Let’s take a deeper look at L.L.A.M.M.A and why it matters.

What is L.L.A.M.M.A and how does it work?

L.L.A.M.M.A stands for Lending-Liquidating AMM Algorithm, an advanced Automated Market Maker specialized to optimize collateral management with btcUSD.

L.L.A.M.M.A employs a unique approach called soft-liquidations, preventing hard liquidations through continuous collateral rebalancing. Specifically, L.L.A.M.M.A splits collateral among a number of concentrated liquidity tranches known as “bands''; each band represents different liquidity ranges where user assets are used as collateral. These bands function similarly to the Concentrated Liquidity Market Maker (CLMM) model used in Uniswap V3.

When the oracle price of the collateral enters one of these bands, the collateral is gradually sold to btcUSD (or repurchased with btcUSD) within the band limits to maintain the desired collateral ratio. This process involves linear trading of the collateral as the price fluctuates within each band, effectively soft-liquidating the collateral without triggering a hard liquidation event. Hard liquidation only occurs when the collateral price has gone through all the bands and fully triggered all soft liquidations, at which point the borrowers already have enough time to process information and manage their positions in advance.

Borrowers have the flexibility to choose the number of bands, ranging from 4 to 50. By increasing the number of bands, borrowers can lower their liquidation threshold.

In L.L.A.M.M.A, borrowers' collateral is converted into Liquidity Provider (LP) positions within the AMM. This means that the collateral is actively managed and dynamically adjusted, ensuring that it can effectively support the borrower's debt position.

L.L.A.M.M.A incentivizes arbitrageurs to perform collateral rebalancing by slightly adjusting the internal collateral price within the AMM relative to the external market price. Essentially, L.L.A.M.M.A always offers a trade discount to arbitrage bots so that they route their trades through L.L.A.M.M.A and rebalance borrowers’ position in the process.

Soft liquidation vs Hard liquidation

In the Web3 lending ecosystem, most protocols rely on hard (one-off) liquidations, where collateral is fully liquidated once it falls below a certain threshold. This approach results in significant losses and position management difficulties, especially in sudden market disruptions.

L.L.A.M.M.A protects user collateral from the market’s transient intraday volatility, which is a major benefit for BTC holders. One compelling reason why these users have not favored DeFi lending protocols is they have to be exposed to high risk of hard liquidations. This type of users demands a flexible approach that allows them to leverage their BTC position in a reasonably safe way, emphasizing a constant exposure to BTC regardless of market fluctuations.

In practice, there has been no actual way to achieve this in DeFi without the nuances of manually adjusting the position, high cost, high risk, and/or compromising different aspects. With L.L.A.M.M.A, BTC holders can finally leverage their BTC with peace of mind, incurring only small additional costs and minor slippage losses due to continuous collateral rebalancing.

Effectively utilizing L.L.A.M.M.A L.L.A.M.M.A is a novel innovation that may pose some technical and implementation difficulties for our users. This part puts in place a number of useful information that would help you effectively utilize L.L.A.M.M.A:

• During a soft liquidation, you won't be able to withdraw your collateral or add more to your position. Additionally, re-collateralized troves may not be 100% replenished due to slippage loss.

• The loan-to-value (LTV) ratio depends on the number of bands. The higher the number of bands, the lower the LTV. More bands result in smaller losses per day during soft-liquidations but increase the duration of the liquidation process and reduce the total borrowable amount, indicating a higher risk.

• Low number of bands should be preferred in anticipation of crab markets/low volatility to reduce rebalancing loss, while high number of bands should be preferred for high volatility conditions since there is a wider spread of collateral and more time to react.

• When a position is in soft-liquidation, losses occur due to the "rebalancing" of collateral and borrowed assets within the bands of the AMM on the way down (converting collateral for borrowed asset) and on the way up (converting borrowed asset back to the collateral asset). These losses cannot numerically be quantified and are heavily dependent on the number of bands used for the loan and generally how efficient the arbitrage was.

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In this article, we explore the various pain-points Bitcoin holders encounter in DeFi and how Lambda Finance solves them with the most capital efficient, low-risk lending protocol.

Bitcoin adoption in DeFi is low - Why?

Research shows that the majority of DeFi activity involves large transactions, typically from sophisticated users and institutions. Nevertheless, according to DeFi Pulse, as of mid-2024, Ethereum-based DeFi protocols account for over 60% of the total DeFi TVL (Total Value Locked), while Bitcoin's contribution through wrapped versions (like WBTC) is less than 2% of the total DeFi TVL.

This does not sound right, considering the majority of BTC holders are whales, long-term holders, and institutional investors. This leads us to the question: why are Bitcoin holders uninterested in DeFi activities? There are a few reasons.

First of all, Bitcoin was designed primarily as a decentralized digital currency and store of value, not as a platform for smart contracts and DeFi applications. This makes it less versatile compared to Ethereum, which was built with a focus on programmability and smart contracts. Most DeFi protocols and decentralized applications today are built on Ethereum, which is not a native platform for Bitcoin. As a result, to use these services, Bitcoin holders have to go through additional complexity and reliance on custodial services.

Second, because Bitcoin is not a priority asset for DeFi products, the number of use cases for Bitcoin within the DeFi ecosystem is extremely limited. Given the limited functionality of Bitcoin within DeFi ecosystems, it makes sense that Bitcoin holders are further discouraged from participating in DeFi activities.

Third, given the ethos of Bitcoin that prioritizes security and trustlessness, we can indicate Bitcoin holders have a low level of risk tolerance. On the other hand, DeFi often involves a lot of risks. In the first quarter of 2024 alone, approximately $336.3 million was lost due to various DeFi exploits and vulnerabilities. As DeFi hacks and scams continue to be a major concern, Bitcoin holders need a battle-tested, safe-and-sound DeFi instrument.

Welcoming Bitcoin holders to the world of DeFi

Lambda Finance is a lending protocol that enables the effective utilization of Bitcoin by allowing users to lend or borrow any assets in combination with btcUSD - our Bitcoin backed stable coin. btcUSD is the first & only licensed fork of crvUSD - a CDP stablecoin with innovative stability & loss protection mechanisms. If you are unfamiliar with btcUSD, please refer to our previous blog post.

https://mirror.xyz/0xB0334902152b61Fb0159dc14be4B868eDd945FfA/0zZYKj3W9I9w57x0ucwnwPnLjPJqz_ny1hptXXXyAh4

Long story short, users can collateralize Bitcoin and Bitcoin equivalents on Lambda Finance to mint btcUSD and leverage their position (up to 9x) with competitively low funding and interest rates. Lending and borrowing are among the most fundamental financial instruments; however, over the years, there has been no “goldilocks” lending solution for Bitcoin because, to borrow, Bitcoin holders are forced to compromise on one or more aspects.

Understanding this, Lambda Finance introduces a novel mechanism called L.L.A.M.M.A (Lending-Liquidating AMM Algorithm). LLAMMA turns borrowers’ collateral into LP positions, enabling it to avoid hard (one-off) liquidations with continuous collateral rebalances (soft liquidations).

L.L.A.M.M.A splits collateral among a number of concentrated liquidity tranches known as “bands''. Each band represents different liquidity ranges where user assets are used as collateral. When BTC price falls within a band range, the collateral in the band is converted into btcUSD to cover closing of the portion of the loan represented by the band. When BTC’s price recovers, the protocol re-converts the btcUSD back into collateral.

With L.L.A.M.M.A and btcUSD at its core, Lambda Finance offers numerous benefits to Bitcoin holders:

• Enjoy the most capital-efficient lending solution with native support for Bitcoin.

• Lend Bitcoin at a high interest rate with $LAMBDA and ve(3,3) tokenomics, along with reduced risk of impermanent loss and price volatility with isolated markets. Additionally, lenders can choose from a variety of lending markets to diversify lending strategies based on risk tolerance and return expectations.

• Collateralize Bitcoin and leverage your position up to 9 times at low cost, low risk while effortlessly managing your position with the soft-liquidation mechanism.

• Each lending market is independently managed (isolated markets), ensuring that risk is isolated within specific pools, preventing cross-market contagion, and avoiding the impact on $btcUSD.

• Deep integrations with DeFi protocols such as Curve, Frax, and Aladdin DAO ecosystems provide myriads of liquidity and use cases for btcUSD, increasing its borrowing demand. We are excited to finally welcome Bitcoin holders to the world of DeFi!

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Let’s take a look at how it works.

How Do the AMOs Work?

When btcUSD > $1

1. AMOs mint additional btcUSD.

2. The newly minted btcUSD is added to Curve liquidity pools.

3. The btcUSD in Curve pools earns swap fees and yields

When btcUSD < $1

1. AMOs withdraw btcUSD from Curve liquidity pools.

2. The withdrawn btcUSD is burned.

3. The market supply of btcUSD is reduced.

By increasing/decreasing the supply of btcUSD, AMOs bring btcUSD price back towards the 1 USD peg. This feature basically balances the supply of btcUSD, like a financial seesaw.

How Does the Adaptive Interest Rate Work?

Complementing the AMO mechanism, Adaptive Interest Rates work in tandem to maintain the stability of btcUSD's peg through dynamic adjustments based on market conditions. The core principle is simple: adjust the borrowing rates to influence supply and demand, thereby stabilizing the peg.

btcUSD > $1: Lower Interest Rates

When btcUSD's price is above $1, the borrowing rate decreases. This reduction makes it more attractive for users to mint and borrow btcUSD, increasing the supply and driving the price back down to the $1 target.

btcUSD < $1: Higher Interest Rates

Conversely, when btcUSD's price falls below $1, the borrowing rate increases. This hike discourages borrowing and encourages redemptions and interest payments, reducing the supply of btcUSD and pushing its price back up to the peg.

The formula for interest rate is as follows:

The adaptive nature of the interest rate helps maintain the peg by responding to changes in market conditions and the outstanding debt of the AMOs. It ensures that the supply and demand for btcUSD are balanced, keeping the price stable.

btcUSD's stability mechanism vs. other stablecoins

btcUSD's maintenance mechanism, which combines AMOs and an Adaptive Interest Rate mechanism, provides several advantages over traditional stability pools and single-method interest rate adjustments. This dual approach ensures that btcUSD can swiftly and effectively respond to market conditions, maintaining its peg with high precision and reliability.

These features would make btcUSD ideally attractive for Bitcoin holders looking for a stablecoin that offers both stability and responsiveness in the DeFi market.

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We’ve been getting a lot of questions about the relationship between crvUSD and btcUSD, especially since crvUSD also accepts Bitcoin as collateral. This begs the question:

Why does btcUSD exist?

The team appreciates the curiosity and support from the Curve and Defi community. We’re excited for the opportunity to differentiate ourselves from our progenitor, but also demonstrate how we can contribute to Curve’s growth and establish crvUSD’s superiority as a stablecoin.

So without further ado, let’s dive in!

1/ btcUSD offers a more targeted approach for driving Bitcoin-backed TVL to Curve

Despite holding nearly 50% of total liquidity, Bitcoin holders are an underserved market. Curve currently lacks a direct method to attract Bitcoin-backed liquidity. Recognizing this opportunity, Lambda leverages crvUSD as its base mechanism to bridge the gap and effectively target Bitcoin holders. This allows us to demonstrate the efficiency of our mechanism in a niche market and expand the reach of both crvUSD and btcUSD.

Lambda functions as a conduit for Bitcoin-backed TVL to Curve and Defi. As a newer, leaner team with fresh backers, and partners, Lambda can directly target Bitcoin holders to capitalize on the emerging Bitcoin Defi narrative, while providing access to a holistic suite of Defi products in Curve’s ecosystem: yield boosting via Convex, yield trading via Napier, automated liquidity strategies via Conic and much more

Our partnerships with Threshold Network and DLC Link offer a streamlined experience for profit seeking Bitcoin holders to permissionlessly bridge their Bitcoin to Ethereum and utilize its liquidity for on-chain transactions.

Nearly every dollar of Bitcoin deposited into Lambda is minted as a stablecoin for swaps and farming, with liquidity trickling upwards to Curve as the ultimate beneficiary.

Which brings us to our second point.

2/ Lambda will subsidize the cost of Bitcoin-backed liquidity on Curve

Lambda will bribe Curve gauges to attract Bitcoin LP to our stable pools on Curve.

At the protocol level, btcUSD only accepts Bitcoin equivalents as collateral. This design is inherently more attractive to Bitcoin holders who do not want collateral exposure to Ethereum. btcUSD’s borrow rates are not inflated by other collateral assets, enabling more Bitcoin to be collateralized for stables for Curve pools. Every dollar of bribes from Lambda goes directly to incentivizing Bitcoin-backed TVL, which is a more direct and efficient way of incentivizing liquidity

3/ Lambda will explore new use cases for btcUSD, standing on the shoulders crvUSD’s innovation

As a team that operates alongside Curve, we have the freedom to explore new use cases and partnerships. One of our strategic pillars involves partnering with various protocols on different chains, including Bitcoin L2s and ETH L2s. The team is working diligently behind the scenes to bring degens back to Defi with ve(3,3,3,3).

While Curve has the potential to do this, Lambda can move faster and more efficiently because we're not bound by the complexities of a DAO with diverse interests and numerous partners. Our streamlined approach allows us to quickly identify and capitalize on opportunities that benefit both btcUSD and the broader Curve ecosystem. In doing so, we can not only drive TVL to Curve but also demonstrate crvUSD’s superiority as a stablecoin protocol.

Conclusion

btcUSD embodies all the strengths of crvUSD while addressing its limitations and catering specifically to Bitcoin holders. btcUSD allows Lambda to cater to the unique preferences and requirements of Bitcoin holders, offering them a tailored solution that aligns with their specific needs and concerns.

By focusing our efforts on this underserved segment, we aim to unlock a significant portion of Bitcoin liquidity and contribute to the growth and vibrancy of Curve & Defi ecosystem.