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

Takuji Arai and Yuto Imai ()
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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

International Journal of Financial Engineering (IJFE), 2025, vol. 12, issue 01, 1-16

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.

Keywords: Barndorff-Nielsen and Shephard model; stochastic volatility model; supervised deep learning; Monte Carlo simulation; Black–Scholes formula (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S2424786324500117

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