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

TL;DR

This paper investigates how model risk affects the optimal exercise strategies of American put options when the true data follows a stochastic volatility model, highlighting the limitations of calibration in mitigating this risk.

Contribution

It introduces a benchmark analysis of model risk in American options using the Heston model as the true process and compares it with misspecified models like Black-Scholes and local volatility.

Findings

Stochastic volatility and return-volatility correlation significantly influence exercise boundaries.

Misspecified models fail to replicate true exercise strategies even after calibration.

Calibration does not fully mitigate model risk in American option exercise decisions.

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.