Archimedes’ Dynamic Emissions: From Mercenary Liquidity to Long-Lasting Partners

7 min readDec 16, 2022


Recently we wrote about the utility of our governance token, ARCH. It’s been a long time coming, but lucky you, we finally invite you G(r)eeks to learn about how unique and robust ARCH’s dynamic emissions are designed.


  • The goal is to avoid overinflation of ARCH and to provide sustainable top-of-market APY to Liquidity Providers
  • In our novel approach, we calculate the ARCH emission volume based on the ARCH price and a target APY based on top pools in the market
  • As a consequence this creates sustainability for all stakeholders involved: lenders, borrowers, Archimedes, and partners alike. Eureka!
  • The resulting emission volume for Year 1 is projected to be between 321,933 and 6,438,653 ARCH.
  • The exact volume will depend on the calculated parameters input, varying with the market, to the emission algorithm.


We G(r)eeks at Archimedes are building an innovative decentralized and overcollateralized lending and borrowing marketplace. The protocol attracts liquidity by offering access to stable, relatively low-risk and top of market returns, enabling Lenders (Liquidity Providers) to earn sustainable APYs from real yield and its innovative dynamic emissions.

Borrowers (leverage takers) then are able to borrow this liquidity to build leveraged positions of up to 10x on yield-bearing stablecoins. That means somewhere up to around a sweet 40–50% APY in current market conditions, all of it with lower liquidation risk. Archimedes then wraps each leveraged position with an NFT, which the user can trade without the need to unwind the position.

So, what are “dynamic emissions”?

In this article, we’ll primarily focus on ARCH token’s dynamic emissions, and what it is designed to do:

$ARCH is the Archimedes governance and utility token.

But what is ARCH’s utility? As you may already know from reading the article about ARCH’s utility, ARCH is used as the ticket to leverage. A very quick refresher for you: Archimedes will be opening leverage rounds from time to time by making leverage available to users. At each round, we run auctions to find the fair price of leverage, and ARCH is needed to purchase the leverage.

Pause there for a second and reflect on how important that is: real utility. Since ARCH has utility, LPs have an incentive to protect this utility so that the price of ARCH is protected from sell pressure, making APYs sustainable in the long term. This means LPs benefit long term from ARCH emission.

If you think this utility is a cool way to add sustainability to our protocol, hold your horses — the dynamic emissions add more spice to the whole thing!

ARCH Dynamic Emissions: Bringing Sustainable Top-level Rewards to LPs

With our ARCH dynamic emission, lenders will enjoy emission rewards that are primarily designed to avoid overinflation of ARCH at any point in time. Isn’t that amazing? Also, as a byproduct and a great benefit to LPs: the Archimedes’ dynamic emissions design should ensure stable top of market APYs for lenders.

Feel free to bask in that thought for a bit. When you’re ready, breathe out and we’ll move forward. It gets to me too.

Before I explain how, let me answer the question “why do we do this?”.

Traditionally, the two main sources for Curve pool rewards are:

  1. CRV rewards: These are a nice bonus, but by itself limits the Protocol’s ability to reward and retain LPs in the long term as the access to CRV emissions are becoming scarcer, more competitive, and expensive — mainly for new protocols.
  2. Governance token emission: The existing protocols typically use a fixed emission schedule of their governance token for their liquidity mining programs. In these, most protocols set a fixed emission schedule to emit tokens to a Curve pool, initially driving high APYs, which quickly falls as TVL grows. But since the emitted token normally has no real utility and LPs benefit from short lasting high rewards, there is a strong sell pressure from LPs wanting to cement their high rewards, reducing the value of the token. As a consequence, those once stellar APYs become small to insignificant, posing doubts about the sustainability of the token and the protocol. Yeah, we’ve seen it many times and it’s not fun for anyone looking for a long term opportunity — LPs and protocols alike.

ARCH token is different from other tokens: it has utility and it is a ticket to leverage. This creates buy pressure, but that might not be enough to oppose any potential sell pressure.

To help change this narrative and protect the health of ARCH tokens, we use a cutting-edge token emission design, in addition to our Real Yield approach. After all, we’re the father of leverage in DeFi, and it’s like they say “happy liquidity, happy leverage”!

But wait… What does that even mean? It means that Archimedes’ groundbreaking approach to emissions will transform current mercenary liquidity providers into long-lasting liquidity partners. We adjust ARCH emission to our Curve pool periodically by using an algorithm that keeps APY in a specific range. The Archimedes protocol’s emission rate is dynamic in order to provide competitive APY at different market scenarios and conditions. This prevents over inflation of token supply, and protects both the token value and the protocol.

Archimedes calculates the ARCH emission volume every two weeks based on the ARCH price and a target APY based on top pools and market APYs.

Now, for our very brave G(r)eeks willing to delve into all of this, we explain the algorithm that determines the ARCH emissions.

The Algorithm

Before going too far into the math, I’d like to mention that our Dynamic Emissions is an experiment and we’ll monitor closely. This also means that we may change or adapt it based on user feedback and behaviors.

The algorithm will first calculate a few parameters:

* “Target APY” is calculated based on the Defillama data

💡 The 20% premium is to compensate lenders for any risk that Archimedes may carry for being a new experimental protocol.

** If ARCH price isn’t available on Coingecko, the algorithm will use ARCH/ETH Uniswap pool data and Coingecko’s ETH/USD (taking the last 7 days average ETH/USD price).

Every two weeks, the algorithm calculates the ARCH emission, which is allocated to the 3CRV/lvUSD Curve pool gauge. The emission amount is calculated as per the following formula:

Annual ARCH Emission Guardrails

For every year until Year 10 (we think long term, G(r)eek), the algorithm sets a minimum and maximum emissions to avoid edge cases, i.e. emission guardrails. Otherwise significant drops in ARCH price or other unexpected event might drive ARCH to overinflate.

The way the guardrail enforcement happens is:

  • The guardrails are defined on bi-weekly basis such that a large volume of the annual allocation is not emitted early on.
  • A simple division of the annual quota across 26 emission periods would still allow large emission at the early stages of the project. To avoid that, 2 weeks limits are calculated and determined for both weeks 1–26 and weeks 27–52 periods.

The Emissions

The min and max ARCH emissions by period until Year 4 are defined as below and are subject to change based on historical data for Year 2+ and/or upon DAO approval for any period:

Year 1

The total max annual emission is set to 6,718,878 ARCH and the minimum is 335,944 ARCH for Year 1.

Years 2–4

We plan to key off of the two 26 weeks periods of Year 1, and gradually increase the min and max.

Years 5–10

From Year 5 on, we determine the max annual emission by calculating the amount of ARCH left to emit divided by 5. We’ll then use the same formula used in Year 1 to determine the actual emission amount every two weeks. If by the end of year 10 there is still ARCH supply to be emitted, we’ll emit all left supply in a single two weeks period.

If necessary or the DAO judges as better for our users, we may run proposals for changes in the future.

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Archimedes is an experimental protocol and carries significant risks: Smart contract risk, economic model risk, risk that the assets Archimedes introduces and many other types of known and unknown risks. Archimedes’ team never provides investment advice. This article is NOT financial advice. DYOR. Participate at your own risk.