Multi-Objective Genetic Algorithm for Heston Model Calibration: A Framework Integrating Pricing and Implied Volatility Criteria

Accurate calibration of the Heston model is essential for reliable option pricing, yet it remains a challenging task due to the nonlinear structure of the model and the presence of multiple conflicting objectives. Most existing approaches rely on single-objective formulations that focus solely on price fitting, which may lead to suboptimal overall performance. To address this issue, this paper proposes a mul-ti-objective genetic algorithm framework for Heston model calibration, in which option price errors and implied volatility errors are jointly optimized. The result-ing bi-objective optimization problem is solved using two representative evolu-tionary algorithms, namely NSGA-II and NRGA. This formulation enables an explicit characterization of the trade-off between pricing accuracy and volatility fitting. Extensive experiments are conducted using real option data from SSE 50ETF and S&P 500 markets, as well as Monte Carlo simulations. The results show that both NSGA-II and NRGA produce consistent and comparable pa-rameter estimates. Compared with conventional single-objective methods, the proposed framework leads to improved pricing accuracy and more stable calibra-tion results. Simulation studies further confirm the robustness of the proposed approach under different noise conditions.