Utility-based pricing and hedging of contingent claims in Almgren-Chriss model with temporary price impact

TL;DR

This paper develops a utility-based hedging strategy for options in the Almgren-Chriss model with temporary price impact, addressing mathematical challenges and deriving explicit pricing expansions to quantify market impact.

Contribution

It introduces a novel approach combining analytic and probabilistic methods to construct feedback strategies and asymptotic pricing in a complex market model.

Findings

Explicit feedback representation of optimal hedging strategy

Asymptotic expansion of utility indifference price

Quantification of price impact in options market

Abstract

In this paper, we construct the utility-based optimal hedging strategy for a European-type option in the Almgren-Chriss model with temporary price impact. The main mathematical challenge of this work stems from the degeneracy of the second order terms and the quadratic growth of the first order terms in the associated HJB equation, which makes it difficult to establish sufficient regularity of the value function needed to construct the optimal strategy in a feedback form. By combining the analytic and probabilistic tools for describing the value function and the optimal strategy, we establish the feedback representation of the latter. We use this representation to derive an explicit asymptotic expansion of the utility indifference price of the option, which allows us to quantify the price impact in options' market via the price impact coefficient in the underlying market.