Concentrated Superelliptical Market Maker

TL;DR

This paper introduces a novel automated market maker capable of handling negative prices, with extensions for skew and concentrated liquidity, applicable to energy and derivatives markets, and compares its features to established models.

Contribution

It presents a new market maker model that allows negative prices and extends liquidity features, contrasting with traditional models like Black-Scholes and LMSR.

Findings

Supports negative and positive asset swaps

Extends liquidity to skew and concentration

Compared invariants with Black-Scholes and LMSR

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.