Cross-Chain Arbitrage

Transcript

[Music] Okay. Hello. Hello. Hello. So I give a presentation on crosschain arbitrage. Um that's um first of all a joint project with a bunch of people at Tio Munich at flashbots at um Lisbon University and I link it a bit to questions of Ethereum uh interoperability.

Okay. So how are prices determined in sort of the current um um design of Ethereum and how is the market structure currently? I mean the the general idea that people have is we have dexes but sort of price discovery is not really happening on dexes right what is the reason there is not as much liquidity as on sexes and there is um sort of a delay right so you have not always a price determined at each point in time so sexes are faster have deeper liquidity those two things are of course related to each other and so we expect that more often new information is

priced in sex rather than a than in a DEX, right? And then sort of the dexes they sync to to the sex, right? And then so you have have sort of a price update to uh the external world offchain. Um we could imagine a different world where we have price discovery sort of between dexes, right? So you have different dexes on different chains maybe or different dexes on the same chain and they might also have different liquidity and different um ways of making a market but somehow the collective of those dexes they might eventually incorporate information in parfully. Okay. So that would be another way of doing it and that is actually not

a hypothetical but in some sense that is a reality but sort of on the very niche of of Ethereum or in the Ethereum ecosystem. So you have some situations where we have sort of price discovery on uh decentralized exchanges and that is mostly very longtail kind of um assets and we what we do in this projects we want to look at this longtail of assets see how people arbitrage between them between different dexes on different domains on different um blockchains L2s and L ones and maybe that gives us an insight of how sort of a fragmented multi-chain world would look in the

future. Or maybe it's just an interesting artifact. Maybe sort of we solve interoperability. Maybe there will be one chain that will rule them all. We don't have this fragmentation. We don't have have this problems of sort of syncing between different domains. And then maybe it's was just a beautiful exercise to study a bunch of meme coins. So either way, um I think it's cool. So what did you do? So we we and by we I mean mostly Burak is is the leading uh driver on the data side of this project. He created or we created a data set studying different um chains EVM chains nine in total and we collected one year of data and we tried to figure out uh things situations that we could classify

as um crosschain arbitrage. So one leg of the trade was done on one chain and the other leg of the train was uh trade was done on a different chain. Maybe there was bridging in between or maybe people held inventory on both chains. But we sort of tried to match traits to uh the same entity on different chains and that gives us a universe of considerable size. So you get 242,000 trades in total with um well mediumsized volume 868 million and let us look at some nice graphs. So here's how it looks like. So we studied these eight um eight

different chains and the period is was from um 2023 September to 2024 September. One nice thing is in between there was Dun which had sort of this nice effect that it decreased fees um on Ethereum mainet. So it made things arbitrageable that were too costly before that that led to certain spike in the activity on Ethereum uh leading um cross domain arbitrage. Okay that's a data set that's a volume so around three $3 million. I mean in the total scheme of things it's might might be little right if you think about uh more like uh um other other portions of uh me or arbitrage but it's

a considerable still considerable size data set I think so what what can we tell about it first of all uh we've tried to correlate it with volume and I think that is true for any kind of me extraction that it's more profitable on average if there is higher um volatility and there's correlation between arbitrage volume and volatility it's dampened a bit because those things are really really really longtail things what do I mean by longtail so um why is price discovery happening onchain rather than offchain either they are not even listed on sexes or there's just that happens very very often actually there are things that are just don't have good liquidity or execution on a sex right so

very very low uh liquidity on a sex and so we Um people trade on dexes primarily. Um what are those things there? I mean either the two two classes basically sort of meme coinish or very longtail uh experimental projects right with uh low market cap and then low market cap synthetic assets like synthetic versions of dollars, synthetic versions of of Bitcoin and so on. So these are the top top 10 tickers. I think there's a euro stable coins. The bitcoin is an aggregate of different sort of versions of bitcoin. We have omniat which is a cat token on omni

chain. Uh we have a non-tradable token like these kind of things right okay um non-playable to coin NPC. Okay. Um so how should we think about arbitrage extraction? So how is arbitrage extraction different if you have longtail assets? So first of all there's an liquidity effect. I don't know whether you have heard about this entire discussion around lever which is sort of prominent among professors but maybe not so much in the community. So people have studied sort of the effect of slippage on arbitrage, right? And so you can adjust the standard theory of of of this um um effect of arbitrage, the

slippage effect, right? The effect that there's limited u liquidity on those dexes. And so you basically get a smaller size arbitrage. So there's this shading factor, this x1 prime divided by x2 prime. So the relative fraction of the um or the relative fraction of the liquidity on the two venues matters for the amount of arbitrage. First of all, there's less of it and it depends on the imbalance in liquidity. Okay, so that's um how we think about it. But there that's a liquidity cost, right? So the cost that there's limited liquidity which makes arbitrage more costly. There are other costs and primarily in our data sets cost is um cost of bridging.

If you really do this arbitrage through bridging using a bridge or you have to maintain inventory and if you have to maintain inventory on different um domains for very longtail risky assets that's very costly to you. So the one thing that we did on the theory side is we tried to have a very stylized um model of this to try to have some kind of um comparison between when does it pay off to to bridge uh and when does it pay off to have inventory right inventory trading is just this thing right so you maintain some I don't know um NPC token on decks on arbitum and he maintains an MPC token on decks on Ethereum and you sell on the arbitrum

and you buy on um on the Ethereum chain, right? That is instant settlement, almost instant settlement, right? There's a maybe difference in how fast those chains uh settle, but you have to maintain inventory. So, it tends to be more costly for that thing for that reason. If you do bridging then basically what you have to do is you have the token you trade it on on on arbitrum then you have to bridge it back to to Ethereum using u maybe native bridge or having uh some um some other kind of bridge solution right and then you trade it back and during that time passes right this is very long time to settlement and you have price uncertainty so it might be risky to do

these kind of things okay so that's the basic thing you have to think about in these kind of things. Um we have then a stylist model where you basically assume okay there sometimes just out of a sun arbitrage opportunities arise sort of through noise trading or for whatever reason somebody wants to um trade these tokens and they tend to sort of be quite you know um they don't compensate for the risk in the sense that the price tends to drift negatively. Okay, so that is our model assumption. So it applies more like to this longtail assets than it applies to to the um to to the synthetic assets. Okay, if you have that then you can assume okay some some

arrival rate of those arbitrage opportunities and then you can do some math around that. So you can uh think about okay um if those arbitrage opportunities arrive more frequently maybe it makes sense to maintain an inventory right but if those arbitrage uh frequency uh opportunities don't arrive that frequ frequently you might think about bridging it because maybe the price doesn't move anyway too much right and there are less opportunity okay benchmark is something like this so if you have a frictionless ideal world that I talked about before also abstracting away from the liquidity effect you have um some some profit function um that is sort of this nicely

convexed uh shaped profit of arbitrage okay but now we have a a cost it comes in two ways and let me first of all talk about the bridging cost so the bridging cost is first of all the cost of using that bridge right that costs you a fee but also you have the price uncertainty. So the price moves might move against you while you're bridging, right? Quite naturally might also move in your favor. Um but it might move against you and that in introduces an implicit cost, right? The cost comes from the fact that you once you've completed the bridge basically your arbitrage opportunity might have disappeared, right? That is a risk and

you have to factor that in. Um so you basically um get a sort of difference of two two two um two two quadratics and you get um a cost that is increasing marginally in the time um that uh that you need to bridge the asset. Okay, that's that's plausible I think plausible model of bridging. So let's compare that also to to inventory. So what's what is the cost of inventory? It's basically the risk cost or also the opportunity cost of holding NPC token or whatever token was in this data set. Right? So you have an opportunity cost and you have a cost of or risk of holding this this asset. You might not be able to sell it or you

might not be in eventually or it might depreciate in value and so on. So basically you have a constant flow cost of holding this asset, right? So you keep it in inventory and the flow cost always in each period it is costly to hold the inventory. And then you have a nice trade-off right you have this formula where you basically compare sort of the expectation of of uh of this um this uh this price uh depreciation of the token versus the frequency of um arrivals of of this arbitrage opportunities. And depending on this you get sort of this mu divided by lambda formula right so the drift um so the price drift relative to the frequency of

opportunity matters for the value that cure and then you have an inequality then you compare right so in principle we have a theory of inventory where this bridge with is sort of straightforward tells you what you would expect it to tell you right the longer it takes to bridge the more costly it is to bridge the more you go for inventory If inventory is very costly to hold because those things are volatile or those things are depreciation depreciating in expectation or they have very low liquidity so you might not get rid of them then you uh refrain from holding inventory. Okay, that's theory.

How does it relate to empirics? And we've also looked into our data set. So first of all there are really arbitrage substantial amount of arbitrage where people use bridges in arbitrageing between these very longtail t token. So they really takes this very long time to to complete or finish the arbitrage 24 uh 2 milliseconds uh in median and you know sort of uh inventory arbitrage by definition is almost immediate uh n um 9 seconds settlement median. Did I say millconds before? Everything is seconds.

Everything is slow in this in this project. Everything is slow. Very slow. Okay. Um majority of course is inventory. Um or not of course it happens to be approximately 2/3s in our data set is inventory based arbitrage and the rest uh you have a bridging transaction in between. There is heterogeneity in bridging times and that and bridging cost and that also gives a heterogeneity in what people do. Right? So there's a difference between um native bridges in in bridging time and these kind of other bridging solutions like wormhole etc. um where where we have usually shorter bridging times and well there's this

sort of outlier there was one searcher very prominently um doing arbitrage on Ethereum and polygon that gives this spike here in in my data. Okay. Um so there's a division between inventory and native versus multi-chain bridging or you know non-native bridging solutions I would should rather say. So the majority were non-native bridging solution but some were done through the native bridge. Okay. So that's that's about this cost and that reflects also in the way people arbitrage these things. Okay. How does the market look like?

It's generally true right that um searching or any form of arbitrage there's um this kind of burto distribution right so few people make all of this all of the gains sort of this sort of uh almost winner takes all game right because of of um of of the basically skill factor involved in that to some degree we also have this kind of um basically few um sort of stylus factor of few searchers extracting most of these uh arbitrage opportunities. So there there are these top addresses that uh account for almost 50% and then during dingun almost 75% of this total

arbitrage volume. Okay, final thing I wanted to do is link sort of these stylus facts and theoretical findings to the broader picture. So this is is a niche as I said right it's a niche it's sort of a beautiful niche of beautiful weird longtail tokens with a funny names and maybe we should ignore that it's also like I mean for finance you know for finance proportion it's not not a large market but there could be a potential world where we have fragmented liquidity we we have multiple chains and cross domain arbitrage would become more and more increasingly more important important right so there could be such

world on the other hand I mean tech tries to to solve some of the frictions that I talked about we should have maybe shorter bridges we should have other interoperability solutions we have cle should have clever ways to route liquidity across different venues on different chains so maybe we can reduce the friction and the cost in um in in these kind of crosschain markets right so those are the two forces and I I think one takeaway of of the paper is if we are in this hypothetical world where we have basically a lot of growth and and uh a lot of fragmentation of liquidity and sort of the technology

doesn't follow that I don't know which you know probability you assign to that world I would assign to it probability lower than 50% but it's it's a possible world then you would have scale economies in searching what is the reason because for this fact that there is a premium of of having capital right so you can maintain inventory there's a premium on um on on being clever in managing risk and all of these factors should be maybe a vector of centralization okay but you can also take it as just sort of a documentation of a weird beautiful world that might disappear in

the future. Okay. Advertisement I promised to do. There are jobs at Flashbots. Scan the bot. And there's a preprint down there. You see the all the authors. And there's another preprint for the theory folks in in the audience that care about arbitrage calculations with brown emotions. Those people might exist. But the other paper is more interesting with a dinosaur, right? That contains all the data. I was one minute too fast. [Applause] [Music]