A Co-evolutionary Approach for Heston Calibration

TL;DR

This paper evaluates a co-evolutionary framework for calibrating the Heston model, highlighting the importance of dataset diversity for robust out-of-sample performance over in-sample fit.

Contribution

It demonstrates that maintaining dataset diversity via Latin hypercube sampling improves out-of-sample stability compared to co-evolutionary data generation.

Findings

Genetic algorithms achieve strong in-sample fit but overfit with concentrated data.

Latin hypercube sampling yields comparable calibration accuracy with better out-of-sample stability.

Dataset diversity is crucial for robust amortized calibration.

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.