Neural Network for Valuing Bitcoin: Conclusion, Acknowledgments, and Funding

13 May 2024

This paper is available on arxiv under CC 4.0 license.


(1) Edson Pindza, Tshwane University of Technology; Department of Mathematics and Statistics; 175 Nelson Mandela Drive OR Private Bag X680 and Pretoria 0001; South Africa [];

(2) Jules Clement Mba, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [];

(3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [];

(4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [].

5. Conclusion

This paper has considered the valuation of the bitcoin call option when the bitcoin price dynamics follow a bivariate Merton jump-diffusion model. This research generally provided a novel pricing framework that described the behaviour of bitcoin prices and the model parameter estimation with the intent of pricing the corresponding derivatives. Since bitcoin is normally affected by investors’ attention and sentiment, we used the continuous-time stochastic jump-diffusion process to capture the dynamics of the bitcoin prices and the transaction volumes affecting the price. In the methodological aspect of the research, we extended the classical Black-Scholes model in order to obtain the extended Black-Scholes equation for the bitcoin options.

By introducing the artificial NN, we proposed a trial solution that solves the associated BlackScholes PDE for the bitcoin call options with European features. As a result, the original constrained optimization problem was transformed into an unconstrained one. The numerical results considered both the normal Black-Scholes model and the Merton jump-diffusion model, and it was observed that the latter resulted in a more efficient valuation process. Hence, we can conclude that the NN can be employed efficiently in solving complex PDE-related problems and can be applied to pricing certain financial derivatives without analytical forms. For the Model I and II comparison, we noted that the Black-Scholes used in connection with Model II showed the out-of-the-money feature of the call option. The option absolutely pays off when the underlying price falls below the strike price. The JMD overprices the out-of-the-money options for Model II, whereas the BlackScholes overprices the call options in Model I. Hence, one of the limitations of this research lies in finding the optimal neural network configuration which ensures the fair pricing of bitcoin options using the proposed two models. This optimal feature will be incorporated to avoid over-pricing or under-pricing of these option values, and future research will focus on this.

One of the limitations of the approach used in this paper is that it may be prone to artificial Google searches affecting sentiment-based data analysis and decisions. Even though search-based measures appear to be more transparent than other social media-driven measures, they seem limited as the volume of data is concerned. Social media like Twitter provides high-frequency data (second, minute, hour, daily, . . . ), which can provide meaningful and instantaneous insights into the price dynamics of cryptocurrencies and bitcoin in particular. Our future work will first examine the correlation between search-based data and tweets data, then compare their performance when included in the valuation process. The tweets sentiment scores will be computed using the stateof-the-art Lexicon-based sentiment analyzer Valence Aware Dictionary and sEntiment Reasoner (VADER).

In addition, this paper focused exclusively on jump-diffusion models for cryptocurrency pricing. Levy processes allow the modelling of heavy-tailed return distributions and large deviations from the mean. Expanding the set of stochastic processes considered would provide a more thorough treatment of cryptocurrency dynamics. Processes like variance gamma, normal inverse Gaussian, and generalized hyperbolic Levy motions have shown promise in modelling assets with frequent extreme moves. Given Bitcoin’s volatility clustering and significant outliers, applying Levy processes could potentially improve model fitting. We acknowledge the limitations of only exploring a jumpdiffusion framework presently. Incorporating alternatives like Levy processes would strengthen the generalizability and robustness of the modelling approach. Building on the initial foundation proposed here, researchers could examine a wider set of stochastic processes for capturing empirically observed features. Comparative testing using historical data would elucidate the relative effectiveness of diffusions, Levy processes, and other probabilistic models.

Extending this work to Levy processes represents a valuable progression for future research. The flexibility of Levy’s motions shows potential for modelling emerging cryptocurrency returns. We hope this paper provides a starting point that can be incrementally improved by incorporating innovations like heavy-tailed processes. Evaluating a range of stochastic models will ultimately enhance financial engineering techniques tailored specifically to cryptocurrencies.


The second author thanks the Research Centre of AIMS-Cameroon for hosting him during the preparation of this manuscript.


This research received no external funding.