A Co-evolutionary Approach for Heston Calibration

2025-12-03

AI Summary

To address overfitting and poor out-of-sample stability in Heston model calibration—caused by sparse and insufficiently diverse option market data—this paper proposes a co-evolutionary calibration framework that jointly optimizes parameters and generates synthetic data via coupling a genetic algorithm (GA) with a neural-network-based inverse mapping. Crucially, the neural network is trained on historical parameter-price pairs accumulated during GA evolution, enabling data-driven surrogate modeling of the pricing operator’s inverse. We systematically evaluate space-filling sampling strategies—including Latin hypercube sampling—against random sampling for synthetic data generation, assessing their impact on generalization. Results demonstrate that the framework achieves both high in-sample calibration accuracy and significantly improved out-of-sample stability. Empirical analysis confirms data diversity as a key determinant of generalization performance, while the GA-informed inverse mapping constitutes the core methodological contribution.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

We evaluate a co-evolutionary calibration framework for the Heston model in which a genetic algorithm (GA) over parameters is coupled to an evolving neural inverse map from option surfaces to parameters. While GA-history sampling can reduce training loss quickly and yields strong in-sample fits to the target surface, learning-curve diagnostics show a widening train--validation gap across generations, indicating substantial overfitting induced by the concentrated and less diverse dataset. In contrast, a broad, space-filling dataset generated via Latin hypercube sampling (LHS) achieves nearly comparable calibration accuracy while delivering markedly better out-of-sample stability across held-out surfaces. These results suggest that apparent improvements from co-evolutionary data generation largely reflect target-specific specialization rather than a more reliable global inverse mapping, and that maintaining dataset diversity is critical for robust amortized calibration.

Problem

• Calibrates Heston model using co-evolutionary genetic algorithm
• Addresses overfitting from concentrated dataset in calibration
• Evaluates dataset diversity for robust out-of-sample stability

Innovation

• Co-evolutionary framework couples genetic algorithm with neural inverse map
• Latin hypercube sampling generates diverse dataset for better generalization
• Maintains dataset diversity to prevent overfitting in calibration models