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A Statistical Learning Approach to Local Volatility Calibration and Option Pricing

In: Transactions of ADIA Lab Interdisciplinary Advances in Data and Computational Science

Author

Listed:
  • Vinicius V. L. Albani
  • Leonardo Sarmanho
  • Jorge P. Zubelli

Abstract

By combining Bayes’ theorem and maximum entropy densities (MED), we propose an accurate and computationally efficient technique for European option pricing and local volatility calibration. The resulting data-driven technique avoids the solution of partial differential equations and the use of Monte Carlo methods. We also show that, under the proposed setting, the price of European options can be expressed as the average Black–Scholes option prices. Numerical examples with synthetic and real data illustrate the effectiveness of the pricing and estimation tools.

Suggested Citation

  • Vinicius V. L. Albani & Leonardo Sarmanho & Jorge P. Zubelli, 2025. "A Statistical Learning Approach to Local Volatility Calibration and Option Pricing," World Scientific Book Chapters, in: Horst Simon (ed.), Transactions of ADIA Lab Interdisciplinary Advances in Data and Computational Science, chapter 4, pages 123-138, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789819813049_0004
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    Keywords

    Computational Science; Data Science; AI Applications; Climate Science; Medical Imaging; Sustainability; Interdisciplinary Research; Data Science; Mathematical and Quantitative Finance;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics

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