Analysis of parametric and non-parametric option pricing models

Area of Science:

• Quantitative Finance
• Computational Finance
• Financial Modeling

Background:

• Option pricing models are crucial for financial markets.
• Existing models like Heston and machine learning approaches have limitations.
• A need exists for more accurate and stable option pricing methodologies.

Purpose of the Study:

• To derive a closed-form analytical solution for option pricing under the Bi-Heston model.
• To empirically compare the Bi-Heston model against parametric and non-parametric (machine learning) models.
• To assess the in-sample and out-of-sample pricing performance and robustness of these models.

Main Methods:

• Derivation of a closed-form analytical solution for the Bi-Heston model.
• Empirical analysis comparing pricing effects of parametric (Bi-Heston, Heston) and non-parametric (machine learning) models.
• Robustness analysis to evaluate model stability.

Main Results:

• The parametric pricing model, particularly the Bi-Heston model, shows superior in-sample pricing performance compared to machine learning models.
• For out-of-sample call options, the parametric model outperforms machine learning; for put options, the Bi-Heston model significantly outperforms others.
• The Bi-Heston model exhibits greater stability in robustness analysis compared to the unstable machine learning model.

Conclusions:

• The Bi-Heston model offers a robust and accurate analytical solution for option pricing.
• It outperforms both the Heston model and machine learning approaches in various pricing scenarios.
• The findings highlight the advantages of the Bi-Heston model for financial practitioners seeking reliable option pricing tools.