If Not Now, Then When? Model Risk in the Optimal Exercise of American Options

2026-03-20

AI Summary

This study investigates model risk in the optimal exercise decisions of American options, focusing on the biases arising from the misuse of the Black–Scholes or Dupire local volatility models—even when these models are perfectly calibrated or frequently recalibrated. By solving for the optimal exercise boundary under the Heston stochastic volatility framework using finite difference methods and comparing it against boundaries derived from misspecified models, the analysis reveals that neglecting stochastic volatility and its correlation with asset returns significantly distorts exercise strategies. The findings demonstrate that such model misspecification introduces non-negligible model risk, thereby underscoring the critical importance of incorporating stochastic volatility dynamics in both the pricing and exercise of American options.

Technology Category

Reasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Mixed Discrete/Continuous SearchGame Theory and Economic Paradigms: Imperfect Information

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: Practical large-scale studies of user experienceEconomics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Model risk arises from the misspecification of probabilistic models used for pricing and hedging derivatives. While model risk for European-style claims has been widely studied, much less attention has been given to American-style derivatives and the associated optimal stopping problems. This paper analyzes model risk in the optimal exercise of an American put option using the benchmark methodology of Hull and Suo [2002]. The true data-generating process is assumed to follow a Heston stochastic volatility model. We compare the optimal exercise strategy of an investor who correctly uses the Heston model with those of investors who instead use misspecified Black--Scholes or Dupire local volatility models. Optimal exercise boundaries are computed numerically via finite difference methods. Stochastic volatility dynamics and return--volatility correlation are found to have a substantial impact on optimal exercise behavior across models, creating a source of model risk. As this behavior is not transmitted to exercise strategies determined by misspecified models, even if such models are fully calibrated to European option prices, calibration fails to mitigate model risk in this context. This issue persists under frequent recalibration of a misspecified model.

Problem

• model risk
• American options
• optimal exercise
• stochastic volatility
• optimal stopping

Innovation

• model risk
• American options
• optimal stopping
• stochastic volatility
• exercise boundary