Asian option valuation under price impact

Paper: arXiv 2512.07154

Authors: Priyanshu Tiwari, Sourav Majumdar

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework combining microstructure price impact with stochastic control and HJB equations for Asian options. However, its empirical validation is limited to synthetic numerical experiments rather than backtests on real market datasets.

Research Flowchart

  flowchart TD
    A[Research Goal: Asian Option Valuation under Market Impact & Execution Costs] --> B[Discrete-Time Quote-Level Model<br>Transient Impact + Permanent Drift]
    B --> C[Continuous-Time Limit & State Coupling]
    
    C --> D1[Exogenous Regime: Independent Impact]
    C --> D2[Endogenous Regime: Hedger Feedback]
    
    D1 --> E1[Closed-Form Solution for Geometric Asian Call]
    D2 --> E2[HJB Equations & CRR Tree-Based Bellman Algorithm]
    
    E1 --> F[Key Findings: Exogenous Impact Effects Are Modest]
    E2 --> G[Key Findings: Indifference Pricing Yields Non-Linear Bid-Ask Spreads]

Cited References (94)

1. Option pricing: A simplified approach (1979) — link
2. Pricing Bounds on Asian Options (2003) — link
3. Efficient pricing of discrete Asian options (2011) — link
4. General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options (2016) — link
5. Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps (2014) — link
6. Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets (2008) — link
7. Small dimension PDE for discrete Asian options (2003) — link
8. A General Framework for Pricing Asian Options Under Markov Processes (2015) — link

1 of 94 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.