The Evolution of the Black-Scholes Model: A Bibliometric Analysis
Abstract
Objective –To investigate the development of the Black-Scholes Model in financial research, identify its key contributors, and map its thematic evolution through a bibliometric analysis.
Methodology –This study employs bibliometric analysis, a research method that uses bibliographic data to analyze trends, patterns, and the impact of scholarly works in the financial research area. The data was extracted from the Scopus database, processed, and visualized using Microsoft Excel, R-Packages software, and the Biblioshiny Web Interface. The data extraction process was conducted on December 25, 2023, identifying 941 relevant documents, with 719 documents determined to be eligible for the analysis.
Results –The analysis reveals significant evolution in academic interest in the Black-Scholes Model since its introduction in 1978, with key contributors from the United States and the United Kingdom. Early research (1978–2000) focused on the theoretical basis of the model, while the period 2001–2010 marked its increasing relevance in economics. The 2011–2020 period saw the integration of the model in a wide range of economic applications. The 2021–2023 period highlights a new research focus on applications in fractional differential equations. The model has become an essential element in modern finance, driving innovation in finance education, policy, and cross-disciplinary applications.
Research limitations/implications –The study is limited by its reliance on data from the Scopus database, which may not encompass all relevant research. Future research could expand the analysis to include other databases and consider qualitative aspects of the Black-Scholes Model's applications.
Novelty/Originality –This research underscores the importance of the Black-Scholes Model in the evolution of modern finance and its diverse applications. It makes a significant contribution to the study of economics and finance by providing a comprehensive bibliometric analysis of the model's development, key contributors, and thematic evolution.
Keywords
Full Text:
PDFReferences
Abdi, N., Aminikhah, H., & Sheikhani, A. H. R. (2022). High-order compact finite difference schemes for the time-fractional Black-Scholes model governing European options. Chaos, Solitons & Fractals, 162, 112423. https://doi.org/10.1016/j.chaos.2022.112423
Albevirio, S., Popovici, A., & Steblovskaya, V. (2006). A NUMERICAL ANALYSIS OF THE EXTENDED BLACK–SCHOLES MODEL. International Journal of Theoretical and Applied Finance, 09(01), 69–89. https://doi.org/10.1142/S0219024906003469
Almeida, R. M. P., Chihaluca, T. D., & Duque, J. C. M. (2022). Approach to the Delta Greek of nonlinear Black–Scholes equation governing European options. Journal of Computational and Applied Mathematics, 402, 113790. https://doi.org/10.1016/j.cam.2021.113790
Ballabio, L. (2023). The Black-Scholes Model in QuantLib. Wilmott, 2023(125). https://doi.org/10.54946/wilm.11135
Bornmann, L., & de Moya-Anegón, F. (2019). Spatial bibliometrics on the city level. Journal of Information Science, 45(3), 416–425. https://doi.org/10.1177/0165551518806119
Buchen, P. (2012). An Introduction to Exotic Option Pricing. Chapman and Hall/CRC. https://doi.org/10.1201/b11589
Capała, K., & Dybiec, B. (2021). Random acceleration process on finite intervals under stochastic restarting. Journal of Statistical Mechanics: Theory and Experiment, 2021(8), 083216. https://doi.org/10.1088/1742-5468/ac1664
Černá, D., & Fiňková, K. (2024). Option pricing under multifactor Black–Scholes model using orthogonal spline wavelets. Mathematics and Computers in Simulation, 220, 309–340. https://doi.org/10.1016/j.matcom.2024.01.020
Chen, J., Li, X., & Shao, Y. (2024). Numerical analysis of fractional order Black–Scholes option pricing model with band equation method. Journal of Computational and Applied Mathematics, 451, 115998. https://doi.org/10.1016/j.cam.2024.115998
Chong, C., Zhang, X., Kong, G., Ma, L., Li, Z., Ni, W., & Yu, E.-H.-C. (2021). A Visualization Method of the Economic Input–Output Table: Mapping Monetary Flows in the Form of Sankey Diagrams. Sustainability, 13(21), 12239. https://doi.org/10.3390/su132112239
Christain, O., Iyai, D., & Uchenna, Amad, I. (2023). A Numerical Approximation on Black-Scholes Equation of Option Pricing. Asian Research Journal of Mathematics, 19(7), 92–105. https://doi.org/10.9734/arjom/2023/v19i7682
Contreras G., M. (2021). Endogenous stochastic arbitrage bubbles and the Black–Scholes model. Physica A: Statistical Mechanics and Its Applications, 583, 126323. https://doi.org/10.1016/j.physa.2021.126323
De Vita, T., & Rosa, R. (2018). The Index for Inclusion. ITALIAN JOURNAL OF HEALTH EDUCATION, SPORT AND INCLUSIVE DIDACTICS, 2(2).
Edeki, S. O., Fadugba, S. E., & Khalique, C. M. (2023). Valuation of deposit insurance Black–Scholes model using Banach contraction principle. Partial Differential Equations in Applied Mathematics, 8, 100571. https://doi.org/10.1016/j.padiff.2023.100571
Figlewski, S. (2002). Assessing the Incremental Value of Option Pricing Theory Relative to an Informationally Passive Benchmark. The Journal of Derivatives, 10(1), 80–96. https://doi.org/10.3905/jod.2002.319192
Gianin, E. R., & Sgarra, C. (2013). Black-Scholes Model for Option Pricing and Hedging Strategies (pp. 123–152). https://doi.org/10.1007/978-3-319-01357-2_7
Grosseck, G., Țîru, L. G., & Bran, R. A. (2019). Education for Sustainable Development: Evolution and Perspectives: A Bibliometric Review of Research, 1992–2018. Sustainability, 11(21), 6136. https://doi.org/10.3390/su11216136
Hanivan, H., & Nasrudin, N. (2019). A FINANCIAL INCLUSION INDEX FOR INDONESIA. Buletin Ekonomi Moneter Dan Perbankan, 22(3), 351–366. https://doi.org/10.21098/bemp.v22i3.1056
Hsu, Y.-S., & Wu, C.-H. (2020). Extended Black and Scholes model under bankruptcy risk. Journal of Mathematical Analysis and Applications, 482(2), 123564. https://doi.org/10.1016/j.jmaa.2019.123564
Jensen, W. A., Szarka, J., & White, K. (2019). Stability assessment with the stability index. Quality Engineering, 31(2), 289–301. https://doi.org/10.1080/08982112.2018.1497179
Jugović, A., Sirotić, M., & Poletan Jugović, T. (2022). Identification of Pivotal Factors Influencing the Establishment of Green Port Governance Models: A Bibliometric Analysis, Content Analysis, and DPSIR Framework. Journal of Marine Science and Engineering, 10(11), 1701. https://doi.org/10.3390/jmse10111701
Kermiche, L. (2014). Too Much Of A Good Thing? A Review Of Volatility Extensions In Black-Scholes. Journal of Applied Business Research (JABR), 30(4), 1171. https://doi.org/10.19030/jabr.v30i4.8662
Krykun, I. H. (2023). The Black-Scholes Exotic Barrier Option Pricing Formula. Trends Journal of Sciences Research, 1(1), 10–18. https://doi.org/10.31586/jml.2023.604
Krzyżanowski, G., & Magdziarz, M. (2021). A computational weighted finite difference method for American and barrier options in subdiffusive Black–Scholes model. Communications in Nonlinear Science and Numerical Simulation, 96, 105676. https://doi.org/10.1016/j.cnsns.2020.105676
Larcher, G. (2023). The Wiener Stock Price Model and the Basic Principles of Black-Scholes Theory (pp. 273–516). https://doi.org/10.1007/978-3-031-23873-4_4
Lazarides, M. K., Lazaridou, I.-Z., & Papanas, N. (2023). Bibliometric Analysis: Bridging Informatics With Science. The International Journal of Lower Extremity Wounds, 153473462311535. https://doi.org/10.1177/15347346231153538
Liang, G., & Wang, X. (2021). Pricing vulnerable options in a hybrid credit risk model driven by Heston–Nandi GARCH processes. Review of Derivatives Research, 24(1), 1–30. https://doi.org/10.1007/s11147-020-09167-z
Liao, X., & Zhuang, J. (2023). The Research on the Pricing of Double Barrier Option Based on the Black-Scholes Model. BCP Business & Management, 37, 320–325. https://doi.org/10.54691/bcpbm.v37i.3582
Mäntylä, M. V., Graziotin, D., & Kuutila, M. (2018). The evolution of sentiment analysis—A review of research topics, venues, and top cited papers. Computer Science Review, 27, 16–32. https://doi.org/10.1016/j.cosrev.2017.10.002
Meng, Z., & Wang, Y. (2023). The comparison between different option pricing models: evidence from Black-Scholes model and Leland model. In X. Li (Ed.), Third International Conference on Artificial Intelligence and Computer Engineering (ICAICE 2022) (p. 258). SPIE. https://doi.org/10.1117/12.2672848
Oh, C., Gavves, E., & Welling, M. (2018). BOCK: Bayesian optimization with cylindrical kernels. International Conference on Machine Learning, 3868–3877.
Otto, E., Culakova, E., Meng, S., Zhang, Z., Xu, H., Mohile, S., & Flannery, M. A. (2022). Overview of Sankey flow diagrams: Focusing on symptom trajectories in older adults with advanced cancer. Journal of Geriatric Oncology, 13(5), 742–746. https://doi.org/10.1016/j.jgo.2021.12.017
Protonotarios, Y., & Tassopoulos, P. (2021). Brownian Motion & The Stochastic Behaviour of Stocks. ArXiv Preprint ArXiv:2110.12001.
Rambau, L. D., Mativenga, P. T., & Marnewick, A. L. (2024). Enhancing frameworks for utilising Sankey diagrams in modelling the water-energy nexus and circularity. Journal of Cleaner Production, 456, 142355. https://doi.org/10.1016/j.jclepro.2024.142355
Rezaei, M., Yazdanian, A. R., Ashrafi, A., & Mahmoudi, S. M. (2021). Numerical pricing based on fractional Black–Scholes equation with time-dependent parameters under the CEV model: Double barrier options. Computers & Mathematics with Applications, 90, 104–111. https://doi.org/10.1016/j.camwa.2021.02.021
Saputro, D. R. S., Prasetyo, H., Wibowo, A., Khairina, F., Sidiq, K., & Wibowo, G. N. A. (2023). BIBLIOMETRIC ANALYSIS OF NEURAL BASIS EXPANSION ANALYSIS FOR INTERPRETABLE TIME SERIES (N-BEATS) FOR RESEARCH TREND MAPPING. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 17(2), 1103–1112. https://doi.org/10.30598/barekengvol17iss2pp1103-1112
Shao, Z. (2023). Pricing Technique for European Option and Application. Highlights in Business, Economics and Management, 14, 14–18. https://doi.org/10.54097/hbem.v14i.8930
Sinha, A., Poonolly, J., Gayathiri, A., & JANARTHANAN, D. (2018). Analysis of option prices using Black Scholes model. J Emerg Technol Innov Res, 5, 12–21.
Swishchuk, A. (2023). Romancing with Black-Scholes Model: An Overview. Wilmott, 2023(126). https://doi.org/10.54946/wilm.11150
Tatum, C. T. S., & Russo, S. L. (2020). Bibliometric analysis for frugal innovation. International Journal for Innovation Education and Research, 8(3), 01–14. https://doi.org/10.31686/ijier.vol8.iss3.929
Verma, S., & Gustafsson, A. (2020). Investigating the emerging COVID-19 research trends in the field of business and management: A bibliometric analysis approach. Journal of Business Research, 118, 253–261. https://doi.org/10.1016/j.jbusres.2020.06.057
Wang, J., Wen, S., Yang, M., & Shao, W. (2022). Practical finite difference method for solving multi-dimensional black-Scholes model in fractal market. Chaos, Solitons & Fractals, 157, 111895. https://doi.org/10.1016/j.chaos.2022.111895
Weatherall, J. O. (2018). The Peculiar Logic of the Black-Scholes Model. Philosophy of Science, 85(5), 1152–1163. https://doi.org/10.1086/699677
Yan, J.-A. (2018). The Black-Scholes Model and Its Modifications (pp. 153–174). https://doi.org/10.1007/978-981-13-1657-9_5
Zhao, L., Yang, M. M., Wang, Z., & Michelson, G. (2023). Trends in the Dynamic Evolution of Corporate Social Responsibility and Leadership: A Literature Review and Bibliometric Analysis. Journal of Business Ethics, 182(1), 135–157. https://doi.org/10.1007/s10551-022-05035-y
DOI: https://doi.org/10.24815/jaroe.v7i3.37925
Article Metrics
Abstract view : 0 timesPDF - 0 times
Refbacks
- There are currently no refbacks.
Published by:
Department of Accounting
Faculty of Economics and Business
Universitas Syiah Kuala
Kopelma Darussalam, Banda Aceh, Indonesia - 23111
E-ISSN: 2621-1041
Journal of Accounting Research, Organization and Economics by the Department of Accounting, Faculty of Economics and Business, Universitas Syiah Kuala is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at http://www.jurnal.usk.ac.id/JAROE/index.