Explore a curated list of academic references on extreme events in financial markets, the use of statistical mechanics in finance, and the application of Topological Data Analysis (TDA).Explore a curated list of academic references on extreme events in financial markets, the use of statistical mechanics in finance, and the application of Topological Data Analysis (TDA).

The Math Behind Finance: A Guide to Relevant Research

I. Introduction

II. Methodology

III. TDA Approach to analyzing multiple time series

IV. Data Analyzed

V. Results and Discussion

A. Obtaining point cloud from stock price time-series

B. EE due to the 2008 Financial crisis

C. EE due to COVID-19 pandemic

D. Impact of COVID-19 on different Indian sectors

VI. Conclusion

VII. Acknowledgments and References

VII. ACKNOWLEDGEMENTS

We would like to acknowledge NIT Sikkim for allocating doctoral fellowship to Anish Rai, Buddha Nath Sharma and SR Luwang. We also like to acknowledge the inputs provided by Kundan Mukhia.

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  3. Y. Choi, R. Douady, Financial crisis dynamics: attempt to define a market instability indicator, Quantitative Finance 12 (2012) 1351–1365.

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  4. M. Mazur, M. Dang, M. Vega, Covid-19 and the march 2020 stock market crash. evidence from s&p1500, Finance research letters 38 (2021) 101690.

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  5. A. Rai, A. Mahata, M. Nurujjaman, O. Prakash, Statistical properties of the aftershocks of stock market crashes revisited: Analysis based on the 1987 crash, financial-crisis-2008 and covid-19 pandemic, International Journal of Modern Physics C 33 (2022) 2250019.

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  11. C. Raymond, R. M. Horton, J. Zscheischler, O. Martius, A. AghaKouchak, J. Balch, S. G. Bowen, S. J. Camargo, J. Hess, K. Kornhuber, et al., Understanding and managing connected extreme events, Nature climate change 10 (2020) 611–621.

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  16. G. E. Carlsson, Topology and data, Bulletin of the American Mathematical Society 46 (2009) 255–308. URL: https://api. semanticscholar.org/CorpusID:1472609.

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  17. T. K. Dey, Y. Wang, Computational Topology for Data Analysis, Cambridge University Press, 2022.

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  18. S. Kulkarni, H. K. Pharasi, S. Vijayaraghavan, S. Kumar, A. Chakraborti, A. Samal, Investigation of indian stock markets using topological data analysis and geometry-inspired network measures, arXiv preprint arXiv:2311.17016 (2023).

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  19. M. Kramar, A. Goullet, L. Kondic, K. Mischaikow, Persistence of force networks in compressed granular media, Physical Review E 87 (2013) 042207.

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  20. T. Nakamura, Y. Hiraoka, A. Hirata, E. G. Escolar, Y. Nishiura, Persistent homology and many-body atomic structure for medium-range order in the glass, Nanotechnology 26 (2015) 304001.

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  21. K. Turner, S. Mukherjee, D. M. Boyer, Persistent homology transform for modeling shapes and surfaces, Information and Inference: A Journal of the IMA 3 (2014) 310–344.

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  23. Y. Yao, J. Sun, X. Huang, G. R. Bowman, G. Singh, M. Lesnick, L. J. Guibas, V. S. Pande, G. Carlsson, Topological methods for exploring low-density states in biomolecular folding pathways, The Journal of chemical physics 130 (2009).

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  31. H. Guo, S. Xia, Q. An, X. Zhang, W. Sun, X. Zhao, Empirical study of financial crises based on topological data analysis, Physica A: Statistical Mechanics and its Applications 558 (2020) 124956.

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  32. P. T.-W. Yen, S. A. Cheong, Using topological data analysis (tda) and persistent homology to analyze the stock markets in singapore and taiwan, Frontiers in Physics 9 (2021) 572216.

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  33. P. T.-W. Yen, K. Xia, S. A. Cheong, Understanding changes in the topology and geometry of financial market correlations during a market crash, Entropy 23 (2021) 1211.

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  34. A. Goel, P. Pasricha, A. Mehra, Topological data analysis in investment decisions, Expert Systems with Applications 147 (2020) 113222.

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  38. H. Guo, X. Zhao, H. Yu, X. Zhang, Analysis of global stock markets’ connections with emphasis on the impact of covid-19, Physica A: Statistical Mechanics and its Applications 569 (2021) 125774.

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  39. H. Guo, H. Yu, Q. An, X. Zhang, Risk analysis of china’s stock markets based on topological data structures, Procedia Computer Science 202 (2022) 203–216.

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  40. A. Mahata, A. Rai, M. Nurujjaman, O. Prakash, Modeling and analysis of the effect of covid-19 on the stock price: V and l-shape recovery, Physica A: Statistical Mechanics and its Applications 574 (2021) 126008.

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  41. D. Gold, K. Karabina, F. C. Motta, An algorithm for persistent homology computation using homomorphic encryption, arXiv preprint arXiv:2307.01923 (2023).

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  42. S. W. Akingbade, M. Gidea, M. Manzi, V. Nateghi, Why topological data analysis detects financial bubbles?, Communications in Nonlinear Science and Numerical Simulation 128 (2024) 107665.

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  43. F. Chazal, B. Michel, An introduction to topological data analysis: fundamental and practical aspects for data scientists, Frontiers in artificial intelligence 4 (2021) 108.

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  44. D. Cohen-Steiner, H. Edelsbrunner, J. Harer, Stability of persistence diagrams, in: Proceedings of the twenty-first annual symposium on Computational geometry, 2005, pp. 263–271.

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  45. P. Bubenik, Statistical topological data analysis using persistence landscapes, Journal of Machine Learning Research 16 (2015) 77–102. URL: http://jmlr.org/papers/v16/bubenik15a.html.

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  47. A. Rai, A. Mahata, M. Nurujjaman, S. Majhi, K. Debnath, A sentiment-based modeling and analysis of stock price during the covid-19: U-and swoosh-shaped recovery, Physica A: Statistical Mechanics and its Applications 592 (2022) 126810.

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:::info Authors:

(1) Anish Rai, Department of Physics, National Institute of Technology Sikkim, Sikkim, India-737139;

(2) Buddha Nath Sharma, Department of Physics, National Institute of Technology Sikkim, Sikkim, India-737139;

(3) Salam Rabindrajit Luwang, Department of Physics, National Institute of Technology Sikkim, Sikkim, India-737139;

(4) Md.Nurujjaman, Department of Physics, National Institute of Technology Sikkim, Sikkim, India-737139;

(5) Sushovan Majhi, Data Science Program, George Washington University, USA, 20052.

:::


:::info This paper is available on arxiv under CC BY 4.0 DEED license.

:::

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