Episode Transcript
SH: Hello it is your host Sam Hansen and I am excited to welcome you back to Carry the Two, the podcast about how math and statistics impact the world around us from the Institute for Mathematical and Statistical Innovation. While we’re in between our more in-depth seasons, we like to bring you something a little different in mini-season format. And for this mini season, we are going to highlight some of the amazing researchers who have presented at IMSI over the past year. Our first guest is
TM: So I'm Thibaut Mastrolia. I'm an assistant professor at the IEOR department at UC Berkeley. So IEOR, this is industrial engineering and operation research.
SH: Thibaut joined us at IMSI for a workshop on Decision Making and Uncertainty where he presented a talk titled Recent advances in auction markets design and regulation policies. And now without any further ado let’s get into my conversation with Tibaut Mastrolia
SH: So yes, Thibaut, please, let's get into this. So first, I'm going to start with a bigger picture
question. Why is it important to look into markets and their design?
TM: OK that's a very interesting question so i propose to i always start with an example because this is something which starts for very simple thing in life which is a notion of transaction and how you design a marketplace recently I bought i'm clarinetist and I bought a new clarinet so instead of taking the example of a clarinet I will take an example of a guitar which is the most traded instrument. And imagine I own a guitar place where my profession is to sell and buy guitar and to meet, basically, it's a marketplace where I meet people who need to buy a guitar and people who need to sell a guitar. So there is two ways to do this business. The first way is, for example, to propose to people to sell or to buy guitar at a price they want to fix. So I receive call and I answer each call and someone tell me, okay, I have a silver sky and I want to sell this silver sky at $2,000. So I record it and I'm like, okay, so I will wait for a customer who is interested in that. Someone else can tell me: Me, I would like to buy a guitar, but I will not buy a guitar more expensive than $15,000, a silver sky. So I say, okay, so I record your order.
These people, this is people who provide the liquidity to my store. So this is these people who make the price and who make the deal. At the opposite, I also have walk-in in my store. So people who arrive and these people, they want aggressively to buy or to sell their guitar. So if someone wants to sell a guitar, they will arrive and they will say, okay, I propose you to sell my guitar, whatever is the price. And I will respond by saying, oh, good news. I have a buyer in my computer who wants to buy a guitar for 1500 and the walk-in say okay so i sell my guitar same thing for a buyer walk in so if we understand that we understand how a market works, a market this is just a meeting between buyer and seller people who want to buy or to sell quickly and aggressively or people who want to wait but to be executed at the best price. The best selling price the buying price. So that this is so important, the market design is to make everything efficient to ensure a large number of trade and to respond to the offer and the demand.
SH: Well, thank you. That actually explains quite a bit of it to me that I don't think I ever put together in my own head. And with that idea of a market, then what would a limit order book be?
TM: So a limit order book, if you think about the example I just gave you, is exactly that, but for financial assets, for the price of some company or more sophisticated financial products. So this is a system, a mechanism, when you record preferences of traders, so what we call the limit order, this is people who are willing to sell or to buy a financial asset at a precise price. And this order, so this is a provision of liquidity, this is what we call the market makers, the liquidity providers, they are recording in the financial place. And in the opposite you have aggressive orders, that is investors or people who are taking the liquidity or consuming the liquidity by buying or selling at the proposed price.
And the main difference with a limit order book and my example with the guitar store is that in the limit order book these transactions are made at a very high speed. And when I say it's a very high speed, this is a scale of fraction of second, millisecond, even less than that. So we even speak about, I mean, this is a high percentage of the speed of light, basically. So everything is fast speed, and simultaneous.
SH: So in the world today, in our highly technological, highly connected world, does that mean now that the ability of the technology of a financial asset trading company can almost be more important than their intelligence?
TM: So that's, somehow we are reaching this point. And I'm glad that you asked this question because this is exactly the debate that people have in terms of market is that, what you understand is that in a market to be competitive, you have to propose a price which is competitive. So you will not propose to sell the guitar at 50 grand. It does not work. Nobody will buy that. And conversely, you will not propose to buy it at $1. So what you would like is to propose a price which is competitive enough.
So this is what we call the competition in price which is healthy for the market because the most competitive you are the more investors are arriving. And this difference between the price to buy and to sell an asset this is what we call the spread in terms of technical word. However in limit order books there is also another component which is important is the speed at which you trade, so by trading very fast you will be able to have better deal basically. And there is this kind of what we call a price competition, but also a speed competition.
And now with the increase of AI and the technology with high fiber speed system, the speed of execution, and there is more, I would say, a race in time in the execution rather than a competition in price, especially with high frequency trading. So is it a problem or not? This is the whole purpose of the debate, is that right now with a limit order book, we observe indeed a race in speed. I would not say that it reverse a competition in price, but it takes more and more room in the marketplace. So that is, with our current technological system, a potential problem.
SH: You mentioned in your talk at IMSI that there were some existing flaws within limit order books. Could you tell us about some of them?
TM: Yes, sure. Also, in fact there is a, I will say I will begin with an example from real-life which happened recently in 2010. An example of a flash crash. A flash crash is typically when you have an investor, so remember my example of the guitar store. I have a seller, a worker, arriving in my starting who wants to sell right now 50,000 guitar. So in the time I will absorb all this volume is very long and if the offer is greater than the demand the price will drop quite drastically. So what will happen is that people will react to that. And a natural way to react is to buy the stock because the stock is decreasing and to resell it to other people. And there is this kind of spiral which is induced by this kind of abnormal big volume arriving in the market, which creates a hot potato effect, where every people take the asset and resell it to someone else because the price is decreasing but never stop to decrease. And it create a spiral where it stop complete, I mean a drop of several percentage. So to prevent that, the exchange they have some, I associate that with a firewall, so they just decide to cut the transaction during some time period. A few seconds to just figure out what is happening and put in standby the transaction.
So we see that the notion of time is important because everything is very quick. And the best preventive method we have for that, or at least one of the methods used by the exchange, is to stop the market, to stop the transaction for some time and wait to see what happens and restart the transaction. So that's the first flow of the limit order book. It creates some big market impact and high volatility in very small period of time. And overflows, which is more mechanical and more technical, has been observed by a very famous paper, and which is also the starting point of my research, a paper of Budish, Crampton and Shim, which is the necessity of batch auction to solve inherent flows of limit order.
So the first thing is that in a limit order book, there is always an asymmetry between price at which you will sell an asset and price at which you will buy an asset. This asymmetry is due by the fact that professional of the market, they want to sell at a higher price at the price at which they will buy it because it generates an income. And this is mechanical to the limit order book. You cannot delay that. Another thing that they observe is a breakdown of correlation. So what I mean by that is that on two different market place, the same financial product or the same tracker of a financial product will evolve at the scale of the millisecond in opposite direction. So for example, on one market place, this price will increase and the other one will be stagnant or decrease. It's on the space of 10 milliseconds. They observe that.
So at this scale, so in theory, there is mechanical arbitrage opportunities or the way to make money without any risk by trading on these two different place. And what they have a kit for is basically to delay this instantaneity the execution to just make the market a little bit slower. So by just not executed the trade simultaneously, but by adding a kind of lag basically in the execution. And this is exactly the purpose of an auction market. An auction market, this is opening a market, but do not do any transaction during 100 milliseconds, one minute two minute, and to liquidate as many orders as possible at the end of the auction. So basically the idea is you open the auction and this auction recalls the order of participants or people who want to sell or to buy at specific price, but no execution are made. And you just postpone the execution, the trading, what we call the clearing of the auction at the end of this period. So that's a way to cure the inefficiency of the limit order book.
And it's something which is used by the exchange a lot. CBOE for example, has a full auction market, periodic auction marketplace, whereas during the running day, so from 9:30 to 4-5, they open it, which coexist with limit order book. So that's the idea of an auction system. So with these auction systems, how long should the auction itself take? Again, that's a very good question. I would say that there is no big answer for that, but I can give some example. The first thing is that, Budish, Crampton and Shim advocate for a length of at least 100 milliseconds, which is very small, but remember that people are trading as fast as 3 milliseconds, so 10 milliseconds, I would say, maybe not 3, but really less than 100 milliseconds.
I did a paper, so the first paper I did on this topic was a collaboration with Mathieu Rosenbaum and Paul Jusselin, in which we have some data from Euronext, the equivalent of the S&P for the French market, and dealing with different company of Euronext. So we have seen that an auction should be as long as 10 minutes for very illiquid asset and as short as a few seconds or one minute for very liquid asset. So this is what we observe. And sometimes we have also observed that a duration of zero, and if you understand the duration of zero of an auction, this is a limit order book because the duration of zero, it means that the order is executed simultaneously at this time. Sometimes it's optimal.
So the main conclusion that we have is that one side does not fit all. This is really depending on the data that you have. When you were digging into that data, like these different places where it would be 10 minutes, 100 milliseconds, zero seconds, was there anything that indicated it should be longer or shorter? Was there a big thing that jumped out or a constellation of things? The main fact that we observe is that in terms of volume, the asset which are less traded on the market, has a tendency to require a longer time for the auction. So for the duration of the auction, just to have time to receive enough order to be profitable for the market.
(Ad music)
SH: If you're getting a lot out of the important research shared on this show, there's another University of Chicago podcast network show you should check out. It's called Entitled and it's about human Rights. Co-hosted by lawyers and law School professors Claudia Flores and Tom Ginsburg. Entitled explores the stories around why rights matter and what's the matter with rights.
(Music Stops
SH: Can you tell me a little bit about the model when you've been doing work investigating this?
TM: Yes, so sure. So the model is that the idea, more precisely, of an auction is that at time zero, so at an initial time, an exchange decides to open an auction. And during this auction, the exchange is receiving order from both people who wants to buy or sell a fixed volume at a price, at a preferred price, or better. So for example, I will say, I'm willing to buy 100,000 assets if the price is lower than 100, something like that.
So this is a kind of order which is recorded. And you have also people who just have an interest to buy or sell whatever is the price fixed by the auction at a specific volume. And the auction is receiving this order. So mathematically, this is counting process. So this is just you count the number of order arriving continuously in time. And at the end of this period, you close the auction and you try to execute as much trade as possible.
So the main challenge is to fix correctly a price at which you will trade the asset. So this is what we call the clearing rule. The clearing price has to be fixed such that you have the highest number of transactions possible. And you have to fix also, optimally, the duration of the auction to improve the market quality. And there is several ways to define the market quality.
So the way we have chosen with Mathieu and Paul was to say that the price of the auction that we fix at the end has to be closed enough to a benchmark price, what we call the efficient price, which can correspond to the perfect price in a perfect word, whereas there is a full equilibrium between supply and demand. And after I have also presented extension of this work, so I don't know if we can go to this direction.
SH: I was going to ask if your work has had any further progress. So please.
TM: Yes, exactly. So that's exactly the point in that. I think you have understood that I'm not completely categorical on the benefit of this system comparing to an over one.
I think this is more complicated than that. And I went to a conference with Mathieu in Iceland, organized by the Bank of Iceland to present this work. And one of the participants was Philippe Guillot, who is the financial market director at the French market authorities equivalent of the SEC. And he approached me and Mathieu by saying that there is a way to create a model to keep the best of both worlds, the best of the limit order book and the best of an auction market,
because a limit order book is also convenient when you want to execute it instantaneously. You cannot wait your position. You want to sell or to buy things right now. So you can just alternate between continuous session of the limit order book and have the possibility to trigger an auction when you need to trigger it.
So we have created with Mathieu, Philippe and one of my former PhD student, Joffrey Derchu, a new mechanism that we have called ahead for ad hoc electronic auction design, which consists into dealing on a limit order book. So with this kind of instantaneous execution, depending on the price set by market maker. But where investors, so if you remember, this is my walk in arriving in my store, sending aggressive order, have the possibility when they want to trigger an auction to say to the exchange, right now, I'm not satisfied with the limit order book. There is things that I don't like. There is not enough liquidity. So please trigger an auction because I will be more likely to liquidate or to buy the asset or to liquidate my position.
Of course, it has a price because the action will not do that for free. They will say, you can do it, but you have to commit to put a volume big enough in this auction so that there is enough liquidity to trigger this auction. And this kind of sequence between continuous session and auction, giving more power to investor, has shown that it was an optimal way, which was basically always optimal comparing to a limit order book and an auction model for the market quality. So for increasing the number of trade and reducing the spread that is the fair price of an asset and the price at which an asset is indeed traded.
SH: You were here at IMSI as a part of a program around uncertainty quantification. It does sound like these markets are very uncertain things. So what is the sort of idea of uncertainty and is your role more to try to make it more certain or just try to be okay with the uncertainty but in a logical way?
TM: Yeah. Yeah, so very good question. I will respond both, but right now, in fact, that's very, I did, I mean, of course, I have continued to work a lot on this topic.
So another work I did later with Joffery and Mathieu was to deal with this uncertainty. For example, you may be uncertain about the price that other participants proposed. So you may have different signal, different estimation of characteristic and we have dealt with this uncertainty to create a market with that. So what does it exist on equilibrium? This is not even clear that there exists a good price to fix to ensure the maximum number of transactions. And what we have seen is that something which is applied in practice and that exchange are doing is to add incentives to people to enter in your auction market because of this uncertainty, because they don't really know what to expect. And this is what they call a rebate.
So what is a rebate? You have, if you remember people who aggressively trade an asset on the market, they say, I want to buy or sell. These people pay something to the exchange because the exchange is a marketplace. So you pay a commission fees. And the notion of rebates, this is to redistribute these fees among more sophisticated trader, people who want to buy or to sell at a specific price in the auction, if it's better or worse, depending on the position. And they receive money for that. They receive a kind of incentive, a redistribution of the fees to incentivize them to enter in this auction despite the fact that there is some uncertainty on the time of the execution, the uncertainty of the characteristic of the other participant. And this is an efficient way to deal with these uncertainties to create some incentives and to bring liquidity in your market.
SH: When you were talking about how to measure these different systems, you mentioned the
idea of measuring against this perfect, efficient price. Now I imagine that some people, myself included, might think, well, if you can figure out the perfect, efficient price, why don't you just use it? So is this something you can only come to post facto? Can you only see it after everything has happened?
TM: So the fact is that you can update your belief depending on what you think is a good price.
Because what can happen is that if you have several auctions or several limit order book, you see what is happening and you say, okay, so I consider a lot of auction. I see that the clearing price is that.
So the fair price should be the mean of all these prices. And you continue this aspect with new auction and you are looking, okay, so now the fair price should be that. So you can indeed update your belief. So in fact, I'm not working at all right now on it, but this is in my to-do list.
This is to just create a learning model and how to learn basically the characteristics of this fair price.So can you learn the volatility? Can you learn different characteristics and frequency of arrival or forwarder in this market with it? So yes, that's something which I think is possible and fascinating.
SH: I just have one last question. I mean, there's so much more we could dive into, but trying to respect both the listeners' and your time. So this last question, like, did your time coming to Chicago and to IMSI, did that help at all? Did you get some new collaborations? Like what was your experience?
TM: Yes, indeed. And again, this is very, it's amazing you asked this question because I went to Chicago, I do my talk and after my talk, I speak with several researchers and including a professor Sergey Nadolci, who is at the IIT, the IIT Institute of Technology. And I see some similarities in my work and what he's doing. And I will go back in March to visit him and to just start some collaboration on this fascinating topic.
So yes, it has helped a lot. I mean, this is something that I really want to emphasize because it's just nice to present your work to colleagues and to bring new ideas to improve what you did.
So that's the main point of research. Well, that is, I'm very, very happy to hear it.
SH: Thibaut, thank you so much for your time.
TM: Thank you so much, Sam.
(Outro Music)
SH: As always, don’t forget to check out our show notes in the podcast description for more about Thibaut’s research and to watch his talk.
And if you like the podcast, subscribe to the show and give us a review on apple podcast or spotify or wherever you listen.
By rating and reviewing the show, you really help spread the word about Carry the Two so that other listeners can discover the podcast.
And for more on the math research being shared at IMSI, be sure to check us out online at our homepage: IMSI dot institute. We’re also on twitter at IMSI underscore institute, as well as instagram at IMSI dot institute!
Do you have any mathematical or statistical questions? Maybe you have an idea for a story on how mathematics and statistics connect with the world around us.
Send us an email with your idea!
You can send your feedback, ideas, and more to sam AT IMSI dot institute. That’s S A M at I M S I dot institute.
We also want to thank Blue Dot Sessions for our Music.
Lastly, Carry the Two is made possible by the Institute for Mathematical and Statistical Innovation, located on the gorgeous campus of the University of Chicago. We are supported by the National Science Foundation and the University of Chicago.
