Pricing American options with exogenous and endogenous transaction costs

2025-08-30

AI Summary

This paper addresses the pricing of American options under liquidity risk and transaction costs. To overcome the limitation of conventional models that treat liquidity as an exogenous constant, the authors innovatively model endogenous liquidity as a mean-reverting stochastic process and jointly incorporate exogenous transaction costs, yielding a coupled system of two nonlinear partial differential equations (PDEs) characterizing the values of long and short option positions. This framework is the first to explicitly capture the feedback effect of trading activity on long-term liquidity levels, thereby more realistically representing the joint impact of market frictions on both option valuation and the optimal exercise boundary. The associated linear complementarity problem is solved numerically using the alternating direction implicit (ADI) method, and model parameters are calibrated empirically via maximum likelihood estimation. Empirical results demonstrate that the proposed model significantly outperforms the classical Leland model, markedly improving pricing accuracy and reliability of exercise boundary identification in transaction-cost environments.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Modeling American option pricing with liquidity risks and transaction fees
• Establishing nonlinear PDEs for holder and writer option values
• Numerically solving linear complementarity problem to analyze cost impacts

Innovation

• Mean-reverting process models liquidity risks
• Alternating direction implicit method for numerical solution
• Maximum likelihood estimation for model calibration