Paper: arXiv 2509.00485

Authors: Dong Yan, Xin-Jie Huang, Guiyuan Ma, Xin-Jiang He

Abstract

We study an American option pricing problem with liquidity risks and transaction fees. As endogenous transaction costs, liquidity risks of the underlying asset are modeled by a mean-reverting process. Transaction fees are exogenous transaction costs and are assumed to be proportional to the trading amount, with the long-run liquidity level depending on the proportional transaction costs rate. Two nonlinear partial differential equations are established to characterize the option values for the holder and the writer, respectively. To illustrate the impact of these transaction costs on option prices and optimal exercise prices, we apply the alternating direction implicit method to solve the linear complementarity problem numerically. Finally, we conduct model calibration from market data via maximum likelihood estimation, and find that our model incorporating liquidity risks outperforms the Leland model significantly.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical and mathematical foundation by combining exogenous and endogenous transaction costs into a system of nonlinear PDEs solved via an ADI scheme. Empirical rigor is supported through maximum likelihood estimation calibration on real market data, demonstrating superior performance over traditional models like Leland.

Research Flowchart

  flowchart TD
    A[Goal: Price American Options with Exogenous & Endogenous Transaction Costs] --> B[Model Formulation: Mean-Reverting Liquidity Risk & Proportional Fees]
    B --> C[Derive Two Nonlinear PDEs / Linear Complementarity Problems for Holder & Writer]
    D[Input: Market Options Data] --> E[Model Calibration via Maximum Likelihood Estimation]
    C --> F[Numerical Solution via Alternating Direction Implicit Method]
    E --> F
    F --> G[Outcomes: Quantified Impact on Option/Exercise Prices & Superior Fit vs. Leland Model]

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