Author(s)

YiFan Zhang^*, Wei Chen, Oliver Schmidt

Affiliation(s)

Department of Industrial & Enterprise Systems Engineering, University of Illinois Urbana-Champaign, Illinois, USA.

Corresponding Author

YiFan Zhang

ABSTRACT

The calibration of stochastic volatility models remains a computationally demanding challenge in quantitative finance, where traditional optimization algorithms often encounter difficulties with numerical stability, convergence speed, and local minima entrapment. This paper presents a comprehensive comparative analysis of deep learning methodologies, particularly Neural Stochastic Differential Equations (Neural SDEs), against conventional calibration techniques for stochastic volatility models. We examine the mathematical complexities inherent in pricing functions, specifically addressing the branch-switching discontinuities in characteristic function representations that create numerical challenges for traditional methods. Through detailed analysis of neural network architectures incorporating exponential linear unit activation functions and multiple hidden layers, we demonstrate how deep learning frameworks can overcome these computational obstacles. Our empirical investigation employs performance metrics including Average Absolute Relative Error (AARE), Root Mean Square Error (RMSE), and Mean Absolute Relative Error (MARE) to evaluate genetic algorithms, adaptive simulated annealing, nonlinear least squares optimization, and neural network approaches across diverse market conditions. The findings reveal that carefully designed neural architectures achieve superior calibration accuracy with AARE below one percent while reducing computational time by orders of magnitude compared to global optimization methods. Specifically, advanced optimization techniques combining lsqnonlin with appropriate initialization strategies demonstrate MARE values as low as 2.33 percent, significantly outperforming genetic algorithms that exhibit errors exceeding 15 percent in challenging calibration scenarios. This research contributes practical insights for implementing production-grade calibration systems that balance accuracy, speed, and numerical robustness, while exploring the theoretical foundations connecting continuous-time stochastic process modeling with modern deep learning architectures.

KEYWORDS

Stochastic volatility models; Neural networks; Heston model calibration; Characteristic function; Branch switching; Deep learning; Optimization algorithms; Exponential linear units; Model calibration; Computational finance

CITE THIS PAPER

YiFan Zhang, Wei Chen, Oliver Schmidt. Deep learning approaches to stochastic volatility model calibration: a comparative analysis of neural SDES and traditional methods. Journal of Trends in Financial and Economics. 2025, 2(4): 13-24. DOI: https://doi.org/10.61784/jtfe3061.

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