Enabling a rate discovery on-chain?

Transcript

before I explain why we couldn't use existing rate model that are using over characterized Landing I will just do a super super quick recap on how the rates are set in overcorder transplanting so if you consider Ade for instance the boring rates are set algorithmically based on demand and Supply in the pool the algorithm are calibrated in order to manage liquidity risk and optimize utilization so the boring rate is not representative of the financial health of the board but rather representative of liquidity risk and Market risk which is fine for overcollatories Lending I guess you know where I'm going but

when you consider over characterized lending the extent to which they enable true borrowing rain agent gets into a position of net depth is limited and it creates a gap with 35 offering we wanted to address that Gap but in order to bridge that Gap we had to reduce the collateral constraint the thing is that when you remove the collateral constraint you introduce a default risk and then a challenge arrives in determining how to set a boring rate that is representative of default risk without relying on a third party or without adding an arbitrary with premium to existing rate model we have set up our own methodology for that that I'm very happy to share with

you today so let's dive in and have a look at Atlantis Landing ports in order to enable Ray discovery on Atlantis we have set up what we call an interest rate order book by the creation of ticks a tick is just a subset of the funds within the Boris pool that corresponds to a specific lending rate so when an LP come into Atlantis they choose the the boring entity that they want to lend to and they also choose their lending rate and then their lending pools are composed of multiple ticks um the the choice of the of their lending race is based on their own credit risk assessment uh on in on their own evaluation of the Boris default

probability they can update their rate as long as they want and as long as their position is not borrowed and then the boring rate is simply the lowest volume weighted average rate that corresponds to the amount board so when a borrower happens on Atlantis the smart contract will just iterate over the different ticks until the target borrowed amount is reached so all this sounds like interesting in theory but we wanted to evaluate our rate Discovery process and we wanted to modalize our rate discovery we before being able to evaluate we had to Define our objectives so when you consider like um auction process usually a common something that is commonly used in order

to evaluate um auction is to look at the revenue of the auctioneers so for us it would be the boring entity we decided to fix different a bit different objectives and we designed decided to fix two objectives the first one was convergence is Atlantis boring right a fair representation of The Border's default probability that is assessed by the market and second we wanted to evaluate the speed of convergence there's a model incentivized transparency in other words there's the speed of convergence improve when the Boris provides more information about their Financial Health so let's move to the fun part register modeling and evaluation part

in order to represent how borrower takes place on on Atlantis as bids are open because they open on chain we came out with the conclusion that the most appropriate tool was to use Game Theory our game is simply composed of two type of players obviously they are the lenders then can perform three action they can deposit not deposit and update their rate on their existing position and another player is obviously the board the board can either borrow or not borrow the game start at the opening of the pool and the start of what we call the book building phase that very depending on our product that period is limited in time and during that period lenders can freely deposit it update their rate or

withdraw their position if they like at the end of that period the borrower makes the decision to either borrow and not or not borrow when deciding which action to perform in the game The Players want to maximize their utility function so it just is simply their payoff so let's say that a company is looking to borrow a certain amount K and they expect to make a certain revenue on their on their boring funds you can call it the ROI so if RB is the boring rate then the Boris payoff is quite simple it's simply K times 0i minus the the cost of borrowing and if they decide not to borrow their payoff

is simply zero in practice we introduce a penalty fee and there's a cost of lots of opportunity in case they're not borrowed but for Simplicity I will just say it's zero um from from the utility function it's quite easy to see that there's a rate above there's a boring rate above which the borrower will likely not borrow because it's when the utility becomes negative and then he's just better off not borrowing from the pool we can call that rate the reserve rate and it's the highest rate above which they will not borrow and that's something that we ask our our players are Boris to publicly declare to all participants so that the

in order to ease the rate Discovery process for Simplicity we can say it's equal to the ri when you go to The Landing side it's a bit different so each lender has its own evaluation of the borrower's default probability we call it P it's based on their own evaluation the risk your own risk aversion Etc and um when deciding whether to deposit into the pool and the choice of lending rate they must also have a look at their utility function um in case so let's say that a borrower wants to borrow one sorry A lender wants to deposit D I don't think R in case the position gets borrowed then he will

receive D times r with a probability of 1 minus P it just corresponds to the interest that remain on the position and if and he expects to receive actually to lose his deposit with a probability of P um in case of default do you so the utility function when the Boris when the position is borrowed is simply the weighted sum of those two so that's something that's what you can see like I was expecting this to be lower because I used to show anything but yeah it's uh but you can see near the equal sign so it's just the sum of those two um similarly to the boring side we can see that there's a

that is a great below which the lender will not be will be willing to lend because this utility function on the right becomes negative and he's just better off he would just be better off not depositing into the pool or um because his payoff would be Simply Be zero we call that um rate the lowest rate at which they're willing to land we call it R star and we can say that it corresponds to the lender's true evaluation um on the full variation of the of the boring rate when deciding which action to perform in the game the lender must also consider their their ability for their position

to get bored because as you can see from there they will only get the the utility on the right if their position is not is borrowed if it's not borrowed they will they will just have a payoff of zero in order for the position to be borrowed two conditions must be met first the boring rate must be lower than the ROI because otherwise as from as from what we saw from the last Slide the borrower will not borrow and second the cumulative volumetric arm might be lower than K because otherwise position that were placed at lower lending rates will get borrowed instead now that we have set up all the rules of

our game we are ready to modulize our game that's the setup that we use we decided to consider two borrowers with the exact same intrinsic default probability so they have the same default risk but they have they differ in the amount of information that they are willing to provide to the participant the Explorer a that provides an extensive amount of information and this borrower beta provides little limited amount of information regarding the lenders the deposit any amount one after the other and they can freely update their rates and then the choice of lending rates are made in order to optimize them to maximize the utility function that we saw um we use the same distribution of P and

R star among lenders for both borrowers because both borrower have the same default risk but we modelize different bidding behaviors to account for increased reservation for a borrower B and lower instance in T4 bar a and by running the simulation we observe the following so in that case there was the borrower were looking to borrow 100K and they declare a reserve rate of 15 and the average or Star among lenders was a 9.5 we can see that at the beginning when the TDL in the pool is lower than the target per the amount um obviously the boring rate corresponds to the reserve rate because there's no incentive for land lenders to lower

their rate because they know for sure their their position is get is going to get borrowed at 15 percent when there's more TV on in the pool we observe that the boring rate sharply declines until they reach the average air star on lenders that corresponds to our Dr star so we observe convergence of the boring rate to a rate that is representative of the market assessment of the default probability we also can see that the Border a is able to achieve now too boring rate at the first to paste and thus it's able to borrow the cheaper rate so by providing more information about the Financial Health they are able to achieve a

cheaper rate even if they both converge to the same red Indian but as a drawback we see that the required TDL amount compared to the Target loan amount must be very high to a low convergence so that's an issue in order to tackle the TDL amount issue we decided to reproduce our previous moisturization and introduce uncertainty in the amount to be borrowed using a Bayesian model so lenders associate the probability of occurrence to several like possible borrowed amount and um and they are not the exact amount to be borrowed is not fixed for sure by running the exact simulation the

exercise simulation we observe and improve Capital efficiency compared with previous model so in blue that's the previous model and in Orange it's the Bayesian model and we see that by adding and sentencing in the amount borrowed we are able to reach the true boring rate at a faster pace that's why we do an Atlantis amount to be bored are cap but they're not fixed so we are providing revolving credit lines with a certain credit limit but lenders are unaware of how much exactly the board will borrow in the end disincentivized lenders to reveal their true valuation to guarantee matching so with the explore Atlantis solution to

avoid centralized rate setting or arbitrary risk premium and a low unknown chain rate Discovery we see that our decentralized rate Discovery Model enable convergence of a borrowing rate that is representative of the market assessment of the default probability and we see that we observe an improved speed of convergence and there's cheaper cost of capital for Boris that that are willing to provide high amount of information regarding their Financial Health this is something that would not be easily achievable in traffic where you're dealing with few banking actors thank you [Applause]