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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.05519 |
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| _version_ | 1866914143306514432 |
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| author | Kazemian, Sina Farhani, Ghazal Yazdi, Amirhessam |
| author_facet | Kazemian, Sina Farhani, Ghazal Yazdi, Amirhessam |
| contents | We present an uncertainty-aware, physics-informed neural network (PINN) for option pricing that solves the Black--Scholes (BS) partial differential equation (PDE) as a mesh-free, global surrogate over $(S,t)$. The model embeds the BS operator and boundary/terminal conditions in a residual-based objective and requires no labeled prices. For American options, early exercise is handled via an obstacle-style relaxation while retaining the BS residual in the continuation region. To quantify \emph{epistemic} uncertainty, we introduce an anchored-ensemble fine-tuning stage (AT--PINN) that regularizes each model toward a sampled anchor and yields prediction bands alongside point estimates. On European calls/puts, the approach attains low errors (e.g., MAE $\sim 5\times10^{-2}$, RMSE $\sim 7\times10^{-2}$, explained variance $\approx 0.999$ in representative settings) and tracks ground truth closely across strikes and maturities. For American puts, the method remains accurate (MAE/RMSE on the order of $10^{-1}$ with EV $\approx 0.999$) and does not exhibit the error accumulation associated with time-marching schemes. Against data-driven baselines (ANN, RNN) and a Kolmogorov--Arnold FINN variant (KAN), our PINN matches or outperforms on accuracy while training more stably; anchored ensembles provide uncertainty bands that align with observed error scales. We discuss design choices (loss balancing, sampling near the payoff kink), limitations, and extensions to higher-dimensional BS settings and alternative dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An uncertainty-aware physics-informed neural network solution for the Black-Scholes equation: a novel framework for option pricing Kazemian, Sina Farhani, Ghazal Yazdi, Amirhessam Computational Finance Applied Physics We present an uncertainty-aware, physics-informed neural network (PINN) for option pricing that solves the Black--Scholes (BS) partial differential equation (PDE) as a mesh-free, global surrogate over $(S,t)$. The model embeds the BS operator and boundary/terminal conditions in a residual-based objective and requires no labeled prices. For American options, early exercise is handled via an obstacle-style relaxation while retaining the BS residual in the continuation region. To quantify \emph{epistemic} uncertainty, we introduce an anchored-ensemble fine-tuning stage (AT--PINN) that regularizes each model toward a sampled anchor and yields prediction bands alongside point estimates. On European calls/puts, the approach attains low errors (e.g., MAE $\sim 5\times10^{-2}$, RMSE $\sim 7\times10^{-2}$, explained variance $\approx 0.999$ in representative settings) and tracks ground truth closely across strikes and maturities. For American puts, the method remains accurate (MAE/RMSE on the order of $10^{-1}$ with EV $\approx 0.999$) and does not exhibit the error accumulation associated with time-marching schemes. Against data-driven baselines (ANN, RNN) and a Kolmogorov--Arnold FINN variant (KAN), our PINN matches or outperforms on accuracy while training more stably; anchored ensembles provide uncertainty bands that align with observed error scales. We discuss design choices (loss balancing, sampling near the payoff kink), limitations, and extensions to higher-dimensional BS settings and alternative dynamics. |
| title | An uncertainty-aware physics-informed neural network solution for the Black-Scholes equation: a novel framework for option pricing |
| topic | Computational Finance Applied Physics |
| url | https://arxiv.org/abs/2511.05519 |