Market Clearing with Semi-fungible Assets

TL;DR

A simple means to compute market clearing prices for semi-fungible assets which have a partial ordering between them, and describes dominant strategy incentive compatible payment and allocation rules for clearing these 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.

Figures (3)

• Figure 1: An example partial ordering on five yield-bearing assets with different ratings and yields, provided by different operators. We assume the operators are not comparable, whereas any buyer prefers a higher rating and higher yield, all else being equal.
• Figure 2: Partial orders on the set of, say, node operators. Some users may be indifferent between the operators $A$ and $B$, while others may be indifferent between $A$ and $C$, and so on.
• Figure 3: Three yield bearing assets with various ratings, and their associated partial ordering.