A Statistical Learning Approach to Local Volatility Calibration and Option Pricing

Vinicius V. L. Albani, Leonardo Sarmanho and Jorge P. Zubelli

Chapter 4 in Transactions of ADIA Lab:Interdisciplinary Advances in Data and Computational Science, 2025, pp 123-138 from World Scientific Publishing Co. Pte. Ltd.

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.

Keywords: Computational Science; Data Science; AI Applications; Climate Science; Medical Imaging; Sustainability; Interdisciplinary Research; Data Science; Mathematical and Quantitative Finance (search for similar items in EconPapers)
JEL-codes: C45 C63 G11 Q54 (search for similar items in EconPapers)
Date: 2025
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