Utility Indifference Pricing with High Risk Aversion and Small Linear Price Impact

TL;DR

This paper analyzes utility indifference pricing in a Bachelier model with linear price impact, deriving a scaling limit for vanishing impact and identifying asymptotically optimal portfolios.

Contribution

It introduces a novel scaling limit for utility indifference prices under small linear price impact and characterizes asymptotically optimal trading strategies.

Findings

Derived explicit scaling limit for prices as impact vanishes

Identified a family of asymptotically optimal portfolios

Provided analytical formulas for exponential utility indifference prices

Abstract

We consider the Bachelier model with linear price impact. Exponential utility indifference prices are studied for vanilla European options and we compute their non-trivial scaling limit for a vanishing price impact which is inversely proportional to the risk aversion. Moreover, we find explicitly a family of portfolios which are asymptotically optimal.