A1429
Title: Simulation-based american option pricing: Primal-dual approaches and machine learning
Authors: Sheng-Feng Luo - Chung Yuan Christian University (Taiwan) [presenting]
Yu-Ying Tzeng - National Chengchi University (Taiwan)
Abstract: An integrated simulation-based framework is proposed for pricing American and Bermudan options, combining a primal-dual bounding approach with machine learning to improve accuracy and computational efficiency. The early-exercise boundary is parameterized using a double-exponential functional form and calibrated via K-fold cross-validation on simulated paths, yielding a lower bound on the option price. This boundary is then incorporated into a martingale duality framework with weighted Laguerre polynomial basis functions to derive an upper bound, forming a confidence interval for the true price. To address the suboptimality inherent in parametric stopping rules, logistic regression is applied by treating the exercise decision as a binary classification problem trained on labeled stopping data pooled across multiple initial asset prices. Numerical experiments benchmarked against finite-difference results demonstrate that the primal-dual midpoint estimator achieves low variance but carries a modest upward bias, while the logistic regression-based estimator substantially reduces bias at the cost of higher variance, illustrating a characteristic bias-variance trade-off. Strong performance is achieved without large training datasets, highlighting the practical advantage of combining parametric structure with data-driven refinement. The framework is computationally tractable and naturally extensible to multi-dimensional settings.
