Asian option valuation under price impact

TL;DR

This paper develops a comprehensive framework for valuing Asian options considering market impact and execution costs, analyzing both exogenous and endogenous impact regimes with numerical methods and revealing how impact influences bid-ask spreads.

Contribution

It introduces a novel continuous-time model for Asian option valuation incorporating transient and permanent market impacts, and provides a closed-form solution in the deterministic volatility case.

Findings

Endogenous impact causes nontrivial bid-ask spreads.

Impact effects are modest in exogenous regimes.

Spreads grow super-linearly with impact parameters.

Abstract

We develop a tractable framework for valuing Asian options when trading the underlying generates market impact and execution costs. Starting from a discrete-time, quote-level model, we construct a reference midpoint suitable for Asian payoffs and separate market impact into a transient component and a permanent drift distortion driven by signed trading. This specification admits continuous-time limits where the midpoint and impact state converge to a coupled system in which the midpoint drift depends on the transient impact state and in the endogenous regime on the hedger's trading rate, with correlated price and order-flow shocks. We study valuation in two complementary regimes. In an exogenous benchmark, the impact state evolves independently of the hedger. When the order-flow volatility is deterministic, we obtain a closed-form expression for the geometric Asian call. In an endogenous regime, trading volumes feed back into prices and costs, leading to a stochastic control problem and Hamilton-Jacobi-Bellman equations. We define reservation bid and ask prices via cost-based indifference which produces an impact-driven bid-ask spread. For computations, we propose a CRR-style tree-based Bellman algorithm. Numerical experiments show that exogenous impact effects are modest relative to frictionless benchmarks, while endogenous indifference prices generate nontrivial bid-ask spreads that grow super-linearly in impact parameters, widen when execution costs are lower, and shrink with faster mean reversion, highlighting the interaction between averaging in Asian options, price impact effects, and strategic trading.