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Option pricing for Barndorff–Nielsen and Shephard model by supervised deep learning

Author

Listed:
  • Takuji Arai

    (Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan)

  • Yuto Imai

    (��Faculty of International Politics and Economics, Nishogakusha University, 6-16 Sanbancho, Chiyoda-ku, Tokyo 102-8336, Japan)

Abstract

This paper aims to develop a supervised deep learning scheme to compute call option prices for the Barndorff-Nielsen and Shephard model with a non-martingale asset price process having infinite active jumps. In our deep learning scheme, teaching data are generated through the Monte Carlo method developed by [Arai and Imai (2024). Monte Carlo simulation for Barndorff-Nielsen and Shephard model under change of measure, Mathematics and Computers in Simulation, 218, 223–234]. Moreover, the BNS model includes many parameters, which makes the deep learning accuracy worse. Therefore, we will create another input parameter using the Black–Scholes formula. As a result, the accuracy is improved dramatically.

Suggested Citation

  • Takuji Arai & Yuto Imai, 2025. "Option pricing for Barndorff–Nielsen and Shephard model by supervised deep learning," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 1-16, March.
    • Handle: RePEc:wsi:ijfexx:v:12:y:2025:i:01:n:s2424786324500117
    DOI: 10.1142/S2424786324500117
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