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

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.