Optimal Liquidation with High Risk Aversion and Small Linear Price Impact

TL;DR

This paper analyzes optimal liquidation strategies under high risk aversion and small linear price impact, deriving asymptotic prices and optimal portfolios within a Bachelier model framework.

Contribution

It establishes a non-trivial scaling limit for vanishing price impact inversely related to risk aversion and explicitly characterizes asymptotically optimal portfolios.

Findings

Derived explicit asymptotic utility indifference prices.

Identified a family of asymptotically optimal portfolios.

Established a non-trivial scaling limit for small price impact.

Abstract

We consider the Bachelier model with linear price impact. Exponential utility indifference prices are studied for vanilla European options in the case where the investor is required to liquidate her position. Our main result is establishing a non-trivial scaling limit for a vanishing price impact which is inversely proportional to the risk aversion. We compute the limit of the corresponding utility indifference prices and find explicitly a family of portfolios which are asymptotically optimal.