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Might Correlation be the Key to Understanding VIX?

Episode 98

Might Correlation be the Key to Understanding VIX?

Posted August 17, 2023
Mandy Xu
Interactive Brokers

What sort of topics arise when two options market veterans sit down for a conversation?  Volatility, correlation, bonds, and of course, 0DTE and Volmageddon.  For the latest IBKR Podcast, Mandy Xu, VP and head of derivatives markets intelligence at Cboe, joins Steve Sosnick, chief strategist at IBKR, to discuss these topics and much, much more.

Summary – IBKR Podcasts Ep. 98

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.

Steve Sosnick 

Hi everybody. Welcome to another edition of IBKR Podcasts. I’m your host today, Steve Sosnick, chief strategist here at Interactive Brokers.  I’m very pleased to acknowledge my guest today, Mandy Xu, Vice President and head of derivatives market intelligence at the Cboe.  Obviously, there’s a lot we can learn from the people at the Cboe.  They do a great job in terms of market stats. Mandy, why don’t you take a few minutes and introduce yourself to the audience, please. 

Mandy Xu 

Thanks, Steve. And I’m very happy to be here.  I recently joined CBOE after 13 years on the sell side where I was head of equity derivative strategy at Credit Suisse.  What I’ll be doing at Cboe is producing a lot of client facing content and market commentary around Cboe’s leading suite of volatility products including obviously the VIX, S&P options, etc. 

Steve Sosnick 

That’s wonderful. Tell me how you ended up in the strategist role at Credit Suisse before you started at Cboe. 

Mandy Xu 

I interned at Credit Suisse straight out of college. Well, actually, while in college, and during my rotation internship, I rotated on the equity derivatives desk, and I loved the fact that it was a little bit more quantitative. And then when I joined the desk there was an opening on the strategy team. And I liked that it was a combination of quantitative and qualitative. There’s a lot of data analysis looking at option Greeks and what’s going on with the data in the market, but also a big component is distilling all that data into actionable market themes and trade ideas for clients.  To me, that strategy role was kind of the perfect combination of what I like to do, which is digging into the data, but also using the data to tell a story about what is happening in the market. 

Steve Sosnick 

Wonderful. Well, you were actually at this game longer than I have because I came to it after 25+ years as a market maker.   I sort of blundered into the strategy role, so I think it’ll be fun to talk to someone who approaches the same topics with a different perspective.  

Let’s dive right in. We can’t have a discussion about volatility, especially one involving the Cboe, without asking, “what do you see going on with VIX?” Most people came into 2023 expecting higher market volatility, but what we’ve gotten instead is a VIX that fell steadily for much of the year, hitting a three-year low with just over a 12 handle in June. What do you see as the main drivers of this and where do you think most people frankly got it wrong? 

Mandy Xu 

To your point, most people came into this year very much expecting, I think, a repeat of last year, which is elevated levels volatility on the back of macro uncertainty. And to me, the move in the VIX this year is actually really very much fundamentally driven. It’s a reflection of the fact that the macro environment has changed.  We came to this year expecting sticky inflation, a potential hard landing recession, and instead what we have gotten is inflation that is has fallen very, very rapidly from a high of, I think, almost 10% last year to a low of 3% now.  Sure, it’s not at the Fed’s 2% target yet, but we’re well on our way there. And at the same time, unemployment remains at historic lows, so we are very much in this Goldilocks situation, and that’s why you’re seeing volatility decline not just for stocks, not just for equities, but across asset classes. So, it’s not just the VIX that’s fallen to near one year lows, but we’re also seeing credit volatility, rates volatility, FX volatility, oil, commodities, across every single asset class volatility has fallen substantially.  That’s why I think most, if not all, of the move is very much fundamentally driven.  

Now, in addition to that though, when we’re talking about equity volatility and particularly the VIX, one thing to highlight is the role that correlation and dispersion kind of play in in into that you know the level of the VIX.  Keep in mind that the VIX is a measure of S&P 500 index volatility.  For the S&P 500 index (SPX), it’s a function of, obviously, not just the volatility of the individual stocks, but also the correlation of those stocks.  And the way that I explain it is that you take it to the extreme and simplify it to an index of just two stocks equally weighted.  If one stock goes up 20% in a day and another stock goes down 20% in a day, at the index level that’s unchanged. So, high stock volatility, but very low index volatility in an environment of extreme dispersion or low correlation. And that’s what we’ve seen this year. S&P 500 correlation went from levels ranging from 40 to 50 last year to a low of 8% earlier this year. And to put that in context, that’s pretty much at or near historic lows.  

The last time we saw index correlation levels that extreme was in 2017 which was a record low vol year for the VIX, when the VIX was at 9, right?  The move in correlation, the decline in correlation of the stocks in the S&P 500, I think is another major contributor to why the VIX has been so low, and the macro reason for that obviously is this decline in recession risk.  That allows investors to move away from looking at the macro more to stock fundamentals and stock picking. 

Steve Sosnick 

Two follow-ups to that. First of all, how can our listeners follow correlation and dispersion? The concept that you described as rooted in covariance.  And when we had a situation where essentially 7 stocks were going up and 493 were treading water, that that fits into it. But the numbers you threw out, where can where can our listeners access those type of statistics? 

Mandy Xu 

Great question. So historically, traditionally correlation and dispersion have been, I would say, fairly esoteric topics. But at Cboe we try to make it more transparent and easier to follow and track for the end user.  We actually have a number of correlation indices: one-month, three-months, six-months, one-year, depending on the tenor that you’re looking at, for implied correlation indices for the S&P.  The numbers I was referencing earlier are based on those indices and then, as kind of as a heads up, we’re also going to be launching a dispersion index next month. So more to come on that. But you know, we’re definitely trying to make these subjects and these topics more transparent and easier to access and easier to follow for investors. 

Steve Sosnick 

I love it when I blunder into new product announcements from our guests. 

Mandy Xu 

You teed it up perfectly for me, yeah. 

Steve Sosnick 

But of course, one thing to keep in mind is you talked about the record lows in late 2017. Those of us who’ve been in the business for a while remember how that came to an end in 2018.   At some level, do you feel the complacency becomes extreme?  We’re off the lows of VIX now.  Just so people understand it, we’re taping this in the afternoon of Wednesday, August 9th.  When I came into the room, VIX was about 16, off its lows of 12 and change. Do you think that investors are getting a little complacent, especially when we head into a seasonally difficult time?  And especially because some of the risks that were perceived earlier in the year, while you acknowledge that they’ve dissipated, they’ve not evaporated?  So, what’s your feeling on investor complacency versus, well, let’s just call it fear and greed. 

Mandy Xu 

So let me address it in two ways.   First, with regard to longer term risks, such as risk of recession, or risk of a policy mistake from the Fed:  Those risks like you have pointed out, they’ve dissipated but not evaporated. However, the VIX is not the index to be looking at for measures of these longer term risks.  Keep in mind that VIX, by design, is a measure of one month implied volatility for the S&P.  In layman’s terms, how much the S&P 500 index is expected to move in the next 30 days. That’s it, right.  You very much could have an environment like now where the VIX is low, but you still have these elevated or potentially elevated longer term risks.  To really kind of get a sense of whether the derivatives market appropriately pricing in these longer term risks, you have to look at the entire volatility curve.   In this instance, looking at longer dated implied volatility for the S&P.    

For example, if we look at one year options on the S&P, I think that would give you a better sense or a better gauge of how markets are pricing in longer term risks like recession, etc.   If we look at the S&P curve right now, it is true that while longer dated vols have come in pretty significantly over the past two months.  One year at-money implied volatility on the S&P went from 18 1/2 at the beginning of June to as low as 15 ½ — a decline of three points in the span of a few weeks. That’s pretty notable. And more importantly, the current level is right around the long term average. So, longer data implied vols in S&P are not really trading at elevated levels currently.  I do think that is a reflection of the fact that, at least in the options market, people see recession fears as easing and I think it’s no coincidence it’s happening at the same time as major banks are reversing their recession calls as we have continued to get good economic data.  The tenor you are looking at when you trying to make an assessment of risk really, really, really matters. 

The second, and then I think even more crucial point. is a lot of times people think that low VIX means that it’s complacent, and high VIX means there is a lot of fear in the market. I don’t think that’s necessarily true. I think you can have VIX that is low but actually pricing in a lot of fear, as well as VIX that is trading high but not actually a pricing in appropriate amounts of risk.  For example, last year VIX was elevated, but it was not trading rich.  This year, I would say similar to what we saw in 2017, if you look at where the VIX is trading versus the S&P’s realized volatility, that spread, that difference, people often call that the “volatility risk premium [VRP].”  It’s a function of how much risk aversion is being priced into the market. That spread is actually very, very elevated right now.  Depending on the tenor you’re looking at, it’s either near one-year highs or at one-year highs.  S&P three-month implied volatility, for example, is right now being priced at about a four point premium to realized volatility.  I think that is a sign that even though the absolute level of the VIX is low, there’s still a healthy amount of risk premium being priced into the derivatives market. You can see in in the in the VRP. 

Steve Sosnick 

People who have been listening and have suffered through my pontification have seen that I’ve often put that link to the CBOE definition of VIX in in my pieces. It’s like bookmarked there and I just drop it in how it’s the market’s best estimate of the volatility over the coming 30 days, and I’ve also said too way too many times, “VIX is not a fear gauge. It just plays one on TV…” 

Mandy Xu 

<chuckles> 

Steve Sosnick 

… but I do find that that one of the analogues, not sort of day-to-day, but when you get to turning points, is that VIX is the price of parachutes when a plane hits turbulence.  This comes from my experience as a market maker.  Nobody really wants umbrellas when it’s when there’s a drought, nobody really thinks about a parachute if the plane is moving along smoothly at 30,000 feet, but as soon as you hit some turbulence, or as soon as the rain clouds develop, people want them and they want them in a hurry. And to me, VIX is still the most efficient way for an institutional manager to hedge his or her risks.  Just, “I want to de-risk quickly.”  I think what explained a lot of what was going on in 2022 was that the initial down wave caught a lot of people by surprise. Everybody was on one side of the trade for the most part, and we started going down, and people needed to de-risk in a hurry.  As the year went on. VIX declined because as people sort of got inside, they got more comfortable with the level of risk in their portfolio.  But it still remained relatively elevated because the historicals were relatively elevated. What is interesting to me is some of the movements over just the past couple of weeks.  The day that it really struck me was when Nikkei reported that the BOJ was making its moves.  I was scheduled to go on TV at 3:00 that afternoon. I was chatting with the host at 1:00 saying how VIX was within .01 of its year’s low that morning.  And by the time we went on air it was about two points higher, if not more.  We’ve seen a few spikes in VIX, and my thesis right now is, especially as you get into seasonally difficult time — and remember, 30 days from early August is early September — I think people are getting a little more mindful of risk.  Please push back upon that if you see fit. Let’s put that theory to the test a little bit. 

Mandy Xu 

I will say that one thing that stands out in terms of what people have been doing this year is that we have seen a lot more hedging activity, particularly in the VIX.  A resurgence in VIX options trading.  Just to kind of give you some volume numbers, we’re up 53% year-over-year in in terms of VIX option volumes. An average daily volume (ADV) of almost 780,000 contracts. I’ve gotten a lot of questions around what is driving that.  Why is there this renewed interest in buying VIX upside calls, call spreads, and overall options trading this year compared to last year, when last year was a more volatile environment?   To your point, when you’re talking about the market environment last year, the way I explained last year is that people buy hedges when there is exposure or risk to hedge or when there are gains to protect.  And last year we had Fed rate hikes and higher inflation on everyone’s radar coming into the year.  So, it wasn’t really a true surprise and what we saw throughout the year was, as you mentioned, institutional investors de-risking very steadily and significantly, and de-risking by moving to cash.  Once you’ve moved to cash, you don’t really need to spend premium or to spend money to buy option hedges, right?  I think that kind of explained why last year we didn’t really see much interest in buying put options on the S&P, or VIX upside calls, or call spreads.   

Whereas this year, particularly in the VIX, I would say people typically use VIX options as a tail hedge.  It’s the hedge for that Black Swan event. Whether that is COVID in February and March of 2020, whether that’s Feb ’18, whether that’s the global financial crisis, they want VIX options for that convexity exposure, for that potential explosiveness when you know VIX quadruples, quintuples, etc.   And that is much easier to do when the VIX is trading in the mid-teens like it is doing today versus obviously when it was in the mid- or high-20s which was very much the range last year.  I think that the very fact that the VIX has declined has made tail hedging more attractive using VIX options. So, I think that’s part of it.  

And the second part I mentioned is: this year as markets rallied and the macro environment has shifted, investors had to put more money to work.  They had to have. They had to increase their allocation to equities, both in discretionary strategies as well as systematic strategies.   As they do that, the need for hedging also increases and that’s why you’ve seen this, not just with VIX options but also with S&P options as well. 

Steve Sosnick 

Someone brought to my attention some of the strategies that people have been using in VIX options. Look at the volumes in 47 1/2 calls and 60 calls and things of that nature, some people going as high as 80 calls. I mean, that is one hell of a tail risk.  And to me it’s an interesting type of hedge because that is purely a disaster hedge.  You’re not you’re not going to see that in in a garden variety correction. You’re only gonna see that in a crazy scenario. What other strategies, VIX or not, are you seeing being very popular, resonating with investors these days? 

Mandy Xu 

Outside of the VIX product complex, if we move on to S&P, the uptick in the S&P trading, I think that is a function of the overall volatility environment declining because keep in mind that implied volatility is the number one driver of option premiums.  In an environment where implied volatility is lower, it means the absolute premium that you’re paying for optionality has also gotten cheaper.  So, it’s cheaper to hedge, but also cheaper for upside.  And we are also seeing an increased uptick in call volumes as well.  I think a function of the fact that people were not positioned the right way coming to this year.  By far the most consensus position among all the investors I spoke to at the beginning of the year across the US, Europe, South America, across regions, everyone was short US equities — particularly US large cap tech and that’s precisely what has led the rally this year.  If you are someone who has been underweight US equities, an easy efficient way to get that upside exposure is through upside calls.  I think that helps explain some of the volumes that we’ve seen on the call side as well.   

Then, last but not least: how can I talk about S&P options without talking about the zero dated (0DTE) options?   Those remain very popular.  Consistently throughout this year, we’ve seen about 40 to 50% of all the volumes in S&P being concentrated in those 0DTE options. 

Steve Sosnick 

That was going to lead into my next point because I had a journalist call me yesterday asking “I’ve seen all this new activity in index options. How much of it is zero dated?”  I’m like, well, probably most of it.  Do you agree? Did I give him the right answer? 

Mandy Xu 

No, technically it’s not most, it’s 40 to 50%. 

Steve Sosnick 

Yeah, OK. Alright. 

Mandy Xu 

It’s substantial but not more than 50%. 

Steve Sosnick 

A plurality, not a majority. OK. 

Mandy Xu 

But I will use this opportunity to plug our upcoming White Paper, which hopefully should be published and available to the public by the time this podcast goes live. [Editor Note: It’s published and available here]  We have put out a very comprehensive white paper on the trend of short-dated options, particularly focusing on zero day options, looking at who’s using it? Why people may use these options, the volume profile, the intraday risk profile.  It’s a very comprehensive, but I would say also very easily digestible white paper. I really encourage those who want to learn more about the space to read the paper. 

Steve Sosnick 

I love teeing up stuff like that, and I’m looking forward to it.  

There have been two real pushbacks that people have had about zero-dated options. I’m just gonna use the term broadly for zero, let’s call it sub five-day.  One is that 0DTE options have injured VIX somehow — and I’ll leave my personal opinion out of this one.  I’ll let you answer it.  The second one is that they bring systemic risk with them — about which I have a very strong opinion as well, and I will defer to your answers, because again, the listeners have probably heard my opinions ad infinitum. 

Mandy Xu 

I think the activity that goes on in zero-dated options, it’s very distinct from the typical volumes that we see in longer dated options.  For example, institutional investors coming to hedge recession risk, as we mentioned, or want to put on a hedge going to year end, that hedging flow is not gonna be replaced by 0DTE options. It’s true that the VIX does not reflect the activity that’s going on in these 0DTE options, but we do have a one-day VIX which is gives you a better sense of the volatility that it’s being priced and embedded and reflected in in these extremely short dated products. So that’s my answer to the first point.  

The second point, the systemic risk, I mean that’s a question that we’ve gotten a lot, and I think you know there have been some very big headlines being made throughout the year by people who think this could potentially lead to another “Volmageddon” or another big systemic event. And I would say for the most part, a lot of the analysis is based on incomplete or incorrect assumptions about who’s trading these products and what they’re using them for.  You read an analysis that for example assumes that most people are short these options.  Therefore, if the market really starts to move there will be a scramble to cover, and that could exacerbate moves in the underlying index.  Or you read that everyone is long. This is just another form of “YOLO”, retail investors buying upside calls.  It’s just another extension of the meme stock craze and therefore market makers on the other side are all short, and therefore when they start to hedge, that’s gonna exacerbate moves on the underlying [stocks or indices].  Those are kind of the various strains of kind of that, that argument.   The reality is that actually it’s much more nuanced, and more importantly, it’s much more balanced than that.  

First, we find that in terms of the who’s trading it, it’s a pretty even split between retail and institutional end users.  We find that in terms of use cases, it’s a pretty diverse set of use cases. Some people use these zero-dated options for yield enhancement.   They’re selling capped call spreads and put spreads on the S&P for income generation.  Other people are using it to hedge overnight risk, other people are using it to play intraday momentum. It’s a pretty diverse set. There are systematic strategies that are being active, and, in this space, there are a lot of discretionary strategies.  So, it’s very diverse. And then most importantly, the last point is it’s very balanced between the buys and the sells — such that if you look actually at the net positioning across [contracts], it’s only a tiny fraction of the overall gross volume. So, people look at the headline volume in these numbers and they think, “Oh my goodness, you know, the risk must be huge. Right?” But because it is so evenly balanced between buys versus sells, the net risk, the net positioning is actually minuscule compared to the gross volume number. And that’s something that we go in in detail in the white paper. So again, for those who want to better understand this product and the space, you know, I do recommend everyone to read the paper. 

Steve Sosnick 

First of all, if you were sitting in the room with me, I’d have given you a big high five along the way cause, because that really synchs up with what I’m thinking, and I really can’t wait to read this. That’s not that’s not blowing smoke. I really do want to see it. 

A couple of that that I’ll now add are: I do think I’ve said all along that I think that the players or the strategies used among short dated option traders are different than the people using 30-day options or VIX, etc.  So, we’re in synch on that one.  And I think that I’ve also been quite vocal in saying that I don’t think these add systemic risk.  At the risk of insulting an exchange — which I don’t want to do — my original read was that the games haven’t changed, they’ve just added more tables at the casino. It’s really just a different set of strategies and I think the more dire the prediction, my feeling is the less that they’ve actually been up to their armpits either as a market maker, as an exchange professional, or as a clearing professional, risk manager, etc.  I think a lot of them have come from 40,000 feet saying these seem really dangerous, but they’re using very well established risk protocols. I think there is the potential for sort of one day, not gonna say hiccups even, but exacerbated moves on an intraday. And I do think we’ve seen that particularly on some of the big upside days.  But I also think that as the product evolves, those who are inclined for income realize that it’s the best day to write an option because [options] decay falls off exponentially. The shorter the option [the faster it decays] There are very few guarantees in life, but I’ll guarantee you there’s no extrinsic value in the option after expiration. And I think people pick up on that idea. 

Mandy Xu 

Right. 

Steve Sosnick 

So, going into the end of the year, where what are you, what are you focused on? What do you think the opportunities are for people in the option space or investors in general? 

Mandy Xu 

Yeah, sure.  When I look across asset classes, and I think I’ve mentioned or alluded to this earlier, but what really stands out to me is interest rate volatility, bond market volatility.  That is still the only asset class where volatility is near extremely elevated levels, near historic levels. It has come off the near-all-time highs that we saw last year, but it still remains very rich. That again is really a reflection of Fed policy uncertainty. Specifically, within the bond market, one of the things I’m watching is the SOFR Curve and the fact that the market has persistently priced about 140 basis points of cuts for next year.  That really hasn’t changed much at all over the past couple of months outside of the March banking crisis period.  This persistent belief that the Fed is going to start cutting rates at the first sign of economic weakness that you know inflation is over or that the Fed’s going to shift this from fighting inflation to supporting growth, that remains to be seen.  

And then one asset class that’s gonna be really interesting to watch is gonna be credit.  Corporate bonds, as we all know, have both duration risk — interest rate risk sensitivity — as well as credit risk.  That’s reflected in the macro outlook.  So that’s an asset class I think that’s right at the crossroad of everything that we’re talking about.  In particular, it’s not just that it’s sensitive to duration, risk and credit risk, but also the correlation between the two.  So, when we have a year like last year, 2022 where you had rates going up because of Fed tightening, and you had spreads going up because of the increase in recession risk, when the two kind of move in the same direction you had a record sell off in in investment grade (IG) bonds.  IG bonds actually sold off more last year than the S&P, despite being quote un-quote “lower risk.”  And that’s why last year if you look at high yield corporate bonds, HYG implied volatility more than quadrupled from a low of four at the beginning in January to over 20.  In both of those underlyings, vols have come in quite a bit this year, so going forward the question is, “what’s going to happen with that correlation between duration and credit risk? Could we see a repeat of last year if inflation proves to be more sticky?”    

To that end, one thing I want to highlight and shout out on this call is the fact that we have launched options on IBOXX investment grade as well as high yield futures corporate bond futures. IBHY. which is the high yield IBOXX high yield index, and IVIG, which is the investment grade corporate bond index futures.  Those have been live for a couple of years now. Early last month we launched options on futures, which again allows you to play the volatility in these underlying assets.   

There are two things I’ll be really quick to highlight on that.  One is that by design these futures and options on futures are designed to tap into the liquidity in the underlying ETF ecosystems.  There are a lot of questions like, “How liquid are these products?”  It’s gonna be as liquid as the ETF.  By design, these futures are designed to track the holdings in the ETF, and as a result allow market makers to hedge with the with the underlying ETF’s and that I think really enhances the liquidity in these products.  The 2nd is “why trade options on these futures when you can trade them on the ETFs?”  And I would say, particularly for those who are looking at selling options in credit and corporate bonds, two complaints that we’ve often gotten or drawbacks that we’ve gotten with those products is that ETF options are American style and they’re physically settled.  Because they pay a very high dividend you have pretty substantial early exercise risk. And for options on futures, because the underlying futures are cash settled and because it’s on a total return index you don’t have that dividend risk.  You do mitigate a lot of that with options on futures. So that’s something I’ll leave you with.  I think corporate bonds as an asset class is something to really watch next year as we enter potentially a different rate regime and particularly options on corporate bonds, I think that would be very exciting. 

Steve Sosnick 

I think that sounds like a very interesting product and I do think that the distinction between cash settled, and [physically] deliverable is underappreciated. And I think a lot of institutions know that, but I don’t think a lot of individuals appreciate it.  I think many of them have learned as they’ve started to trade SPX short term options, but there are distinct advantages in that. I think I’ve written something about it, and I’ll drop it in this for our listeners if I have it. 

Mandy Xu 

Perfect. 

Steve Sosnick 

Mandy, this was this was a real eye opener, and I hope this is the first of several dialogues that you and I can have on the topic.  For everybody who’s listening, if you’ve just tuned in now, shame on you. We’ve been talking to Mandy Xu, VP and head of derivatives market intelligence at the Cboe, and we’ve been we’ve been having a great discussion.  Hopefully this is chapter one in an ongoing discussion. 

Mandy Xu 

Looking forward to more. Thank you. 

Steve Sosnick 

And please give a shout out for where they might be able to find the stuff that’s out there, some useful Cboe links if they don’t already have them, or if there’s any more that you have. 

Mandy Xu 

Will do, yeah. 

Steve Sosnick 

And on that note, I wish you all farewell. This has been I beat the latest edition of IBKR Podcasts. Please tune in next time and look for this one as well as all your as all our other podcasts at all your favorite podcast destinations, including of course IBKR Campus and ibkrpodcasts.com. Thank you, everybody. Take care.  Bye. 

Useful Links:   

VIX Definition: From VIX Index (cboe.com) : “The VIX Index is a calculation designed to produce a measure of constant, 30-day expected volatility of the U.S. stock market, derived from real-time, mid-quote prices of S&P 500® Index (SPX℠) call and put options.” 

An explainer about the differences between cash settled index options and equity options that deliver underlying shares: Understanding Index Options | Traders’ Insight (ibkrcampus.com) 

Cboe Implied Correlation index Indices: Implied Correlation (cboe.com) 

Cboe® iBoxx® iShares® Corporate Bond Index Futures and Options on Futures: IBHY/IBIG-Cboe Corporate Bond Index Futures 

Cboe White Paper: The Rise of SPX & 0DTE Options (cboe.com) 

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