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Neural Network for Valuing Bitcoin Options Under Jump-Diffusion and Market Sentiment Model

Author

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  • Edson Pindza

    (Tshwane University of Technology)

  • Jules Clement

    (University of Johannesburg)

  • Sutene Mwambi

    (University of Johannesburg)

  • Nneka Umeorah

    (Cardiff University)

Abstract

Cryptocurrencies and Bitcoin, in particular, are prone to wild swings resulting in frequent jumps in prices, making them historically popular for traders to speculate. It is claimed in recent literature that Bitcoin price is influenced by sentiment about the Bitcoin system. Transaction, as well as the popularity, have shown positive evidence as potential drivers of Bitcoin price. This study introduces a bivariate jump-diffusion model to capture the dynamics of Bitcoin prices and the Bitcoin sentiment indicator, integrating trading volumes or Google search trends with Bitcoin price movements. We derive a closed-form solution for the Bitcoin price and the associated Black–Scholes equation for Bitcoin option valuation. The resulting partial differential equation for Bitcoin options is solved using an artificial neural network, and the model is validated with data from highly volatile stocks. We further test the model’s robustness across a broad spectrum of parameters, comparing the results to those obtained through Monte Carlo simulations. Our findings demonstrate the model’s practical significance in accurately predicting Bitcoin price movements and option values, providing a reliable tool for traders, analysts, and risk managers in the cryptocurrency market.

Suggested Citation

  • Edson Pindza & Jules Clement & Sutene Mwambi & Nneka Umeorah, 2025. "Neural Network for Valuing Bitcoin Options Under Jump-Diffusion and Market Sentiment Model," Computational Economics, Springer;Society for Computational Economics, vol. 66(3), pages 2305-2342, September.
    • Handle: RePEc:kap:compec:v:66:y:2025:i:3:d:10.1007_s10614-024-10792-1
    DOI: 10.1007/s10614-024-10792-1
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    References listed on IDEAS

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    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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