An Updating AMM to Bootstrap Liquidity in a Stable Manner | Neel Tiruviluamala - Forte

[Music] about Forte um Forte creates onchain and offchain tools that allow developers to build market economies around their assets and we serve developers across the entire web3 ecosystem um those working with real world assets and stable coins defi platforms gaming Studios ranging from independent developers to more established Studios like Zinga and Jam City so what have we built uh we've built an amm that doesn't require upfront collateral the option to configure price stability by tuning parameters instead of by adding Capital we in our mechanism allow for Price Discovery beyond that of a fixed bonding curve and we allow for smart fees that incentivize early participants okay so we're going to talk about how all that works uh first we'll start with some of the challenges of managing liquidity and limit limit order books in amm during bootstrapping we will talk a little bit about our design decisions and solving those challenges we'll go over some of the properties of what we've built which is the albc or the adjustable linear token bonding curve and all that will make sense uh we'll go through some simulations so you can see how that works and we'll launch our eth Denver 2025 trading game so if for no other reason stick around for a chance to win one eth okay so let's go over our motivation in designing what we designed let's start by defining what an order book is many of you know know but just for completeness um we're going to focus on the supply side of the order book in this talk so imagine we have n suppliers each one holding one token and each one having a price at which they're wanting to sell that token so for example I might want to sell my token at $10 um if I stick in $113 into this quantity function it'll count all the suppliers for whom you know $13 is an acceptable selling price which in this example would include me uh so it's a sum of indicator functions a graphical representation might be clearer to people um you can see that at a price of 12 in this order book uh there's one person willing to sell at a price of 37 there are four people willing to sell at a price of 40 there's B for people willing to sell it takes raising the price to 55 to get that last person okay so we wanted to start by understanding some of the empirical properties of order books in the wild and this has been a area of research and Mark market microstructure for decades so this paper is two decades old uh NES and Shelt torp studied companies in the Oslo Stock Exchange and they wanted to understand how the slope of the limit order book was related to other properties so there are two companies here one company is a an established 50,000 employee company and the other company here is an upand cominging 100 employee company so I don't know maybe Take 5 Seconds to think about which is which or which one you think is which okay well it turns out that the one on the left on your left is the more established company it has a deeper order book and one on the right is the upand cominging company has a gentler sloped order book and researchers these researchers and other researchers after them found that the slope of the order book can tell you a great deal about upcoming volatility in the in the market and also the dispersion of about the dispersion of beliefs of prices of analysts so on the right analysts were more divided over the correct price whereas on the left analysts honed in more on a on a price um so generally speaking a gentler order book slope is correlated with an increased dispersion of beliefs about the price and increased volatility and trading activity um in the real world given assets liquidity profile uh including its slope constantly is adjusting right to arriving trades and order book is alive in the real world and bootstrapping kind of involves managing liquidity in a way that we intelligently adjust that slope so you might ask okay what about automated market makers this is defi what about constant function market makers okay so here is an example of two constant product market makers uh one has more liquidity than the other again maybe Take 5 Seconds to think about which one has more liquidity so the orange one does the orange one has a higher liquidity parameter than the blue um so it's a deeper pool and again a deeper liquidity pool corresponds to a high order book slope and you know Less Price impact with each trade but what's interesting about this is that these sort of slopes are formulaically determined by the constant product formula and the only way to update them is at the behest of liquidity providers coming online so for bootstrapping this is kind of challenging right you have to use either a limit order book or an amm uh limit order book encodes a very complex landscape of beliefs it we know it's computationally expensive and if you can get yourself listed on a centralized exchange it's financially expensive you also potentially have to pay market makers um on the other hand amm give you a nice programmatic way of determining your liquidity Contour but the way it gets updated is dependent on third party liquidity providers and when you're first starting it sort of maybe hard to align your incentives in a way that liquidity providers make the trading experience good so our goal is to sort of solve this problem and offer an evolving yet simple liquidity landscape for bootstrapping liquidity okay so what are some of our design decisions so we we we thought okay what if we did have a well- behaved collection of of suppliers what would they do well they wouldn't sort of like pull their collateral and act in it erratic ways and they would also try to coordinate in such a way that the limit order book was adapting to what the market was what signals the market was providing and this is what the albc in our our view achieves okay so what are the axioms that determine the behavior of the albc so one there's the continuity of the order book in other words this gives us a well-defined way of selling fractional quantities of goods it's just the Natural Area here right depicted here if you if you changed and wanted to buy 3.5 or 2.7 you could do any of those things by using the corresponding area why do I say it's natural well imagine you wanted to move from the discret Supply World to The Continuous Supply World what you could do is you could add more and more suppliers but they're sort of providing fractions of tokens at different prices and in the limit you'll get this continuous continuous World okay uh another Axiom is we always want our order book to be linear so this is constantly updating but it's always a line that's a simple Axiom right okay our third Axiom is collateral conservation so these suppliers that are basically selling they don't pull any of the collateral from the system and they wait around to buy back right um and you can see this visualized here um the area of this trapezoid if we sort of update the order book to this the steeper line or the shallower line here the area stays the same you can see that kind of by where the midpoints cross and the most interesting update rule is the slope update rule how exactly do we update the slope of the order book well we update it linearly in the size of the trade and how aggressively updated is a parameter that we give developers access to so it's this W constant and the idea would be that every time a large trade comes in or a small trade comes in the slope of the order book gets deeper and so so when the outstanding Supply is large your trading experience is less volatile something interesting that arises from that Axiom is path independence of slope so what this means is you get some telescoping Ser series here if you look at the left RN is the slope after n updates if you look at the right you see that it's only depend dependent on Z right which is the total outstanding Supply so that's really a nice property it lets you say okay I my price impact is just going to be a function of my outstanding Supply and that sort of differentiates us from things like you know constant function market makers because for them price is a function a deterministic function of outstanding Supply we are a little bit more General than that okay so let's illustrate the axioms through an example order flow so we have here is imagine someone buying seven units right the continuity axium says okay the cost of buying seven units is this area which is $52.32 fixed right so this is the collateral conservation Axiom the slope update Axiom really nails down which of these slopes we pick so in this case the developer has chosen a stability parameter of Wal 17th and that totally determines that we're going to move from the blue line to this green line and you might be asking okay wait a minute what happens to these sellers um after purchase are made from them well they wait around with this collateral looking to buy back to make the trading experience smooth for your ecosystem and so you can see two parts of this curve the blue part represents previous sellers who are now buyers and if you want to visualize that in the order book world just do a vertical flipping and you see the V on the right so again our mechanism is just a limiting order book that has nice simple properties in terms of how it evolves so notes on the axioms uh these these axioms you can probably feel fully determine the market making mechanism and the decision to proportionally increased slope with the trade size is gear towards projects who want their prices to stabilize in a healthy way but we have other designs in the pipeline for more risky projects as well okay so a lot of people are more used to the sort of inverse inverse look right where X has quantity and Y has price that's sort of the standard token bonding curve world so let's just look at our mechanism in standard token bonding curve world it's just an updated bonding curve um so in this case you can see that the current spot price is eight okay so let's look at a trade in in token bonding curve curve world so imagine that the supply outstanding Supply used to be four someone comes to the market maker and buys two right what happens well technically they're going to move up this original blue line from 4 to 6 right calculate that area they're going to pay that amount and then the entire collateral in the system is conserved as you can see by this midpoint Crossing and this red curve is the new updated linear bonding curve so what then happens when someone tries to sell back those two tokens we end back at xal 4 or qal 4 and something interesting happens we don't end at the same price right we don't have the property that price is a deterministic function of outstanding Supply instead though we have the property that slope is so you can see the SL slope has remained constant and in fact the line has risen a little bit and that is a very nice property of our albc which encodes this feature called smart fees and this sort of differential area between these two lines of the same slope is basically acing to the community it's acing to the early token holders to the project own owner to early liquidity providers which that's V2 we haven't introduced liquidity providers yet but we will in the month of March so stay tuned for that um you might be asking I'm used to seeing things in amm land uh what what are all these token bonding curves well there's an equivalent story in amm land um you basically can take a token bonding curve integrate it to go from price to quantity space and then do a horizontal flipping on the x-axis to go from outstanding token to in standing token right because amm sort of are what's in my balance or what's in my wallet Centric right so it's it there's some mathematical transformation that you can do and all we have is an updating amm that's principally updating based on Market information okay so what are some properties of this price monotonicity this is an obvious one you want when people buy things the price should go up it might seem obvious it's not as obvious because the line's updating here's a visual so you can see look sure prices move up on a line but the line isn't staying the same uh we have a proof in our white paper if you want to see it but you can see the price moves up as people buy more and more token something really interesting emerges as a mathematical object the limiting TBC is what we call it and it's basically if you make very very small trades this system degenerates to a single sort of logarithmic token bonding curve now it's never in practice going to be this because you can never make INF asmal trades in our system but if you wanted to think about what was happening you'd be moving around this logarithmic token bonding curve if you made very very small trades but in practice this curve is drifting up every trade it's drifting up right and that's capturing collateral that can be shared among early participants of the ecosystem it's also making us have some nice me resistance properties so yeah the upward drifting limiting TBC we talk more about this in our white paper it has a lot of nice implications it sort of locks in collateral um it also makes there be a cost for things like wash trading right so sandwich attacks where you try to you know put in that buy order and then sort of put in a sell order afterward there's a cost and that cost is heris related to how much that um limiting TBC Rises okay so you know as an example we have bounded maximum extractable value fix a trade size of Q and imagine a sandwich attacker of size s trying to come in buy s wait for your trade sell s in something like a constant product Market maker the profit is unbounded I mean it's not practically unbounded because of of various you know slippage features and things like this but from a mathematical standpoint it's unbounded in our model the profit is bounded there's a maximum trade size that's profitable for the sandwich attacker and after a certain point it actually they lose money right and this again links to theistic of the limiting TBC Rising gradually trade by trade so let's take a look at some simulations first how does this practically work it's actually quite simple you're going to deposit some of your tokens into our amm you're going to choose a collateral token as well so let's just say usdc you're going to set a starting price and a Target price on a token distribution marker so you might say okay after 10% of the tokens are sold I want the price to be this right at least you're going to set a stability parameter we kind of touched upon it earlier and you're going to set a reward parameter for liquidity providers and the liquidity provider um add-on is scheduled for completion in March 2025 we're really excited about it and that's it it's really simple so we're going to compare the albc with a fixed price range Unis swap V3 pool no liquidity providers right so you're sort of Sting a low price a high price and a liquidity parameter we're sort of Apples to Apples tuning Our albc and then we're piping in five trade paths into both of them to see what happens so let's look at a slightly bigger picture here um so let's look at this blue trade path this blue trade path corresponds to this blue trade path the second one is happening in the univ V3 single range position um and what do you notice about the trade PS in the univ V3 position yeah they get to the high price at different times but they always get to the same top price right there's no price Discovery if you have a single V3 position um you you're not able to change the low and high prices unless liquidity providers come online whereas in our system without liquidity providers there's still going to be price Discovery and the more trading there is in the system the higher the final price will be so that's an interesting feature another thing to note notice how the stability profile looks for a univ V3 position starts off really stable then gets more volatile right as as the outstanding Supply increases now now that's supposed to be tempered by the fact that liquidity providers are coming online but again if you can't incentivize liquidity providers properly at the beginning that's kind of risky in our system you start off with more price Discovery and then the price path stabilizes okay so in conclusion we've introduced the adjustable linear token bonding curve the albc a mechanism for bootstrapping liquidity while maintaining Market stability um and it's supposed to replicate the real world know sort of living aspects of an order book right without requiring thirdparty liquidity or collateral upfront um slope is path independent as a function of outstanding Supply and the system naturally rewards early participants which hopefully ensures a sustainable ecosystem thank you so much we have a forte Booth uh please please visit us on Thursday or Friday or email me at neil. real quick to plug our trading game um you can win an eth basically go to that QR code um get you know use the faucet to get your tokens and then start trading and people with the most amounts of one of two tokens will each win one eth um and we'd love to have lots of activity there here are some references flashing them so people can see them and if you want to learn more about Forte please visit the website thank you so much