Author(s)

Stephen Kelvin Sata

Affiliation(s)

ICOF Global University, Lusaka, Zambia.

Corresponding Author

Stephen Kelvin Sata

ABSTRACT

Algorithmic or quantitative trading, using arithmetic models and statistical tools, has become the essence of today’s financial markets. An excellent theoretical background is crucial for evolving as an expert in this field, and constant training is necessary since different trading models demand linear algebra, calculus, and other forms of mathematics.

Linear algebra encompasses matrix operations and vectors, which help sort and analyze big financial data. They help traders understand the relationships among assets, improve their portfolios, and build a new strategy based on factors. Math, which emphasizes derivatives and integrals, is helpful for rates of change, fluctuations, and significant market trends. Combined, these fields provide people with a highly effective arsenal of tools and methods for modelling the market and predicting its action.

These skills can be pre-installed in high school and university STEM programs by applying linear algebra and calculus to real-life lessons. For example, using a matrix, students may engage in activities which include optimizing a portfolio and using correlation coefficients in a given risk and return scenario. Some calculus problems that could be used in the teacher instructions could be differentiation to determine the rate of change of an asset price or integration in the determination of accumulative returns.

Apart from theory, quantitative trading requires computational skills to support it. Languages such as Python and R make it possible to automate the processing and analysis of large datasets. By integrating mathematical concepts with programming, students are placed in a position where they are Programming Application: Through programming, students can implement simple trading strategies and test them using actual market data.

By adopting these interdisciplinary approaches to STEM, students are capable of entering finance-related careers, data science, and other careers. When curricula are aligned with market requirements, educational institutions prepare a generation of people with strong mathematical backgrounds and technology literacy capable of working in a data society.

KEYWORDS

Quantitative;Trading; Linear algebra; Calculus & sTEM

CITE THIS PAPER

Stephen Kelvin Sata. Building quantitative trading skills: integrating linear algebra and calculus into STEM programs. World Journal of Mathematics and Physics. 2025, 3(1): 10-21. DOI: https://doi.org/10.61784/wjmp3007.

REFERENCES

[1] Glasserman P. Monte Carlo methods in financial engineering. Springer, 2003.

[2] Brigo D, Mercurio F. Interest rate models - theory and practice: With smile, inflation, and credit (2nd ed.). Springer, 2006.

[3] Hull J C. Options, futures, and other derivatives (10th ed.). Prentice Hall, 2017.

[4] Lee M J, Lee Y K. Mathematical underpinnings of portfolio optimization using linear algebra. Journal of Quantitative Analysis, 2020, 8(4): 352-370.

[5] Stochastic Calculus for Option Pricing. University of Washington program notes, 2023. Retrieved from https://acms.washington.edu.

[6] Stochastic Calculus for Option Pricing. University of Washington program notes, 2023. Retrieved from https://acms.washington.edu.

[7] Mathematical Economics and Quantitative Finance Program. University of Washington course catalog, 2023. Retrieved from https://acms.washington.edu.

[8] Lee M J, Lee Y K. Mathematical underpinnings of portfolio optimization using linear algebra. Journal of Quantitative Analysis, 2020, 8(4): 352-370.

[9] Stochastic Calculus for Option Pricing. University of Washington program notes, 2023. Retrieved from https://acms.washington.edu.

[10] Stojanovic M, Rais R. Advances in applying machine learning to financial risk modeling. Journal of Financial Risk Management, 2021, 14(3): 234-250.

[11] Kempthorne P, Xia J. Topics in mathematics with applications in finance. MIT OpenCourseWare, 2013.

[12] Stony Brook University. Numerical methods in finance course outline, 2022. Retrieved from https://www.stonybrook.edu.

[13] Kim S. Matrix applications in stochastic modeling for quantitative finance. Mathematics in Industry, 2019, 12(1): 67-81.

[14] Seydel R U. Tools for computational finance (6th ed.). Springer, 2017.

[15] Stojanovic M, Rais R. Advances in applying machine learning to financial risk modeling. Journal of Financial Risk Management, 2021, 14(3): 234-250.

[16] Applied Mathematics and Statistics Department. Machine learning in quantitative finance syllabus. Stony Brook University, 2022. Retrieved from https://stonybrook.edu.

[17] Stochastic Calculus for Option Pricing. University of Washington program notes, 2023. Retrieved from https://acms.washington.edu.

[18] Brigo D, Mercurio F. Interest rate models - theory and practice: With smile, inflation, and credit (2nd ed.). Springer, 2006.

[19] Stony Brook University. Numerical methods in finance course outline, 2022. Retrieved from https://www.stonybrook.edu.

[20] Stochastic Calculus for Option Pricing. University of Washington program notes, 2023. Retrieved from https://acms.washington.edu.

[21] Hull J C. Options, futures, and other derivatives (10th ed.). Prentice Hall, 2017.

[22] Kim S. Matrix applications in stochastic modeling for quantitative finance. Mathematics in Industry, 2019, 12(1): 67-81.

[23] Kempthorne P, Xia J. Topics in mathematics with applications in finance. MIT OpenCourseWare, 2013.

[24] Applied Mathematics and Statistics Department. Machine learning in quantitative finance syllabus. Stony Brook University, 2022. Retrieved from https://stonybrook.edu.

[25] Mathematical Economics and Quantitative Finance Program. University of Washington course catalog, 2023. Retrieved from https://acms.washington.edu.

[26] Kim S. Matrix applications in stochastic modeling for quantitative finance. Mathematics in Industry, 2019, 12(1): 67-81.

[27] Kempthorne P, Xia J. Topics in mathematics with applications in finance. MIT OpenCourseWare, 2013.

[28] Seydel R U. Tools for computational finance (6th ed.). Springer, 2017.

[29] Stochastic Calculus for Option Pricing. University of Washington program notes, 2023. Retrieved from https://acms.washington.edu.