Data driven neural network approaches for pricing options
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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier B.V
Abstract
This paper presents two data driven approaches, the purely data driven (PDD) and physics informed neural network (PINN) approach for solving asset pricing problems. The PDD approach relies purely on available data and does not require any governing partial differential equation (PDE) to solve a pricing problem. On the other hand, under the PINN approach, the pricing is done by solving a governing PDE. Both models are calibrated to observed market prices, and their implied volatilities are compared to those derived from market data and the classical Black–Scholes model. The absolute errors and maximum absolute errors metrics relative to observed implied volatilities and prices and the prices obtained from the classical Black–Scholes model were used in measuring the goodness-of-fit of the two proposed techniques. Several hyperparameter tuning techniques were employed to optimize the performance of the two methods. In addition, we analyze the probability density functions (PDFs) derived from each method and verify that they are valid by demonstrating positivity and proper normalization. Theoretical results, including propositions and theorems, are presented to establish conditions under which the PINN, trained using the Adam optimizer and initialized via the Xavier method, converges to an optimal solution, i.e., a set of trainable parameters that minimize the loss function. In further extensions, the PINN approach was applied to pricing European put options under a Heston stochastic volatility model (HSVM) model. While both methods exhibit competitive performance when calibrated, our empirical findings indicate that the PINN approach yields superior accuracy and stability.
Description
Keywords
Heston stochastic volatility model, Implied volatility, Neural networks, Numerical methods, Option pricing
Citation
Nuugulu, S.M., Patidar, K.C. and Tarla, D.T., 2025. Data driven neural network approaches for pricing options. Physica D: Nonlinear Phenomena, p.134992.