Concentrated Superelliptical Market Maker

ArXiv ID: 2410.13265 “View on arXiv”

Authors: Unknown

Abstract

An automated market maker where the price can cross the zero bound into the negative price domain with applications in electricity, energy, and derivatives markets is presented. A unique feature involves the ability to swap both negatively and positively priced assets between one another, which unlike traditional markets requires a numeraire in the form of a currency. Model extensions to skew and concentrate liquidity are shown. The liquidity fingerprint, payoff, and invariant are compared to the Black-Scholes covered call and the Logarithmic Market Scoring Rule invariants.

Keywords: Automated Market Maker (AMM), Negative Prices, Liquidity Concentration, Logarithmic Market Scoring Rule, Invariant Design, Energy / Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper presents advanced mathematical derivations including special functions, Legendre transforms, and Lamé curves, but lacks empirical backtesting, datasets, or implementation metrics, focusing instead on theoretical model construction and comparisons.

  flowchart TD
    Goal["Research Goal: Design an AMM supporting negative prices for energy/derivatives, eliminating the need for a currency numeraire"]
    Data["Input: Stylized Facts from Energy Markets<br>(e.g., Price Skew, Volatility, Negative Regimes)"]
    Method["Methodology: Derive Superelliptic Invariant<br>x^p + |y|^p = k"]
    Sim["Computational Process: Calibration & Simulation<br>(Price Impact, Payoffs, Liquidity Fingerprints)"]
    Comp["Comparison: <br>Black-Scholes Covered Call & LMSR"]
    Outcomes["Key Findings: <br>1. Flexible Price Domain (incl. Negative)<br>2. Liquidity Concentration via Skew<br>3. Unique Payoff/Invariant Profile"]