Financial Principles

Multiswap is built on a set of core financial principles that fundamentally differentiate it from traditional automated market makers (AMMs). These principles are designed to address the inefficiencies and limitations of existing DeFi protocols, offering a mathematically sound and self-consistent framework for liquidity provision, price formation, and trading execution.

Below, we outline the five foundational principles that define Multiswap:

1. Discrete Mathematics

Traditional AMMs rely on continuous calculus-based models (e.g., Uniswap’s constant-product formula), which assume markets behave as infinitely divisible functions. However, real-world markets are discrete—price movements are driven by finite transactions, order books, and liquidity shifts.

Multiswap is designed with discrete mathematics, treating transactions as stepwise events rather than infinitesimally small perturbations. This approach allows for:

• Pools with an unlimited number of tokens activating every possible trading pair with zero fragmentation of liquidity for extreme capital efficiency.
• Dynamic weights on every trade to drive any desired price impact opening an infinite new design space.
• Near perfect value preservation as opposed to constant-product AMMs that leak significant value on every trade.

2. Balanced Value

In Multiswap, the total value of assets in the pool is always equal to the value of the LP tokens in circulation. Among other things, this means that the LP token is effectively a share of the undelrying asset portfolio giving you market exposure similar to a new kind of yield-bearing decentralized ETF.

This principle is not unique to Multiswap—most AMMs satisfy this fundamental equality. However, what sets Multiswap apart is how this principle integrates with deterministic post-trade weights and self-financing transactions to form a new market structure.

3. Discrete Self-Financing

Multiswap introduces the concept of discrete self-financing transactions, ensuring that the value flowing into the pool on a trade is always equal to the value flowing out. The discrete product rule decomposes the change in pool value into two components:

1. Value flow due to trading activity: Emerges as the quantity of the token traded multiplied by the post-trade price indicating that all trades are naturally executed at the post-trade price minimizing value leakage and preserving LP wealth.
2. Value change due to market movements: Emerges as the pre-trade token quantity multiplied by the change in price capturing how the pre-trade quantity of an asset is revalued as its price changes over time.

A transaction is self financing if the total value flow due to trading over all tokens involved in the trade is precisely zero ensuring that no value is created or destroyed during a trade.

4. Internal Numeraire

In Multiswap, we introduce a quantity we call "scale" that serves as an internal unit of value that allows all asset prices to be expressed in a common unit, ensuring consistent valuation across trades. Instead of denominating prices in an external reference asset, we define internal prices in terms of scale.

For each token, we associate a scale and the price of that token in terms of scale, i.e. the scaled price, is just its scale divided by the quantity of that token in the pool.

The LP token scale, consistent with its role as value, is the sum of asset scales and the weight of an asset is given by the ratio of its scale to the LP token scale and is independent of the numeraire. The price of one token in terms of another token is simply the ratio of their scaled prices.

5. Dynamic Weights

There are two ways an AMM can impact intrinsic prices of pool assets:

1. Hold the weights constant, while changing the reserves, i.e. trading.
2. Hold the reserves constant, while changinig the weights, i.e. reallocating.

Most AMMs focus on trading for price impact. Curve's stableswap is an example of an AMM that takes advantage of both, but in a roundabout and highly-convoluted manner.

Multiswap has dynamics weights naturally integrated into its core for extremely flexible asset allocation, opening up an infinite design space for future products.

Target Weights

The first new dynamic-weight model we're releasing introduces the concept of target weights. When each asset has a target weight, the actual weights are partitioned into two regions: overweight or underweight. When a trade moves an asset closer to its target weight, that asset experiences precisely zero price impact. When a trade moves an asset away from its target weight, price impact increases and can become severe as the deviation grows.

This creates a market dynamic where the actual weights change with every trade, yet, under normal circumstances, they should hover near the target weights. Under extreme market stress, e.g. a Terra / LUNA scenario, the actual weights and target weights can deviate significantly providing a powerful risk management mechanism to protect liquidity providers.

With this model, we also introduce a new dual governance mechanism that allows liquidity providers to stake their LP tokens to an asset to

1. Earn yield in that asset.
2. Set the target weights, which are stake weighted.

This adds a second layer of risk management for liquidity providers who can now effectively remove assets by allocating their stake away from a troubled asset.

Strategic Asset Allocation

We imagine working with digital asset managers to disrupt the asset management industry. Each Multiswap pool is a portfolio and the asset manager could actively set the target weights. This is a powerful new tool for asset allocation.

Typically, large institutions such as pension funds and insurance companies manage large asset portfolios across many asset classes. A large effort goes into establishing strategic asset allocations. These asset allocations go into investment mandates that form instructions to asset managers who execute and maintains the asset allocations. This process comes at a significant cost to the institution. With Multiswap, we turn this expense into a revenue. By directly setting the target weights according to a desired strategic asset allocation, the market does the trading for you generating transactions fees that go directly to the institution's balance sheet. Multiswap is the futre of asset management.

Index Funds

Another unlock from our dynamic-weight model is that we can easily create decentralized index funds. These index funds could be driven entirely by onchain data sources or we could incorporate oracles. For example, using an oracle, we could easily construct tradeable market-weighted indices.

Derivatives

Dynamic weights allow us to programmatically implement any investment strategy including delta hedging. A large class of derivatives products can be replicated via hedging strategies. This opens the door for us to offer various derivatives products via Multiswap.

Prediction Markets

Multiswap's multi-asset scalability and dynamic-weight model introduce a novel approach to prediction markets. Traditional prediction markets often suffer from liquidity fragmentation, where each outcome is treated as a separate pool or market, making it difficult to trade efficiently across multiple outcomes.

With Multiswap, all outcomes of a given event can coexist within a single pool, sharing liquidity and adjusting probabilities dynamically as traders buy and sell outcome tokens.

The Governing Equation

Bringing all the financial principles above together, we can finally write down the fundamental equation that governs Multiswap

$$\Delta \alpha_0 \frac{s_0+\Delta s_0}{\alpha_0+\Delta\alpha_0}=\sum_{i=1}^n \Delta \alpha_i \frac{s_i+\Delta s_i}{\alpha_i+\Delta\alpha_i}.$$

See our Technical Paper for details.

Key Implications

• Scalability with Unlimited Assets: Multiswap pools can accommodate an unlimited number of assets, automatically activating all trading pairs. This design ensures capital efficiency scales with the number of tokens in the pool.

• LP Tokens as Decentralized Index Shares: Liquidity Provider (LP) tokens act as shares in a decentralized index fund, giving holders proportional exposure to all assets in the pool.

• Reduced Value Leakage: Swaps executed at post-trade prices significantly reduce value leakage, minimizing single-trade impermanent loss and mitigating loss-versus-rebalancing effects.

• Adaptable for Advanced Financial Instruments: Multiswap’s foundational principles make it suitable for more complex financial applications, including fixed-income products and derivatives, while ensuring proper accounting of all value flows.