Concentrated Superelliptical Market Maker

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.