Market Clearing with Semi-fungible Assets

TL;DR

This paper introduces a method to compute market clearing prices for semi-fungible assets with partial ordering, applicable across traditional, private, and decentralized markets, using convex optimization and duality.

Contribution

It presents a novel convex optimization framework and duality approach for pricing semi-fungible assets with partial orderings, enhancing market clearing efficiency.

Findings

Efficient computation of market clearing prices for semi-fungible assets.

Application of convex duality to estimate prices.

Framework applicable to various asset classes and markets.

Abstract

As markets have digitized, the number of tradable products has skyrocketed. Algorithmically constructed portfolios of these assets now dominate public and private markets, resulting in a combinatorial explosion of tradable assets. In this paper, we provide a simple means to compute market clearing prices for semi-fungible assets which have a partial ordering between them. Such assets are increasingly found in traditional markets (bonds, commodities, ETFs), private markets (private credit, compute markets), and in decentralized finance. We formulate the market clearing problem as an optimization problem over a directed acyclic graph that represents participant preferences. Subsequently, we use convex duality to efficiently estimate market clearing prices, which correspond to particular dual variables. We then describe dominant strategy incentive compatible payment and allocation rules for clearing these markets. We conclude with examples of how this framework can construct prices for a variety of algorithmically constructed, semi-fungible portfolios of practical importance.