Bonding Curves Explained

Understanding DeFI Bonding Curves

In order to fully comprehend DeFI Bonding Curves, a quick refresher on the exact definition of a “token” is necessary.

Token Basics

An Ether token on the Ethereum network (or other blockchains) is housed within a smart contract. The inception of this concept traces back to the creation of a smart contract designed to oversee token balances. Essentially, it functions as a ledger, mapping addresses to numerical values representing the balance associated with each address. Tokens serve as value counters held within a contract. The following Solidity contract serves as a straightforward demonstration of the fundamental principles underlying tokens:

Within this example smart contract, when an individual purchases tokens, they initiate the transaction by sending Ether along with the call, thereby using Ether to acquire tokens. In this contract, the exchange rate is set at 1 Ether for 1,000 tokens. Conversely, when selling (or burning) tokens, one must specify the quantity of tokens to be burned as a parameter. Assuming the token holder possesses adequate tokens, they will receive the corresponding value in Ether for the tokens exchanged.

Note, however, that the underlying token is still not an ERC20 token, but rather communicating with one during the buy/sell function.

That is, tokens merely serve as numerical representations of value within contracts. Standards play a crucial role in ensuring consistency among tokens, facilitating broader acceptance and utilization. Although numerous token standards exist, only a select few gain significant traction. Proposed standards are initially introduced as Ethereum Request for Comments (ERCs), and upon garnering substantial community support, they advance to become Ethereum Improvement Proposals (EIPs). EIPs undergo rigorous evaluation by Ethereum core developers before being integrated into the system.

Bonding Curve Basics

The fundamental principle behind a bonding curve is straightforward: The price of a token is directly linked to its supply. As more tokens are distributed, the price increases accordingly.

Bonding curves within decentralized finance (DeFi) utilize smart contracts and mathematical algorithms to dynamically regulate a token’s price in accordance with its supply. These curves, implemented as smart contracts, automatically compute a token’s price relative to its circulating supply. With each token purchase, the price escalates, while token sales or removals from circulation prompt price decreases. In simple graphical form, we find:

Bonding Curves serve as a method to solidify the correlation between the price and supply of tokens. Put simply, when the token supply changes by X amount, the price fluctuates by Y, which can be either a fixed value or a percentage.

This mechanism bears resemblance to Automated Market Makers (AMMs), albeit with a key distinction: no initial liquidity is required to prime the pool. Instead, Ethereum (ETH) or stablecoins can be deposited directly into the curve, allowing for on-demand token minting without the necessity of pre-existing liquidity to facilitate exchanges.

Bonding Curve Operations

Using the most basic of scenarios found in the above graph, it is perhaps easiest to understand by example.

The above graph represents a bonding curve scenario where no tokens exist initially, and each mint or burn operation results in a price adjustment of ‘1 ETH.’ The inaugural token’s minting price is set at 1 ETH. Here we go…

  1. Kevin enters the scene, investing 1 ETH into the bonding curve, acquiring one token in return. This action shifts our position along the curve, incrementing both X and Y to 1. Subsequently, the cost to mint the next token elevates to 2 ETH.
  2. Intrigued by Kevin’s minted token, Megan decides to jump in. She mints the subsequent token for 2 ETH and another one thereafter, now priced at 3 ETH. In total, Alice has contributed 5 ETH to the curve and obtained 2 tokens.
  3. Observing the increased price, Kevin elects to capitalize on his token for profit. With the price now at 3 ETH, Kevin redeems his token to receive 3 ETH, thereby retracting the curve’s position and reducing the price to 2 ETH.

This scenario encapsulates the essence of a basic bonding curve. The intrigue deepens when we explore various curve shapes and dynamics. What if the price increment is 10%? What if it shifts by 0.5 ETH until reaching 100 tokens, after which it flattens, adjusting by only 1% per mint or burn? Moreover, what if the curve morphs based on product milestones validated by an oracle? Such a curve could reward early adopters who minted tokens during the riskier phase, evolving to become steeper as the product matures.

Price Discovery

Utilizing mathematical modeling empowers projects to tailor bonding curve tokenomics, defining unique curves dictating how a token’s price fluctuates with its supply. The range of potential curve designs is theoretically limitless, but the most prevalent ones typically fall into several categories:

Linear Curves
Linear bonding curves employ a straightforward mathematical approach where the token price increases proportionally with the number of tokens sold. Each additional token minted or sold raises the price by a predetermined fixed amount. An example of a Linear Bonding Curve can be found in the simple graph provided above.

Exponential Curves
Exponential curves link the token price exponentially to the supply. Consequently, a doubling of the supply leads to more than a doubling of the price, resulting in significant price surges with even minor increments in token addition. This model predominantly benefits early adopters, incentivizing their participation by offering the potential for substantial returns if the project succeeds.

Logarithmic Curves
Logarithmic curves initially trigger rapid price escalation as more tokens are introduced. However, as the supply expands, the rate of price increase diminishes, ultimately leading to a leveling off of prices over time. This structure favors early investors, as their tokens experience swift value appreciation early on, potentially attracting liquidity providers with the promise of rapid early gains.

Beyond the linear, exponential, and logarithmic models prevalent in DeFi, a plethora of diverse bonding curve types exist. Examples include S-Curves for phased growth and stabilization, Step Curves for milestone-triggered price adjustments, and Inverse Curves to decrease prices as supply expands. Each of these curve types is tailored to specific economic outcomes and project objectives within the realm of bonding curve dynamics.

Bonding Curves & the Crypto Markets

The primary importance of a Bonding Curve is that it offers automated token liquidity and adaptable pricing mechanisms, supporting various endeavors such as projects, trading, stablecoins, communities, and governance. Moreover, Bonding Curves serve as a cornerstone for automated liquidity bootstrapping, particularly in initial decentralized exchange offerings (IDOs), empowering projects to introduce new tokens with liquidity pool reserves that dynamically adjust over time. This departure from conventional order books ensures a seamless and algorithmic adaptation of liquidity in response to real-time demand. The versatility of dynamic pricing, facilitated by bonding curves within the blockchain framework, opens up innovative avenues for token distribution and trading.

Bonding curves stand out for their role as automated market makers, distinguishing them from traditional centralized exchanges where prices are dictated by buy and sell orders (and often manipulated as a result). Instead, the price is determined by a predetermined curve, creating a self-regulating mechanism that offers several advantages:

  1. Always Liquid: The built-in market maker of bonding curves guarantees continuous availability of tokens for buying or selling, eliminating reliance on external parties.
  2. Transparent Pricing: Participants can anticipate how changes in supply will affect the token’s price, thanks to the predetermined nature of the curve and its formula.
  3. Equitable Distribution: Leveraging bonding curves for initial token distribution is often perceived as fairer since it begins from the lowest price point, promoting broader access.
  4. Capital Generation: Projects can utilize the funds represented by the area beneath the curve for various developmental activities, facilitating capital generation.
  5. Inherent Token Worth: By maintaining a basic price floor, the curve ensures that tokens always possess value, enabling trading based on the current pricing dictated by the curve.

Bonding Curve in Web3.0

Below are some Web3.0 platforms leveraging bonding curves and the rationale behind their adoption:

  1. Uniswap: This decentralized exchange employs a constant product bonding curve, enabling decentralized token exchanges. The curve maintains relative stability in token prices within the pool, even amid fluctuations in token quantities.
  2. Curve Finance: Another decentralized exchange utilizing a constant product bonding curve, Curve Finance specializes in trading stablecoins. By ensuring prices closely align with their pegs despite changes in supply and demand, Curve Finance facilitates stablecoin trading effectively.
  3. Aave: Operating as a lending platform, Aave utilizes a constant product bonding curve to offer low-interest lending services. The bonding curve maintains stability in the supply of Aave’s lending tokens (aTokens) despite fluctuations in lent amounts, contributing to the platform’s ability to keep interest rates low for borrowers.
  4. SushiSwap: Similar to Uniswap, SushiSwap is a decentralized exchange employing a constant product bonding curve. However, it distinguishes itself by offering reduced fees and a more user-friendly interface, enhancing the overall trading experience.
  5. Balancer: This decentralized exchange employs a constant elasticity bonding curve, offering greater flexibility compared to the constant product curve. Balancer’s curve accommodates a wider range of assets, allowing for more diverse trading options on the platform.

Compliance Questions

There are three (3) primary areas to consider when implementing Bonding Curves.

First, the same issue it always seems to be with everything in crypto: Simply put, what is the nature of the tokens being traded pursuant to the functions of the Bonding Curve.

The regulatory status of bonding curves remains uncertain. Many jurisdictions have not offered explicit guidance on whether Automated Market Makers (AMMs), such as bonding curves, fall under the purview of regulated trading venues or securities issuances. In nearly all jurisdictions, a securities exchange license or alternative such as an Alternative Trading System license is required to facilitate the trading of security tokens.

Stick to obvious utility tokens – you will be fine. No dividends, governance rights, etc, etc.

Second, the possibility of price manipulation. Recent decisions, even in the context of utility tokens, have found that not only the traders engaging in price manipulation and insider trading, but the exchanges themselves, to be liable for … securities fraud (huh?)

Auditing smart contracts responsible for executing bonding curves is essential to mitigate potential exploits that may undermine price integrity. Additionally, optimizing smart contracts to reduce gas costs associated with automated trades is imperative. Moreover, securing smart contracts governing bonding curves is paramount to prevent vulnerabilities that could lead to arbitrage or manipulation. Measures such as formal verification, bug bounties, and thorough audits aid in mitigating these risks.

Finally, third, adhering to prevailing AML & KYC regulations. There appears to be this (misguided) belief that DeFI protocols are exempt from AML and KYC regulation – triggered by the requirement to register as a Money Service Business or otherwise obtain digital asset licenses in certain jurisdictions because of the “decentralized” nature of a DEX, etc. As I have mentioned in other blogs and vlogs (read: ranting missives), there are no “listless ships” in international law. Even if a DeFI protocol is truly decentralized insomuch that no single member has the ability to control of otherwise direct the operations of the platform (a rare occurrence anyways), that doesn’t mean that the efforts of an individual or small group of individuals were deployed to design, fund and launch said protocol. Courts in the United States and elsewhere have increasingly been of the opinion that an organization once centralized can never truly become decentralized so as to avoid regulation.


Bonding Curves are an integral – and to some extent necessary element of any DeFI platform that relies on liquidity and fair price discovery. But, of course, the implementation, disclosure relating to and ongoing compliance with ever-changing laws requires significant consideration and planning.

If you have questions regarding Bonding Curves and surrounding issues, be sure to reach out

You can also book a free consultation here.

About Adam Tracy

Adam Tracy is a payments expert and entrepreneur who specializes in payment systems, blockchain technology, digital currencies, and other emerging technologies. He is the founder of Blockrunner, LLC that provides consulting services to clients in the blockchain, payments and cryptocurrency arenas.

Tracy has been involved in the payments industry as an attorney, consultant and entrepreneur since 2005, while he was become an expert in blockchain and cryptocurrency since its advent in 2013. Tracy has worked with a wide range of clients, including startups, established businesses, and investor – both in the United States and worldwide. He has advised clients on a wide range of compliance, legal and operational issues related to payment transfer systems, crypto token generation and architecture, cryptocurrency exchanges, regulatory licensing, smart contracts, and other blockchain applications.

In addition to his consulting work, Tracy has founded several companies in the payments, blockchain and cryptocurrency space, including a digital asset hedge fund, licensed electronic money institution and a blockchain-based tokenization platform. He is also a proponent of decentralized finance (DeFi) and has been involved in various DeFi projects.

Tracy is also a frequent speaker and writer on blockchain and cryptocurrency topics. He has been featured in a wide range of publications, including Forbes, Hollywood Reporters, CNBC, Reuters, CoinDesk, and

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