‘Mathless Greeks”. And I just want to take this opportunity to dive a little bit further into the subject. I kind of wanted to start high level overview, how did you come up with this concept of this ‘Mathless Greeks? 

Mat Cashman 

Yeah, I think it’s a good question. The kind of dance that we always do as educators is that we’re talking about pretty high-level concepts like Greeks and all of the math that’s behind the contracts that we trade as far as options are concerned. And I was having a conversation with the Executive Director of the Investor Education Department at OCC. His name is Ed Modla. He suggested to me one time that we talk about trying to teach these concepts of Greeks without using the math.  

He basically said like, have you ever thought about trying to do it this way? And to be honest with you, at first I kind of brushed it off a little bit and then I started to dig into it a little bit more. And I realized that it might be a pathway that doesn’t currently exist for some people that aren’t necessarily particularly math minded people to be able to understand these concepts without all of the overt math in front of them. 

Jeff Praissman 

Yeah, I think even before we go into these ‘Mathless Greeks’, we probably should just start for our listeners and obviously for the ones that aren’t super familiar with options, maybe just defining the Greeks.  

So just concentrate on the big three of Delta, Gamma and Theta. And if you don’t mind kind of walking through our listeners the textbook definition of each. And also their importance in options trading just so we can give everyone a good firm background on what we’re about to talk about. 

Mat Cashman 

Absolutely. Yeah. It’s always good to start with that kind of basis of understanding. So what we’re going to cover today are Delta, Gamma and Theta, which are really the top three Greeks that most people have on their risk radar at any one point in time.  

If you were to take a step back and just talk about Greeks more generally, the thing that I like to think about that Greeks do for option positions is they’re kind of like a dashboard in your car in some ways, right?  

And that’s kind of where some of this idea came from. In the same way that the dashboard of your car tells you kind tells you how the car is running and what the status of all of the things in your car are without having to actually open up the hood and look inside the engine while it’s running.  

It’s a really good way for you to be able to actually tell how the car is running without getting out and opening the hood. Well, the Greeks are kind of like that but for options. They give you a really good metric. A really good way to evaluate the risk of your position and be able to tell what’s going on beneath the hood of the actual options position without having to necessarily fully dig into each single option that you have on. This becomes especially pertinent when you have either larger positions or more complex positions where you have both long and short options, or you have different durations of options because the Greeks can give you a more holistic idea of how the actual risk is playing out for your entire options position, without having to dig into each individual line of your position itself. 

Jeff Praissman 

Let’s start with Delta. Textbook Delta is really the sensitivity of an options price to change in an underlying asset price. So if something is like a 20 Delta, for every $0.20 the stock moves, that option is going to change. It also kind of represents the possibility that the stock will finish on that strike and the money. As far as option Delta as a metaphor, what would you tell our listeners? How would you explain Delta to them? 

Mat Cashman 

Absolutely. So I think it’s really important to start with exactly what you said, which is that the technical definition of Delta is an option value sensitivity to underlying movement. So if you think about that, what you’re really trying to evaluate here is if the underlying moves a certain amount, how much is my option going to theoretically move, as far as my model is concerned? Well, when I started to think about this, I started to think about what’s a good metaphor for this especially? And it lends itself well to thinking about it in kind of an automotive sense, just like that dashboard that I just talked about more broadly. For all of the Greeks, Delta really kind of lines up well with the speedometer of your car. It’s kind of like looking at the speedometer of your car. When you’re in your car and you’re driving, you don’t need to stick your head out the window to know whether you’re going 40 MPH or you’re going 20 MPH. The speedometer is right there telling you how fast you are going. 

Well think about this. Delta is kind of like that for your option position. It’s going to tell you how much theoretically your option is going to move for every $1.00 move in the underlying stock. And so it’s a little bit like evaluating how fast your option position is going, right? It’s like the speedometer for your option position in a way. That’s how I think about, as far as metaphor is concerned, how I think about Delta. 

Jeff Praissman 

Let’s talk about Gamma then, right? So, Gamma is really the rate of change of delta. Well, Delta is the rate of change of the stock and Gamma is the rate of change of Delta. So obviously we could sit here and talk about the mathematical formulas that come into it. But I think our listeners are definitely more interested in kind of, obviously this is Mathless Greeks. So what is the metaphor to help explain Gamma to our listeners? 

Mat Cashman 

Yeah, absolutely. I think it’s really important to talk about. So while we’re talking about Delta, previously, Delta is one of those things that can change over time as well, right? Like Delta is not a static thing. It can move as the underlying moves. And so just like the speed in your car can move like you’re speeding up or slowing down, your Delta can move. But when you think about how much your delta is moving, you need to bring in the concept that gives you an idea of a metric that might be able to measure that. And that’s Gamma. 

Gamma tells you how much your actual Delta is going to move per. $1.00 move in the underlying. So it’s the actual second derivative that we’re talking about here. It’s like, how much does the option move when you’re talking about Delta and then Gamma tells you, well, how much does the Delta move with that same $1.00 move. So, the way that I think about it, when I try to zoom out and think about it from a metaphorical standpoint, especially if you keep that automotive kind of theme going through here, is that Gamma is the potential change in the options’ Delta. So it measures how quickly that Delta can change. So I want you to think about it in terms of what kind of car you’re driving, right?  

The race car, the F1 car that you see at the F1 race in Dubai or wherever it is has an incredible ability to change direction and to accelerate and decelerate. Both of those things and laterally move, right? It has the incredible ability to do that very quickly. Very, very quickly. Whereas if you have a car that is, let’s think about it as a semi-truck that you see on the freeway all of the time, those take a lot of energy in order for them to slow down or speed up. That’s the difference that you can think of metaphorically as far as options are concerned. With Gamma you would consider a race car that has the ability to accelerate or decelerate very quickly. You can think of that like an option that has very high Gamma and the reason why is because the Gamma of that option is going to change the actual Delta by a very large amount if it has a large Gamma for every $1.00 move. It’s going to either accelerate or decelerate very quickly, whereas an option that has a much lower Gamma is going to have a lower rate of change of Delta as the underlying moves. It’s just a slower moving kind of option. It has lower Gamma, it has lower potential to change is the way that I would kind of try to get that metaphor across. 

Jeff Praissman 

And by the way, I absolutely love these metaphors. I really think that they’re going to help our listeners understand the Greeks. And it’s such a creative way to look at it. 

Let’s move on to Theta. So Theta is time decay, right? So all options have Theta and just for our listeners let’s just say it’s February and I’m buying a July option, there’s a value in that time and then as we get closer to expiration, that time kind of ticks away. And so I’m really curious what the metaphor for Theta is.  

Are you sticking with the car theme or are we going to go somewhere else with it? What was the metaphor that you were able to come up with to teach our listeners about Theta? 

Mat Cashman 

Yeah. Well, we can go two ways with this. And you and I have discussed this a little bit beforehand. If you want to stick with the car theme, you can think about it kind of like a gas tank, right? Like it might have a certain amount of gas in your gas tank. And every time you get in your car, just generally speaking, there’s a little bit less gas in it, right? And that’s kind of how Theta works. It just generally and slowly overtime pulls away at the actual decay of the option, at the actual value of the option, and that speaks to the idea of what Theta really is, right?  

Let’s talk about Theta most generally. It is just a measure of decay of how much that option is going to be worth basically at this time tomorrow. So if you really want to look at Theta and look at it from a really specific idea from your model’s perspective, you’re really just advancing your clock to the same point in the day that you are now, tomorrow.  

And then looking at how much less theoretically that option is going to be worth tomorrow at this time. So because of the eventuality and the kind of part of the metaphor in the car theme that doesn’t necessarily work with the gas tank, is that it doesn’t speak to the idea that Theta is always happening, right? It’s a pervasive force that is constantly happening, regardless of what’s going on out in the world. And so, the way that I teach it when I talk about it most generally is that Theta doesn’t care if the exchange is open or closed. Theta doesn’t care if it’s a weekend. It doesn’t care if it’s Memorial Day. Theta happens as a function of time.  

So the other metaphor that I tend to use when I’m thinking about it is like an hourglass. Think about an hourglass. And as you turn the hourglass over and the top of the sand starts to filter down and come through, right?  Like sands through the hourglass, so are the days of our lives. That’s the exact kind of idea that I want you to have when you’re thinking about Theta relative to options. It’s a constant force and the minute that you turn that hourglass over, the sand starts to come through to the bottom side of that hourglass.  

And that kind of represents, you can think about it like it’s the value of your option, decaying slowly through that narrow band in the hourglass that comes through to the bottom side. And when all the sand gets to the bottom then that’s kind of like the expiration of the option. That’s when the option comes to its expiry and actually settles for the intrinsic value, as all of that extrinsic value that is represented by time premium, oftentimes, comes through that hourglass to the bottom of the actual hourglass.  

Now the thing that you can also think about, and I want you to consider when you’re thinking about this metaphorically, is that Theta is not purely linear. That’s an important concept to get across. As you get closer to expiration, Theta starts to speed up exponentially at times. So what you need to think about in that case, another metaphor that I use is to think about it as it’s a stopwatch that you might be using that actually speeds up as you get closer to the finish line of your race. As you’re looking at the stopwatch at the beginning of the race, when you click it, the stopwatch is moving at a regular pace. And then as you get closer, as people start to get closer to the finish line of the race, all of a sudden the stopwatch starts to move exponentially faster as it goes. That’s really getting to the heart of how Theta works mathematically, right? It actually increases exponentially as you get closer to expiry. That’s a really hard metaphor to find, right? Like one particular metaphor that actually drives that point home. So in this case, I had to kind of do a little pastiche of three of them together to really explain what part of Theta I really wanted to. So it’s a little bit more complicated, but it’s a complicated topic. 

Jeff Praissman 

I absolutely love the hourglass analogy. As we’re talking, I started thinking okay, so as soon as that option trades, that hourglass gets flipped over and the sand starts going through the hole.  

But thinking a little bit more about it, the buyer of the option contract is the top of the hourglass who is losing that value and the seller of the option is actually the bottom of that hourglass. And time decay is the seller’s friend because when they sold that option, whether it’s a call or put doesn’t matter. Every day that ticks by and let’s just say, all things being equal, price of the underlying being equal, everything else being equal, let’s just say everything’s kind of frozen, except for time, that option is becoming less and less valuable. So the time decay that they sold, they’re getting a little value back every day, whereas the buyer is losing a little, so I actually really, really like the hourglass analogy. 

Mat Cashman 

Yeah. Well, if you think about it, one of the things that we use, part of the nomenclature of the options world, when you’re dealing with Theta is you actually talk about it as in are you paying or are you collecting Theta, right? Many times when people are short a lot of Gamma which creates generally, a positive Theta amount, you’re collecting. People talk about it like collecting Theta.  

That’s like being at the bottom of the hourglass, where as the sand falls, it’s falling into your account, right? That’s the actual the metaphor in actual real-life terms. It’s coming towards you. Whereas if you’re at the top of the hourglass and you’re buying those options, you are paying or losing value over time. 

Jeff Praissman 

To me, again, I think I said in the beginning of the podcast, but this to me is such an original way of teaching it. We’ve both been in the business probably 20 some odd years each and this is really the first time I’ve heard this learning theory. What are your thoughts as far as the effectiveness of being able to use metaphors for newer investors to kind of understand these complex concepts, how they could possibly simplify the learning process and maybe tips for them to apply these in real trading situations? 

Mat Cashman 

Yeah, absolutely. Part of what, in my trading kind of journey, I started in 1999 learning options in a very “blacksmithy” kind of model, right? I sat across from the head trader of the firm in the CBOE member’s lounge during lunch and I got him a Caesar salad every day and he would go through on the back of a napkin and teach me Put-Call Parity or options modeling ideas and things of that nature.  

And as I learned them, it takes so long to actually immerse yourself in these ideas and be able to understand them intuitively that that’s kind of what brought this to my mind. It took six months of intensive hours long kind of angry teaching sessions from the head trader on the back of a napkin over a Caesar salad for me to have what I always call my “aha” moment. It’s one of those things that comes to you and if you talk it to anyone who has a really long history with options, I think most of them will be able to give you an idea of their “aha” moment. It’s when you’ve beaten your head against the wall so many times with these concepts, and oftentimes they’re mathematical concepts that are pretty complicated. Especially for someone who’s not a math major or someone who studied Econ. It’s one of those things where you beat your head against the wall over and over again, and then finally you have your “aha” moment where you’re like, oh, that’s why this guy’s been talking about Delta this whole time. That’s what it means.  

And so the build-out of this idea was to try to get to the heart of some of those people who don’t necessarily understand the math part of it. To be able to give them an alternative path to their “aha” moment because everyone needs that aha moment in order to really conceptualize and internalize these concepts to be able to understand how the Greeks work. And that always gives you a better idea of how much risk you have on, right? It’s one of those things that’s like if the metrics are there for you to use, but you don’t understand where they come from, you’re not necessarily going to have the best idea of how to manipulate the metrics. Or when they change, why are they changing? What does it mean? And so this sometimes gives people a better metaphorical understanding of an alternative way to think about it, and hopefully we’ll bring some more people into the fold that may be turned off by the actual math. The brute force math behind these concepts. And that’s really where it came from and kind of why the idea started to blossom in my mind after Ed suggested it to me. 

Jeff Praissman 

Yeah, I know. Like I said before, this was fantastic. I mean, such an original way to teach people about the Greeks. Any other final thoughts you want to leave us with? 

Mat Cashman 

Yeah, I mean I always think that the more you learn about optionality and the more you understand the behind-the-scenes concepts of how these things work, the better equipped you are going to be to make decisions about the risk that you have on or that you’re thinking about putting on.  

Because every single market environment is dynamic. Nothing ever stops moving forever. And so you need to be equipped to understand how those option contracts actually work, and the actual theoretical basis for those option contracts because oftentimes as soon as I say a call is the right but not the obligation to buy a stock at the strike price on or before the day of expiration, people’s eyes completely glaze over. And so part of what I’m trying to do here and part of what I’ve been trying to do kind of forever as I’ve been doing this is to break those really complicated ideas down. Give people an easier way to understand them. But the overriding message is, the more you understand about the options, the more equipped you’re going to be to make good risk decisions that align with your own risk tolerances, and that’s what we’re all looking for. 

Jeff Praissman 

And for our listeners, if you’re interested in learning more about the subject, like I said, Mat just got done a terrific webinar. The recording is up on our website. The link is in the study notes. It’s called Mathless Greeks.  

You can go to, you can click on contributors, look for the OIC. You can see it. You can go to webinars and look for past webinars. It was just a really good webinar to kind of dive a little bit deeper into the subject than we can’t even do on the podcast because he’s able to show charts and graphs. And just in general to see more educational material from the OCC, just go to our website, click on education and look for the campus and look for our contributors and look for OC. 

Thank you again for listening. Until next time, I’m Jeff Praissman With Interactive Brokers. 

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5 thoughts on “No Math, No Problem: Learning Options Greeks through Metaphors”

  • I appreciate the idea to simplify the greeks with analogies, but my sense is that any options trader that does not understand greeks in fairly good depth is really asking for trouble (same is true for volatility and esp IV, because all of these have such a significant input on options prices. So along with your idea for this webinar, I suggest you recommend some good books on Greeks – My favorite is Dan Passarelli’s Trading Options Greeks. Finally, thinking it is a wise idea to be trading options with understanding the math is perhaps not such a good idea. I welcome your feedback and thanks for the webinar.

  • Congratulations to Jeff and Mat for your work and Effort, to think on different way. Mathematics will give 2D View. I am trying to covert it to 3D View, Connecting Dots, Black Hall Theory Concept..

  • Think about how much Theta speeds up when you’re stuck on the highway during rush hour, your gas tank is on empty, and the next exit with a gas station requires a big detour with confusing road layouts.

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