Endogenous inverse demand functions

TL;DR

This paper develops an equilibrium model for endogenous inverse demand functions, analyzing price impacts in asset liquidation scenarios with considerations for utility-based market participant behaviors.

Contribution

It introduces a generalized equilibrium framework for price impacts, extending the Buhlmann equilibrium and studying properties like existence, uniqueness, monotonicity, and concavity.

Findings

Existence and uniqueness of clearing prices established.

Price impacts depend on utility functions such as exponential and power utilities.

Portfolio properties like monotonicity and concavity are analyzed.

Abstract

In this work we present an equilibrium formulation for price impacts. This is motivated by the Buhlmann equilibrium in which assets are sold into a system of market participants, e.g. a fire sale in systemic risk, and can be viewed as a generalization of the Esscher premium. Existence and uniqueness of clearing prices for the liquidation of a portfolio are studied. We also investigate other desired portfolio properties including monotonicity and concavity. Price per portfolio unit sold is also calculated. In special cases, we study price impacts generated by market participants who follow the exponential utility and power utility.