Error Analysis of Option Pricing via Deep PDE Solvers: Empirical Study
Rawin Assabumrungrat Kentaro Minami Masanori Hirano
Option pricing, a fundamental problem in finance, often requires solving
non-linear partial differential equations (PDEs). When dealing with multi-asset
options, such as rainbow options, these PDEs become high-dimensional, leading
to challenges posed by the curse of dimensionality. While deep learning-based
PDE solvers have recently emerged as scalable solutions to this
high-dimensional problem, their empirical and quantitative accuracy remains not
well-understood, hindering their real-world applicability. In this study, we
aimed to offer actionable insights into the utility of Deep PDE solvers for
practical option pricing implementation. Through comparative experiments, we
assessed the empirical performance of these solvers in high-dimensional
contexts. Our investigation identified three primary sources of errors in Deep
PDE solvers: (i) errors inherent in the specifications of the target option and
underlying assets, (ii) errors originating from the asset model simulation
methods, and (iii) errors stemming from the neural network training. Through
ablation studies, we evaluated the individual impact of each error source. Our
results indicate that the Deep BSDE method (DBSDE) is superior in performance
and exhibits robustness against variations in option specifications. In
contrast, some other methods are overly sensitive to option specifications,
such as time to expiration. We also find that the performance of these methods
improves inversely proportional to the square root of batch size and the number
of time steps. This observation can aid in estimating computational resources
for achieving desired accuracies with Deep PDE solvers.