Neural Network for valuing Bitcoin: References

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 [].


[1] Aarts, L. P. and Van Der Veer, P. [2001], ‘Neural network method for solving partial differential equations’, Neural Processing Letters 14(3), 261–271.

[2] Bataineh, M. and Marler, T. [2017], ‘Neural network for regression problems with reduced training sets’, Neural networks 95, 1–9.

[3] Black, F. and Scholes, M. [1973], ‘The pricing of options and corporate liabilities’, Journal of Political Economy 81(3), 637–654. URL:

[4] Bukovina, J., Marticek, M. et al. [2016], ‘Sentiment and bitcoin volatility’, MENDELU Working Papers in Business and Economics 58.

[5] Caporale, G. M., Gil-Alana, L. and Plastun, A. [2018], ‘Persistence in the cryptocurrency market’, Research in International Business and Finance 46, 141–148.

[6] Chaim, P. and Laurini, M. P. [2018], ‘Volatility and return jumps in bitcoin’, Economics Letters 173, 158–163.

[7] Cheah, E.-T. and Fry, J. [2015], ‘Speculative bubbles in bitcoin markets? an empirical investigation into the fundamental value of bitcoin’, Economics Letters 130, 32–36.

[8] Chen, K.-S. and Huang, Y.-C. [2021], ‘Detecting jump risk and jump-diffusion model for bitcoin options pricing and hedging’, Mathematics 9(20), 2567.

[9] Cretarola, A., Fig`a-Talamanca, G. and Patacca, M. [2017], ‘A sentiment-based model for the bitcoin: theory, estimation and option pricing’, arXiv preprint arXiv:1709.08621 .

[10] Dissanayake, M. and Phan-Thien, N. [1994], ‘Neural-network-based approximations for solving partial differential equations’, communications in Numerical Methods in Engineering 10(3), 195-201.

[11] Du, K.-L. [2010], ‘Clustering: A neural network approach’, Neural networks 23(1), 89–107.

[12] Dwyer, G. P. [2015], ‘The economics of bitcoin and similar private digital currencies’, Journal of Financial Stability 17, 81–91.

[13] Eskiizmirliler, S., G¨unel, K. and Polat, R. [2020], ‘On the solution of the black–scholes equation using feed-forward neural networks’, Computational Economics pp. 1–27.

[14] Glau, K. and Wunderlich, L. [2022], ‘The deep parametric pde method and applications to option pricing’, Applied Mathematics and Computation 432, 127355.

[15] Grohs, P., Hornung, F., Jentzen, A. and Von Wurstemberger, P. [2018], ‘A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of blackscholes partial differential equations’, arXiv preprint arXiv:1809.02362 .

[16] Hanson, F. B. and Zhu, Z. [2004], Comparison of market parameters for jump-diffusion distributions using multinomial maximum likelihood estimation, in ‘2004 43rd IEEE Conference on Decision and Control (CDC)(IEEE Cat. No. 04CH37601)’, Vol. 4, IEEE, pp. 3919–3924.

[17] Hilliard, J. E. and Ngo, J. T. [2022], ‘Bitcoin: jumps, convenience yields, and option prices’, Quantitative Finance 22(11), 2079–2091.

[18] Hornik, K. [1991], ‘Approximation capabilities of multilayer feedforward networks’, Neural networks 4(2), 251–257.

[19] Hou, A. J., Wang, W., Chen, C. Y. and H¨ardle, W. K. [2020], ‘Pricing cryptocurrency options’, Journal of Financial Econometrics 18(2), 250–279.

[20] Hussian, E. A. and Suhhiem, M. H. [2015], ‘Numerical solution of partial differential equations by using modified artificial neural network’, Network and Complex Systems 5(6), 11–21.

[21] Jiang, Q., Zhu, L., Shu, C. and Sekar, V. [2022], ‘An efficient multilayer rbf neural network and its application to regression problems’, Neural Computing and Applications pp. 1–18.

[22] Kabaˇsinskas, A. and Sutien˙e, K. [2021], ‘Key roles of crypto-exchanges in generating arbitrage opportunities’, Entropy 23(4), 455.

[23] Katsiampa, P. [2017], ‘Volatility estimation for bitcoin: A comparison of garch models’, Economics Letters 158, 3–6.

[24] Khoo, Y., Lu, J. and Ying, L. [2021], ‘Solving parametric pde problems with artificial neural networks’, European Journal of Applied Mathematics 32(3), 421–435.

[25] Kim, Y. B., Lee, J., Park, N., Choo, J., Kim, J.-H. and Kim, C. H. [2017], ‘When bitcoin encounters information in an online forum: Using text mining to analyse user opinions and predict value fluctuation’, PloS one 12(5), e0177630.

[26] Kim, Y. B., Lee, S. H., Kang, S. J., Choi, M. J., Lee, J. and Kim, C. H. [2015], ‘Virtual world currency value fluctuation prediction system based on user sentiment analysis’, PloS one 10(8), e0132944.

[27] Kristoufek, L. [2013], ‘Bitcoin meets google trends and wikipedia: Quantifying the relationship between phenomena of the internet era’, Scientific reports 3(1), 1–7.

[28] Kristoufek, L. [2015], ‘What are the main drivers of the bitcoin price? evidence from wavelet coherence analysis’, PloS one 10(4), e0123923.

[29] Lagaris, I. E., Likas, A. and Fotiadis, D. I. [1998], ‘Artificial neural networks for solving ordinary and partial differential equations’, IEEE transactions on neural networks 9(5), 987– 1000.

[30] Liu, S., Borovykh, A., Grzelak, L. A. and Oosterlee, C. W. [2019], ‘A neural network-based framework for financial model calibration’, Journal of Mathematics in Industry 9(1), 1–28.

[31] Marghescu, D. [2007], ‘Multidimensional data visualization techniques for financial performance data: A review’, Turku Centre for Computer Science .

[32] Matsuda, K. [2004a], Introduction to merton jump diffusion model.

[33] Matsuda, K. [2004b], ‘Introduction to merton jump diffusion model’, Department of Economics, The Graduate Center, The City University of New York, New York .

[34] Merton, R. C. [1973], ‘Theory of rational option pricing’, The Bell Journal of economics and management science pp. 141–183.

[35] Merton, R. C. [1976], ‘Option pricing when underlying stock returns are discontinuous’, Journal of Financial Economics 3(1-2), 125–144.

[36] Nakamoto, S. [2008], ‘Re: Bitcoin p2p e-cash paper’, Email posted to listserv 9, 04.

[37] Nazemi, A. and Dehghan, M. [2015], ‘A neural network method for solving support vector classification problems’, Neurocomputing 152, 369–376.

[38] Nwankwo, C., Umeorah, N., Ware, T. and Dai, W. [2023], ‘Deep learning and american options via free boundary framework’, Computational Economics pp. 1–44.

[39] Olivares, P. [2020], ‘Pricing bitcoin derivatives under jump-diffusion models’, arXiv preprint arXiv:2002.07117 .

[40] O’Dea, P., Griffith, J., O’Riordan, C., Griffith, J. and Riordan, C. [2001], ‘Combining feature selection and neural networks for solving classification problems’, Information Technology Department, National University of Ireland .

[41] Philippas, D., Rjiba, H., Guesmi, K. and Goutte, S. [2019], ‘Media attention and bitcoin prices’, Finance Research Letters 30, 37–43.

[42] Sarveniazi, A. [2014], ‘An actual survey of dimensionality reduction’, American Journal of Computational Mathematics 2014.

[43] Scaillet, O., Treccani, A. and Trevisan, C. [2017], ‘High-frequency jump analysis of the bitcoin market’, Swiss Finance Institute Research Paper (17-19).

[44] Sene, N. F., Konte, M. A. and Aduda, J. [2021], ‘Pricing bitcoin under double exponential jump-diffusion model with asymmetric jumps stochastic volatility’, Journal of Mathematical Finance 11(2), 313–330.

[45] Setiono, R. and Thong, J. Y. [2004], ‘An approach to generate rules from neural networks for regression problems’, European Journal of Operational Research 155(1), 239–250.

[46] Sirignano, J. and Spiliopoulos, K. [2018], ‘Dgm: A deep learning algorithm for solving partial differential equations’, Journal of computational physics 375, 1339–1364.

[47] Tang, F. [2018], ‘Merton jump-diffusion modeling of stock price data’.

[48] Tankov, P. [2003], Financial modelling with jump processes, Chapman and Hall/CRC.

[49] Teli, M. N. [2007], ‘Dimensionality reduction using neural networks’, Intelligent Engineering Systems Through Artificial Neural Networks 17.

[50] Umeorah, N. and Mba, J. C. [2022], ‘Approximation of single-barrier options partial differential equations using feed-forward neural network’, Applied Stochastic Models in Business and Industry 38(6), 1079–1098.

[51] Watana Be, T. [2006], Excess kurtosis and conditional skewness in stock return distribution: An empirical examination of their impacts on portfolio selection in Japan, Yale University Working Paper.

[52] Xu, R. and Wunsch, D. [2005], ‘Survey of clustering algorithms’, IEEE Transactions on neural networks 16(3), 645–678.

[53] Yadav, N., Yadav, A., Kumar, M. et al. [2015], An introduction to neural network methods for differential equations, Springer.

[54] Yermack, D. [2015], Is bitcoin a real currency? an economic appraisal, in ‘Handbook of digital currency’, Elsevier, pp. 31–43.

[55] Yermack, D. [2017], ‘Corporate governance and blockchains’, Review of Finance 21(1), 7–31.