Pricing in an equilibrium based model for a large investor

TL;DR

This paper develops a model for pricing securities considering the impact of a large investor's trades on market prices, providing explicit formulas and asymptotic expansions for pricing under utility maximization.

Contribution

It introduces an equilibrium-based model incorporating price impact, with explicit recursive pricing formulas and asymptotic analysis for small demands.

Findings

Explicit recursive pricing formula for exponential utility

Asymptotic expansion for small simple demands

Model captures large investor impact on illiquid securities

Abstract

We study a financial model with a non-trivial price impact effect. In this model we consider the interaction of a large investor trading in an illiquid security, and a market maker who is quoting prices for this security. We assume that the market maker quotes the prices such that by taking the other side of the investor's demand, the market maker will arrive at maturity with the maximal expected utility of the terminal wealth. Within this model we provide an explicit recursive pricing formula for an exponential utility function, as well as an asymptotic expansion for the price for a "small" simple demand.