Opposites Attract: the Inverse Relationship Between Implied Volatility and Gamma

Mat Cashman, Principal of Investor Education at the Options Clearing House, joins IBKR’s Jeff Praissman to discuss the often-misunderstood inverse relationship Gamma and Implied Volatility have.

Summary – IBKR Podcasts Ep. 200

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. This is Jeff Praissman with Interactive Brokers Podcast. It’s my pleasure to welcome back to our podcast studio, Mat Cashman, the Principal of Investor Education at the Options Clearing Corporation. Mat, great to have you with us. 

Mat Cashman 

It’s wonderful to be here, Jeff. 

Jeff Praissman 

Today we’re going to dive into a pretty nuanced, but critical topic for options traders. And this is how Gamma and implied volatility interact, and more specifically, why they’re negatively correlated, which may seem a little bit counterintuitive at first, but trust me, by the end of today’s episode we’re going to have everything laid out for you guys, and you’re going to really enjoy this. 

Mat, I’m going to turn it over to you, and I know we talked about this offline a bit. And honestly, when we first started talking about it, it took me a few minutes for it to click that Gamma implied volatility or negative correlated, it makes you pause for a second. 

It’s really one of those concepts that unless you deal with it directly, like I said before, it can feel a little counterintuitive. And I think, though, before we get too far ahead for our listeners, maybe we could start with the basics, give them a quick rundown of Gamma and Delta. 

Mat Cashman 

Yeah, absolutely, Jeff. I think it’s good to start at the beginning when we’re talking about something that’s as nuanced as this idea is. So let’s start with Delta and Gamma specifically. Delta.. they’re both Greeks, obviously. Delta is one of the Greeks that’s used in options trading. It represents how much the price of an option, so the price of the option should theoretically move for every one move in the underlying asset. 

For example, if an option has, let’s say a Delta of 50, which is often expressed as a decimal. So in this case, it would be .50, 50 Delta, you would expect that option, relative to your model, is going to move $0.50 cents for every $1.00 that the underlying moves. 

So that’s why sometimes people think about it as like a percentage chance of it. It’s a percentage of the actual underlying move that the option should move in price. Now that’s in price terms. That’s Delta for price. Gamma, on the other hand, is a measure of the rate of change of Delta. So it measures how much your Delta should move for that same one dollar move. 

Now, because it is a, let’s call it a measure of a measure, right? People think about it as a second derivative in the derivatives marketplace, people think about it as the second derivative because it tells you how much your Delta should move. So those are the two kind of like foundational concepts of this larger concept we’re going to talk about.  

Jeff Praissman 

And that’s a great foundation, Mat. Thank you for explaining that to our listeners for ones that are new to option trading, and it’s always just a good kind of review for ones who are inexperienced ones.  

Gamma is really the measure of how much your Delta is going to change the market moves, like how fast your steering wheel will turn as the road curves, correct? 

Mat Cashman 

Yeah. If you want to use that as a metaphor, I think that’s one way to think about it. Another way people think about it is that Delta is like the speedometer of your car that measures how fast you’re going. And Gamma is like how fast your car accelerates or decelerates. It’s how quickly you can change. 

Jeff Praissman 

And that actually reminds me of our previous podcast of ours that we discussed Greeks without math, I believe.  

Mat Cashman 

Yeah. Yeah. Called the Mathless Greeks. 

Jeff Praissman 

I highly recommend it to our listeners as well if you haven’t checked it out.  

But, here’s where it gets interesting. Mat, Gamma itself is not constant. As you said, it changes as Delta changes and Delta changes as the underlying moves, underlying price moves. So what role does implied volatility play in this dynamic? 

Mat Cashman 

That’s a really good question. And that gets at really the heart of this matter. The first thing you need to understand is that both, like you said, Gamma and Delta are constantly moving around based on where the stock is or where the underlying is relative to where your strike is and how much time is in that option. 

But implied volatility is another part of this equation that’s really important. Now, implied volatility is the market’s expectation for future volatility of the underlying asset going forward. So it’s a forward-looking metric and it plays a really big part in how much options are worth, their prices. 

As implied volatility rises, something interesting happens to Delta. It becomes less sensitive to price changes in the underlying. I’m going to say that again. As implied volatility rises, Delta becomes less sensitive to price changes in the underlying. 

The reason why is because higher volatility implies a wider range of potential price outcomes for the underlying, meaning the Delta for all of the options out there, every single option on the board, starts to compress toward the 50 Delta. 

It’s really interesting. In other words, as volatility increases, the distinction between the in the money options and the out of the money options starts to blur a little bit, which means Gamma starts to decrease in those options. It’s one thing that I think about when I talk about this a lot is that there’s one thing that we use on an everyday basis that people can like, always think about it as a 50 Delta, and that’s something that has a 1 out of 2 probability of happening, and that’s a coin flip. 

When you flip a coin, you have a 50% chance, always, of getting heads or tails. And I use that to center people’s thinking into how those Deltas are starting to compress toward the 50 Delta bound. Everything starts to behave more like a coin flip. 

Jeff Praissman 

Just to recap, as implied volatility increases, the Delta flattens out, and since the Delta is flattening out, the Gamma is decreasing. Because Gamma is the measure of how Delta changes, the less the Delta changes, the less Gamma to measure. So in normal markets, going back to how this is a little counterintuitive, I think for most traders, that you get used to looking at strikes around the current stock price and you see the Delta spread out pretty nicely, right? 

So you have a 65 Delta, 50 Delta, 35 Delta and so on. But when things get extreme, that relationship changes. And you shared a fantastic example from 2008 offline that you went through during the financial crisis that really drove this information home. 

Could you walk the listeners through that scenario? 

Mat Cashman 

Yeah, of course. So this is one of those stories that I use when I talk about Delta and implied volatility an awful lot, because I think it’s a good way to drive this home. So 2008, obviously the great financial crisis, I was trading S&P options in the S&P pit. Back during this period, it was incredibly chaotic, right? 

Things are happening all over the place. I tend to use the term goat rodeo to describe this time during 2008 because anything can happen in a goat rodeo, right? Anything can happen. It’s an environment where things are extremely chaotic. So volatility and particularly delivered volatility, which means how much something is actually movinh, how much does it move on a day-to-day basis, is through the roof at this point in time.  

Large moves in the underlying are happening regularly, almost every day. Sometimes you’d walk in and it would be five standard deviations away from the previous close. Now, normally, in normal, placid, regular markets, these kind of moves would be completely unheard of. 

But during that period of time, they became relatively commonplace. They were like a daily occurrence. That sets the stage for the environment in which you’re dealing with trading options. Now, I want you to imagine pricing or trading options during this time period if you were to wake up one morning and go to work and someone were to walk up to you outside the pit before you walked in and said, today, we’re going to close six standard deviations away from where we were yesterday. 

In a normal marketplace, you would think that was crazy. You’d be like, you would dismiss that person and say, that’s crazy. There’s no way that’s going to happen. What would make that happen? That’s crazy. But during that time period, when you’re dealing with high levels of both delivered and implied volatility, it’s almost expected. You almost expect those things to happen. And so what happens in a market like that, not only from a trading perspective, but from a modeling perspective, from an options modeling perspective, is that the options pricing gets flipped around on its head. You also have to flip your mental model around because of what you’re expecting on a daily basis. 

But the pricing gets flipped as well. Suddenly, these options that were theoretically out of the money start behaving a lot more like at the money options because of that phenomenon that I described earlier, which is that as implied volatility starts to rise, all of the options start to take on the qualities of a 50 Delta option because every single price iteration on that curve becomes, theoretically, equally as likely to happen as you get to a situation in which implied volatility goes to, say, infinity. 

Once you get to infinity, what you’re dealing with is something that usually has curvature to it, which is a normal price distribution that looks like a straight line because everything all of a sudden has a 50 Delta. And if everything has a 50 Delta and you move from this point on the curve to this point on the curve, your Delta changes from 50 to 50, which means it doesn’t change at all, right? 

And if it doesn’t change at all, at any point on the curve, what happens to Gamma? Gamma is the measure of the change of the Delta. The Gamma goes to zero. And so that’s why I use that example when I talk about it because what’s happening is actually the curvature of the price distribution is starting to flatten and it becomes more like a straight line. 

Jeff Praissman 

That’s a great example, Mat. And so really what you’re saying is as the market becomes more volatile, options that we would normally consider out of the money really are in, at the money again. And, because that implied volatility is so high. So almost every option has a decent chance of finishing in the money just because of the complete volatility in that market. 

How does this tie into the idea of fat tails, which we hear about so much in these volatile markets? 

Mat Cashman 

That’s a good question. I think that can tie it into two things that people hear about in the way that people talk about the market. So fat tails are referring to the idea that extreme price moves, those extreme price moves I was talking about happening in 2008, that are several standard deviations away from the mean, become more likely in volatile markets than they are in normal markets.  

So a normal market has, like I referred to, a bell curve of price distributions of prices where the majority of the outcomes are near that average price. And extreme moves out here to the like 3,4,5,6 standard deviation in either direction are relatively rare and that’s why their actual distributions on the edges start to get narrow. 

It becomes less of an occurrence as it goes out away from the mean. Now, as the distribution flattens out, those tails become more likely. There are more occurrences that go from where we have in the mean that gets spread out to the actual tails, and those become fatter, meaning those extreme moves become more probable. 

This widening and flattening of the price distribution is why all those options start to move toward that 50 Delta in those extreme environments. And like I said before, as I mentioned, the Gamma of those options starts to diminish because when all those strikes behave similarly, you’ve got these fat tails on the edges coming up. And you have the meat of that bell curve distribution starting to widen and flatten. 

This is when volatility becomes extremely high, options become less sensitive to price change because the potential for these extreme moves is flattening out and becoming more likely in every possible single scenario. And so that’s why it starts to look that way. And that’s why people talk about fat tails. 

Jeff Praissman 

That really helps clarify things, Mat. So it’s really like when volatility is high, the market’s pricing these options as if every strike is equally likely to be hit. So there’s really less differentiation between in the money and out of the money options.

But, now that we’ve broken down how Gamma is impacted by implied volatility, I’m really curious, what initially made you want to bring this topic into focus for traders? 

Mat Cashman 

That’s a good question. When I come up with ideas to talk about, as far as educational opportunities, it comes down to just numbers of conversations that I have with people over the years. And in this case, it’s even with people that I would consider quite experienced, as far as options trading are concerned. 

And this is a concept that would come up over and over again, even with people that are really experienced, where it’s not perfectly codified in their mind that this relationship is actually negatively correlated. I think it’s natural for people to assume that in a more volatile market, everything gets more intense, meaning more Delta, more Gamma, more of everything. 

But what’s really the case is that for Gamma, that isn’t actually what happens when you understand how Gamma and implied volatility are actually correlated. It can really change how you approach options trading, especially when things are moving around a lot, especially in volatile times. It’s really a crucial part of managing risk. 

And if traders don’t recognize that Gamma decreases when implied vol increases, you can see a scenario in which they would overestimate. or underestimate how their position might react when something moves around a lot, when there’s a giant move in the underlying. And so you can see where someone might think that it was going to perform a certain way and it doesn’t perform that way at all. 

And that’s because your assumptions about Gamma and implied volatility are flawed, really. They’re the exact opposite of the way that the relationship actually works. It’s a negatively correlated relationship. And so I think it’s something that would really help people to understand in those market circumstances where things are moving around all the time, it’s going to help them to understand why their positions are moving in the way that they are.  

Jeff Praissman 

Yeah, I can see how this could be a game changer for many traders. Especially in turbulent times, not just like in 2008 where it was so extreme, but even more recent volatile periods. So for our listeners today who might be new to this, what’s one key takeaway you’d like them to have about the Gamma implied volatility relationship? 

Mat Cashman 

I think the real key takeaway here is to pay attention to it closely and to understand from a very basic level that it’s negatively correlated. And so when you’re in an environment where things are moving around a lot and then implied volatilities generally go higher in that environment, it’s important for people to understand that just because implied volatilities are higher and that the market is necessarily moving around a lot, it actually means that the options that you’re either buying or selling have less Gamma in them if their implied vols are higher. 

And that’s just a natural part of the relationship that occurs between Gamma and implied vol. They’re negatively correlated. And just, if you’re looking for a way to get coverage in a marketplace where there’s a lot of movement and the implied vols are very high, you need to think really deeply about what it means to, for instance, buy that option that you’re thinking about buying. 

Is it going to perform the way that you’re expecting it to perform when something moves? Because when you raise the implied vol to extreme levels on options, they don’t always perform the way that you’re thinking they’re going to perform because of the correlation between Gamma and implied. 

Jeff Praissman 

Now, that’s great insight, Mat. And, unfortunately, we’re about out of time, but this episode will definitely leave our listeners with plenty to think about. And it’s always great to have you in the studio bringing your years of option experience into our education program and out to our listeners. 

Thanks again for stopping by Mat. Really appreciate it. 

Mat Cashman 

Yeah, it was a pleasure, Jeff. I’m always happy to talk options with you guys.  

Jeff Praissman 

Excellent. And to our listeners, thank you for tuning in. As always, our podcasts are available on our website under education. You can find them on, normal. YouTube, Spotify, Amazon Music, Google Music, and so on, Apple Music. And until next time we will see you at IBKR Podcast Studios. 

Thank you. 

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