Neural Network for valuing Bitcoin: References

This paper is available on arxiv under CC 4.0 license. Authors: (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 [edsonpindza@gmail.com]; (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 [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction Methodology Neural Network Methodology Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations References References [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: https://doi.org/10.1086/260062 [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. This paper is available on arxiv under CC 4.0 license. Authors: (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 [edsonpindza@gmail.com]; (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 [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (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 [edsonpindza@gmail.com]; (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 [jmba@uj.ac.za]; (3) Sutene Mwambi, University of Johannesburg; School of Economics, College of Business and Economics and P. O. Box 524, Auckland Park 2006; South Africa [sutenem@uj.ac.za]; (4) Nneka Umeorah, Cardiff University; School of Mathematics; Cardiff CF24 4AG; United Kingdom [umeorahn@cardiff.ac.uk]. Table of Links Abstract and Introduction Methodology Neural Network Methodology Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations References Abstract and Introduction Abstract and Introduction Methodology Methodology Neural Network Methodology Neural Network Methodology Numerical results, implementation and discussion Numerical results, implementation and discussion Conclusion, Acknowledgments, and Funding Conclusion, Acknowledgments, and Funding Availability of data, code and materials, Contributions and Declarations Availability of data, code and materials, Contributions and Declarations References References References [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: https://doi.org/10.1086/260062 [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.