# Motivation

In this proposal, we present the Vesta Reference Rate to replace the redemptions feature on the protocol. We will also soon introduce the Vesta Safety Vault.

The redemption function was intended as the main mechanism to defend peg by allowing holders of VST tokens, including those who have purchased VST in a secondary market, to redeem the stablecoin for the underlying collateral, even though they are not the primary borrowers.

When VST is under the $1 peg, redemptions provide a way for users to arbitrage the price of VST back to$1. Redemptions are first exercised against vaults that have the lowest collateralization ratios. This means that if User A has the lowest collateralization ratio at the time of a redemption by User B, then the vault created by User A will be impacted, such that the loan will be repaid by an amount equal to the redemption amount of User B, while the collateral will also be reduced and transferred to User B in an amount equal to the redemption amount. In other words, other VST holders are able to pay off someone else’s VST loans and take their collateral.

While this effectively improves the collateralization ratios of vaults that are close to being liquidated, it essentially alters the borrowers portfolio by enforcing the liquidation of their collateral even though they satisfy the minimum collateralization ratio (MCR) requirement. Hence, redemptions impact the borrowers in the system by changing their balances, adding uncertainty and severely undermining user experience, as this defeats the purpose of allowing borrowers to maintain an intact exposure on the collateral asset should they meet the protocol’s borrowing requirements.

Moreover, in the case when the stability pool is empty (i.e. the pool of VST tokens that is used to settle vault debts during liquidations) or becomes empty due to liquidations, every borrower will be credited a portion of the liquidated collateral and debt of the vaults that have become eligible for liquidation. Again, this can significantly alter the collateralization ratios of all remaining users. Thus, even though users may be obtaining a small gain in terms of the new collateral relative to the new debt they are being credited, they are now responsible for a larger debt amount, which might be outside of their risk tolerance.

We have already taken steps to mitigate the impact of redemptions on the system. Previously, the redemption fee was at 0.5%. As Vesta onboarded more collaterals, lots of users started utilizing Vesta as a platform for leverage, effectively repeating the process of taking out loans and then selling the loans to acquire the collateral again. While such an activity bootstrapped a sizeable portion VST origination, it also puts VST under severe selling pressure, pushing VST below the peg. Since then, we have changed the redemption fee to 2%, making redemptions unprofitable unless VST goes below $0.98. However, this was only meant as a temporary solution as it now effectively puts VST at a peg of$0.98. We are now proposing novel developments to bring VST back to peg: Vesta Reference Rate and Vesta Safety Vault.

# Technical Overview

## Vesta Reference Rate

### Technical Framework

Update Nov. 3, 2022: the below still provides context but the final model is updated. For detail on the latest model please view the bottom of this post where the models are linked.

We introduce the Vesta Reference Rate (VRR) as a mechanism to replace the current redemption model as a price stabilizing framework.

As part of this new proposal:

• Users will no longer be able to redeem VST against the collateral of other vault owners.
• Users will no longer pay a front-end mint fee when minting/borrowing VST, but rather pay a continuously compounded fee based on the VRR.
• We will introduce the Vesta Safety Vault, where a portion of the VRR that is paid by borrowers will be given as a reward to depositors in the Vesta Safety Vault, thus offering another incentive for holding VST.
• Changes in the baseline VRR will be driven by the dynamics of supply and demand forces of VST around the peg.
• When VST is below the peg (i.e. too much VST supply in the market), a higher VRR is charged to borrowers to incentivize them to repay their loans, while also prompting users to deposit VST in the Vesta Safety Vault to earn the higher VRR. These incentives will motivate users to purchase VST in the open market, thus driving the price upward towards the peg.
• When VST is above the peg (i.e. too much VST demand in the market), a lower VRR is charged to borrowers to incentivize them to borrow more, while also prompting users to deposit less VST in the Vesta Safety Vault. These incentives should motivate users to sell VST in the open market, thus driving the price down toward the peg.
• The interest rate model may also allow for negative interest rates, which could be used as a more extreme tool to prompt users to borrow more and save less, especially when the price of VST is significantly above the peg. This would imply that users would be paid an interest rate to borrow, and charged an interest rate when saving. However, this should only be used in extreme cases.

#### The Vesta Reference Rate Model

• The VRR is based on a non-linear generalized logistic model that allows the protocol to set minimum and maximum baseline interest rates over a range of price deviations from the peg.
• The model also has a parameter to adjust the curvature or steepness of the interest rate curve, as well as a parameter to shift the curve along the range of price deviations from the peg.
• Mathematically, the VRR model is given by:
VRR_{\Delta P} = VRR_{max} + \frac{VRR_{min} - VRR_{max}}{1 + I \times e^{-C \times \Delta P}} \ \ \ \ (1)

where

• \Delta P: deviation of the price from the peg, given in cents;
• VRR_{max}: maximum interest rate for the baseline VRR;
• VRR_{min}: minimum interest rate for the baseline VRR;
• I: shift of the VRR’s inflection point along the x-axis, which represents the range of price deviations from the peg, given in cents;
• C: curvature or steepness of the VRR curve.

Equation (1) can be re-written as:

VRR_{\Delta P} = VRR_{max} + \frac{VRR_{min} - VRR_{max}}{1 + e^{-C \times (\Delta P - \Delta P_{0})}}

where \Delta P_{0} = log(I)/C , and represents the deviation from the peg that results in a half-maximal rate.

The initial model parameters that will be used are as follows:

• VRR_{max} = 2%
• VRR_{min} = 0.5%
• I = 0.01
• C = 5

The above parameters will give the following baseline VRR.

• The VRR is the baseline interest rate that will be applied equally to all assets on the Vesta protocol.

#### Collateral-Specific Rate

• In order to account for collateral-specific risks, Vesta will charge borrowers a collateral-specific premium that will be added to the VRR.
• The collateral-specific premium is also calculated using Equation (1), such that a dynamic premium is added to the VRR for different price deviations from the peg.
• Vesta will categorize collaterals into three risk groups labelled as low, medium, and high, where the maximum collateral-specific premiums will be 0%, 1%, and 3%, respectively, and the minimum collateral-specific premiums will be 0%, 0.25%, and 0.75%, respectively.
• Note that these maximum and minimum collateral-specific premiums are subject to change in the future.
• The effective interest rate (EIR) charged to borrowers will include the VRR plus the collateral-specific premiums, such that:
EIR_{\Delta P, Collateral} = VRR_{\Delta P} + Premium_{\Delta P, Collateral}
• The effective interest rate curves for the three categories of collaterals will look as follows.

### Empirical Reasoning

• Historically, the price of VST has been fluctuating within a -2% deviation from the peg, as can be seen in the chart below.

• The distribution of the price deviations from the peg are also illustrated below.

• The aim of the new interest rate framework is to bring the price of VST as close as possible to the peg and to minimize the magnitude of the fluctuations around the peg. This would greatly improve on the notion of VST being a reliable stablecoin.
• Given this new framework, users will be incentivized to shift the price of VST closer to the peg in order to reduce the EIR they are being charged for borrowing or minting VST.
• The incentive comes from an asymmetric improvement in the EIR (i.e. lower EIR) for a unit change in the price deviation from the peg.
• To illustrate this point, we plot the VRR interest rate curve with the 20th and 80th percentile deviations according to the real data shown above.

• For a VST price improvement from the lower 20th percentile price of 0.983 to the upper 80th percentile price of 0.997 (i.e. a 1.32% price increase), borrowers with low, medium, and high risk collaterals will experience reductions in their EIR of [0.58 /1.96 - 1] = -70.4%, [0.87 /2.96 - 1] = -70.6%, and [1.46/4.91 - 1] = -70.3%, respectively.
• These significant reductions in the EIR are thus a sizeable incentive for users of VST to keep the price as close as possible to the peg.

## Update Nov. 3, 2022

After reviewing the interest rate values at each price level, we have come up with the final proposal that utilizes an exponential model alternative for the VRR. For context, please review [PASSED] Introducing the Vesta Reference Rate - #9 by token_master for context and [PASSED] Introducing the Vesta Reference Rate - #13 by token_master for the final model.

## Vesta Safety Vault

Vesta Safety Vault will be a place for people to deposit VST and thus achieve the goal of taking VST off-market, playing an instrumental part in Vesta’s monetary balancing. We are still in process of drafting this feature so please keep an eye out for a new proposal on this soon.

The (\Delta_{Price-Peg}, EIR) coordinates for the three collateral type models are:

# Timeline

We hope to solicit feedback on this proposal for 7 days before putting this through a vote. Our engineers have already started looking into implementing this model. The voting stage will last for 72 hours.

2 Likes

Thanks for very well-thought-out and detailed proposal, I think I’m overall in favor of the presented changes.

One thing I’d like a little more information about is the collateral-specific rates. Are you able to say specifically which assets will fall into which category? Some assets (GLP) already have a fairly significant admin fee on their yield; would this be taken into account when choosing their EIR?

Also I know there will be a separate safety vault proposal later, I just want to put it out there that an interest-bearing token (iVST?) would be pretty nice to have rather than a static vault contract of some sort.

1. What portion of the VRR will be paid out to Vesta Safety vault depositors? and in what token?
1a. is the rest of the VRR paid out to the treasury?
2. Agree with other commenters - would love to hear more about how you plan to balance current GLP management fees with the VRR. If the initial parameter adds 2% interest rate, and then an additional 3% because it’s considered ‘risky’ collateral plus the 20% fee on glp yield + treasury currently keeps all esGMX rewards…
2a. IMO if the protocol is going to start charging interest rate across the board, GLP should be treated just like any other collateral… keep the esGMX yield and additionally charge only the VRR + collateral-specific premium.

Hi everyone, that’s a great proposal.

I would like to see bit more information on how collaterals will be classified into risk groups. For example, what determines the risk of a collateral: is it its price volatility, the % of VST minted against it?

Also, one minor point to help make the VRR model clearer. I would rearrange the denominator in the rhs of Eq 1 so that it reads:
1 + exp ( -C * (ΔP - ΔP0) )

where ΔP0 = log(I)/C. I think as it stands parameter I is difficult to interpret, whereas ΔP0 has a clear interpretation (ie deviation from the peg that results in a half-maximal rate)

Thanks for all your comments! Below I’ll reply to a couple to points.

From a strictly technical perspective, the performance fee applied on GLP is a fee applied on the “staking” part of the protocol. Vesta’s staking feature is unique and not offered anywhere else at the moment. The upcoming interest rate is concerned with a totally different subject, which is managing supply of the token relative to the peg.

However, we hear your concern loud of clear. The team recognizes how the interest fee may render the product unattractive especially during times of de-peg. After a long discussion, @token_master and I have concluded it would be reasonable to lower the performance fee to 10% as we push out the interest rate module.

As we wrap up the design of interest rate and hand the project over to engineering for implementation, the research team is now spending majority of our efforts on devising the new vault and the staking module (or the staking module with the vault in it?!). I’ve personally not found any good reason for tokenizing a vault deposit if we set one up. Would appreciate it if you could elaborate a bit here.

This is yet to be determined. I would assume something like a 60-40 or 70-30 split would be used, with the majority supporting VST related vaults and the minority going to support the governance token.

1 Like

Very well written post.
My 3 cents:

This should come with auxiliary mechanisms, that would be able to absorb back the VST that is minted due to the negative interest rate.

Intuitively, it feels to me that the interest rate should spike even more below -2 cent peg, as the situation in -5 cents peg is much worse than the one with -3. Is this just an illustration and different max and min value would be able to take care of it?

Maybe it is a matter for a different post, and maybe it is even part of the future plans already, but personally i feel that once introducing interest rate, the users who borrow against riskier collateral should pay interest rate (aka fee) also when VST is fully peg.
This will allow for more flexibility in the risk parameters, as the accumulated fees could compensate the protocol for the insolvency risk. And the insolvency risk is orthogonal to the deppeging risk. In fact, when VST < \$1, the insolvency risk is smaller.

@mv_kr you are correct. The modified function will yield exactly the same result, but may be interpreted more intuitively by users.

I will add also the modified version of the function.

This is the case as per the current proposal. We will charge an interest rate whether the price is below, at, or above the peg as the user is effectively borrowing VST no matter the market price. However, the rate will be higher when the price is significantly below the peg in order to encourage borrowers to purchase VST and pay back their loans, thus pushing the price back to peg.

## UPDATE: An Exponential Model Alternative for the VRR.

• After receiving great feedback from the community, a key concern about the initially proposed logistic model that underlies the VRR is that it is not dynamic to further declines in the price of VST relative to the peg.

• We have looked at other crypto markets and financial products in order to determine what would be a simple and efficient way to make the Effective Interest Rate (EIR) more reflective of market conditions, as well as the state of VST.

• As a result, we are proposing an exponential function for the EIR, which results in exponentially higher interest rates as the price of VST falls further and further.

• Specifically, we fit the exponential functions for the low-risk, medium-risk, and high-risk collaterals by defining two point coordinates (X,Y) for each EIR function; we define the EIRs at the -5% price de-peg and when the price is at the peg (i.e. equilibrium EIR for the collateral).

• These coordinates, (\Delta_{Price-Peg}, EIR ), are given as:

Collateral Risk Category \Delta_{Price-Peg} EIR
Low -5% 2%
Low 0% 0.5%
Medium -5% 3%
Medium 0% 0.75%
High -5% 5%
High 0% 1.25%
• Note that these values, to a certain extent, have been inferred from the logistic model that was proposed previously.

• Given these coordinates, the EIR functions for the three risk category collaterals are given as:

EIR_{Low \ Risk, \Delta P} = 0.5 \exp^{−0.2773 \times \Delta P}

EIR_{Medium \ Risk, \Delta P} = 0.75 \exp^{−0.2773 \times \Delta P}

EIR_{High \ Risk, \Delta P} = 1.25 \exp^{−0.2773 \times \Delta P}

• The resulting plot for the three EIR functions would look as such:

• While these rates may seem extreme for cases where the price of VST is below the peg by ~20%, these numbers are in line with what is observed for the funding rate in perpetual futures markets.

• Moreover, we aim to use a portion of these rates in our Vesta Safety Vault program, thus incentivizing users to buy VST in the open market, thus driving the price back to peg and towards the equilibrium EIRs.

With the new interest rate curve, there is a non zero interest (aka fee) also when the price is fully pegged.
This is fine if intentional, but might deserve a more in depth or separate function on how the interest rate function should like like.
Unless the plan is to have this discussion later, and then just to add the EIR on top of it. If this is the case, you might want to normalise the EIR so it will be 0 when delta P = 0.

There’s indeed a base interest that’s being charged even when the token is at peg. You can see the correlating interest rate at the table from @token_master ’s latest comment. These are in place to account for each collateral’s inherent risk and it’s subjected to governance vote.

Since users who mint VST are effectively borrowing VST (regardless of the price) then there will be an interest rate that is charged. This includes cases when VST is at the peg as well as above and below.

The interest rate will be lower when the price is above the peg to encourage more minting and potentially bringing the price back. down to peg.

• The general exponential function we propose for the VRR for the different collateral groups is given as:

VRR_{collateral, \Delta P} = \beta_{collateral} \exp^{C \times \Delta P}

• where:

• \Delta P: is the deviation of the price of VST from the peg measured in cents;
• \beta: is the baseline reference rate of a collateral group when the price of VST is at the peg;
• C: is a constant factor that determines the curvature of the exponential function.
• After reviewing the interest rate values at each price level, we have come up with the following final proposal.

• The baseline reference rates (\beta_{collateral}) for the low, medium, and high risk collateral categories are set to 0.5%, 0.75%, and 1.25%. Again, these values represent the annualized VRR for each collateral group when the price of VST is at the peg.

• The (\Delta_{Price-Peg}, VRR) coordinates for the three collateral type models are:

Collateral Risk Category \Delta_{Price-Peg} VRR
Low -2% 4%
Low 0% 0.5%
Medium -2% 6%
Medium 0% 0.75%
High -2% 10%
High 0% 1.25%
• Given these coordinates, the VRR functions for the three risk category collaterals are given as:

VRR_{Low \ Risk, \Delta P} = 0.5 \exp^{-1.0397 \times \Delta P}

VRR_{Medium \ Risk, \Delta P} = 0.75 \exp^{-1.0397 \times \Delta P}

VRR_{High \ Risk, \Delta P} = 1.25 \exp^{-1.0397 \times \Delta P}

• As the price of VST moves significantly below the peg, the VRR increases exponentially, and as the price increases significantly above the peg, the VRR may go into negative territory. To avoid extremely large or negative values for the VRR, we set minimum and maximum caps, such that the VRR will be calculated over the range of [-5\% , 5\%] price-peg ratio.

• This means that the VRR models will have a maximum cap that equals the interest rate at the -5\% price/peg ratio, and a minimum cap that equals the interest rate at the +5\% price/peg ratio.

• Mathematically, this is written as:

VRR_{collateral, \Delta P} = \begin{cases} \beta_{collateral} \exp^{C \times -5}, & \text{for } \Delta P \leq -5 \\ \beta_{collateral} \exp^{C \times \Delta P}, & \text{for } -5 < \Delta P < 5 \\ \beta_{collateral} \exp^{C \times 5}, & \text{for } \Delta P \geq -5 \end{cases}
• The resulting models will look like this:

2 Likes

Passed Snapshot on Nov 3, 2022, 3:20 PM