Binding curves in DeFi, explained.
Understanding connection curves in DeFi
Bond Curves Decentralized Finance (DeFi) uses smart contracts and mathematical formulas to dynamically adjust the value of tokens based on supply.
Bond curves are smart contracts that algorithmically determine the value of a token based on the implied supply. When more tokens are purchased, the price adjusts upwards, and when tokens are sold or removed from circulation, the price adjusts downwards.
This automated pricing mechanism ensures liquidity for new tokens without the need for traditional order books or external liquidity providers. It does this by embedding the liquid directly into the token's smart contract.
In particular, coupling curves use the economic principles of supply and demand. As demand for a token increases, reflected in increased purchases, the smart contract will raise its price accordingly. And when sales activity indicates a decrease in demand, the smart contract will reduce its price.
This dynamic adjustment is caused by an algorithm that simulates the relationship between price and quantity supplied based on a predefined curve. Thus, coupling curves allow for automated decentralized liquidity that responds to real-time market conditions.
Determining the value of the binding curves
Binding curves in DeFi align token prices with supply, supporting various economic strategies and market dynamics.
Mathematical modeling allows projects to customize Bonding Curve Tokinomics by defining specific curves that determine how token value changes based on supply. In theory there is no limit to the types of braids, but the most common ones come in many forms.
Linear curves
A linear correlation curve is a simple mathematical model in which the value of a token increases in proportion to the number of tokens sold. In this model, each additional token created or sold increases in value by a certain, predetermined amount.
Below is a simple graphical representation of a linear curve, with the X-axis (horizontal) representing the supply of tokens and the Y-axis (vertical) showing the value of each token at that supply level.
Exponential curves
Exponential curves make the price of a token highly dependent on supply. This means that if the supply doubles, the price will more than double. Even adding a few more tokens can lead to a big price jump. This makes the token very expensive very quickly.
These curves greatly reward early buyers. Later when demand increases, the first users can sell their tokens at a higher price. Therefore, exponential curves work well for projects that want to encourage early engagement. The first users take the most risk, but if the project is successful, they can make more profit.
Logarithmic curves
Logarithmic curves cause token value to increase rapidly at first as more tokens are added. But as the supply expands, the price goes down. So the price increases initially but decreases over time. This benefits early investors more as their tokens will gain value quickly up front. The opportunity to make quick early profits can be attractive to first-time buyers to provide liquidity.
In DeFi, in addition to linear, exponential and logarithmic models, there are different types of pairing curves. For example, S-curves for growth and stabilization, step curves for critical price increases, and inverse curves for reducing prices as supply grows, are each designed for specific supply curve economic outcomes and project goals.
Binding curve applications in crypto
Bond curves provide automated token liquidity and dynamic pricing to facilitate projects, transactions, stablecoins, communities and governance.
Binding curves serve as a basic mechanism for automated liquidity initialization, allowing projects to launch new tokens with dynamically adjusted liquidity pool concentrations. This model departs from traditional order books, ensuring continuous and algorithmic adjustment of liquidity based on real-time demand. The dynamic value exchange in the blockchain enabled by binding curves creates new opportunities for token distribution and trading.
Platforms like Uniswap and Curve use pairing curves to make an autonomous market, enhance liquidity and enable more efficient trading for many types of tokens, especially those that may suffer from low liquidity.
Bond curves are crucial in Stablecoin protocols for building cash reserves and maintaining peaks through algorithmic supply adjustments, ensuring the stability of the fully decentralized nature of these digital currencies. However, this approach carries risks, as algorithmic stablecoins rely entirely on correlation curves and programmed supply changes to maintain their stability.
For example, algorithmic stablecoin TerraUSD (UST) lost its $1:1 peg in May 2022 after a dramatic bank run drained its reserves. This shows that decentralized algorithmic stablecoins still have stability challenges when compared to asset-backed models.
When demand drops rapidly, algorithmically stable coins cannot adjust supply quickly enough to maintain their bonds. Thus, while coupling curves allow for decentralized stability mechanisms, they have not yet proven fully resilient to bank runs compared to linked options.
Bond curves facilitate automatic liquidity triggering in DeFi, autonomous market making and token models with dynamic prices adjusted to real-time demand.
Decentralized Autonomous Organizations (DAOs) play an important role in governance, allowing voting tokens to be purchased through bonding curves, aligning investment with governance participation and ensuring that pricing reflects the level of commitment to the DAO.
Decentralized exchanges (DEXs) and link curves
Bond curves enable custom, automated decentralized liquidity and pricing for various decentralized exchanges (DEXs).
Uniswap
Uniswap uses a fixed yield formula, a type of correlation curve, for its Automated Market Maker (AMM) protocol. This formula ensures liquidity by maintaining a constant yield between the amounts of the two assets in any given pool of liquidity. For example, if the pool contains Ether (ETH) and another token, their quantity production remains constant, which determines the price based on the dynamics of supply and demand. This approach provides continuous liquidity and price discovery without the use of traditional order books.
Curb Finance
Curve Finance focuses on DeFi as a stablecoin and uses a unique correlation curve optimized for assets of equal value. Its linking curve is designed to minimize slippage and maintain stable prices for closely held assets, such as various stablecoins pegged to the United States dollar. The curve is flat for pairs with the same value, making it efficient to trade between Stablecoins, reducing the impact of trading on price changes.
A balancer
Balancer uses a generic version of the constant product formula, allowing custom fluid pools at any weight for up to eight properties. This flexibility allows users to create their own balanced portfolios and liquidity pools with a custom bond curve that defines the relationship between the pool's asset value and volume. The balance sheet approach extends the utility of correlation curves beyond dual asset pools, accommodating a wide range of trading strategies and portfolio management practices.
Challenges associated with applying coupling curves
Bond curves face modeling, security, and legal challenges that require extensive testing, auditing, and compliance analysis to properly design, deploy, and monitor automated pricing systems.
Designing appropriate curve shapes that align incentives and encourage desired market behavior requires extensive modeling and experimentation. For example, very steep or shallow curves can encourage price manipulation.
Smart contracts that enforce binding curves should be security audited to protect against exploits that could compromise price integrity. There is also a need to facilitate smart contracts to reduce gas costs through automated trading.
Ensuring the security of smart contracts that manage engagement curves is critical, as flaws can lead to arbitrage or fraud. Regular verification, bug bounties, and audits can help reduce this risk. Ongoing research is focused on enabling dynamic curves that can be algorithmically adjusted to respond to market conditions.
The control treatment of bonding curves is still an open question. Most jurisdictions do not provide clear guidance on whether AMMs, such as bond bonds, are regulated trading venues or collateral offerings.
Projects should carefully analyze the rights granted by tokens sold on a jurisdiction-by-jurisdiction basis. Local regulations related to crypto assets and securities vary by region.
For example, tokens for profit, management rights, etc. If you grant access, they may be considered warranties in some jurisdictions that require compliance with applicable security regulations.
However, other jurisdictions may be more flexible in allocating utility tokens, ancillary profits or management rights. Therefore, projects should review regulations in their target markets.
Many projects follow a utility token model, where tokens only give holders access to a project's products or services without any profit rights or management capabilities. This limited token design avoids meeting security legal specifications in many cases.
However, Know Your Customer (KYC) and Anti-Money Laundering (AML) regulations may still apply to pure utility tokens as well. These regulations require verification of user accounts and funding sources.
Projects should seek legal advice to navigate this complex landscape. The regulatory treatment of crypto tokens continues to evolve across jurisdictions. Ongoing legal developments may provide clearer frameworks for designing compliant token implementation and engagement curve systems.
