Paper: arXiv 2603.19984

Authors: Luna Rigby, Rüdiger Frey, Erik Schlögl

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework for evaluating model risk in American option exercise using stochastic volatility and local volatility models via finite difference methods. However, it relies primarily on theoretical simulation and synthetic market setups rather than extensive empirical backtesting on real market data. Its key contribution lies in demonstrating that recalibration fails to eliminate exercise-related model risk under model misspecification.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Analyze Model Risk in Optimal Exercise<br>of American Put Options"] --> B["True Market Data Process:<br>Heston Stochastic Volatility Model"]
    
    B --> C["Model Calibration & Misspecification:<br>Calibrate Black-Scholes & Dupire Local Vol<br>to Heston European Option Prices"]
    
    C --> D["Computational Process:<br>Compute Optimal Exercise Boundaries<br>via Finite Difference Methods"]
    
    D --> E["Evaluation:<br>Compare True vs. Misspecified<br>Optimal Exercise Strategies"]
    
    E --> F["Key Findings:<br>Stochastic Volatility & Correlation<br>Significantly Impact Exercise Boundaries"]
    
    F --> G["Key Outcome:<br>Calibration & Frequent Recalibration<br>Fail to Mitigate Model Risk"]

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1 of 86 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.