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All Journal International Journal of Global Operations Research Indonesian Journal of Applied Mathematics and Statistics
Suharto, Istiqomah
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Mathematics Public Health

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Exploring Interest Rate Models: Implications on Bond Value Measures in a Dynamic Financial Landscape Suharto, Istiqomah; Yuningsih, Siti Hadiaty
International Journal of Global Operations Research Vol. 5 No. 2 (2024): International Journal of Global Operations Research (IJGOR)m May 2024
Publisher : iora

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47194/ijgor.v5i2.301

Abstract

This paper investigates the impact of various one-factor no-arbitrage interest rate models on key bond value measures, specifically effective duration. Employing numerical methods based on binomial or trinomial lattices, the study assesses five prominent interest rate models: Ho and Lee, Kalotay, Williams, and Fabozzi, Black, Derman, and Toy, Hull and White, and Black and Karasinski.The analysis begins by outlining the theoretical foundations and assumptions underlying each model, highlighting their distinctive features and implications for bond valuation. Through a meticulous numerical solution process, the study generates risk metrics for bond portfolios, considering the dynamic nature of interest rates and the complex interactions between price, duration, and convexity.Comparisons across the models reveal nuanced differences in the computed effective duration and convexity measures, shedding light on how the choice of an interest rate model may influence risk assessments in fixed-income portfolios. The paper discusses practical implications for investors and portfolio managers, emphasizing the importance of model selection in navigating the challenges posed by interest rate fluctuations. Additionally, it addresses the potential limitations and challenges associated with each model, offering insights into their relative strengths and weaknesses.By presenting empirical examples and conducting sensitivity analyses, this research contributes to the ongoing discourse on interest rate modeling and its implications for bond markets. The findings offer valuable insights for practitioners seeking to enhance their risk management strategies in fixed-income investments, providing a foundation for future research in this dynamic and evolving field.
An Exploration of Principal Component Analysis using Module Theory Suharto, Istiqomah; Sylviani, Sisilia
Indonesian Journal of Applied Mathematics and Statistics Vol. 2 No. 2 (2025): Indonesian Journal of Applied Mathematics and Statistics (IdJAMS)
Publisher : Lembaga Penelitian dan Pengembangan Matematika dan Statistika Terapan Indonesia, PT Anugrah Teknologi Kecerdasan Buatan PT Anugrah Teknologi Kecerdasan Buatan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.71385/idjams.v2i2.25

Abstract

With big data becoming more and more prominent in the world, high-dimensional data is a relevant issue due to the challenges that it imposes to meaningful analysis. The exponential growth in space leads to data becoming sparse thus making it difficult to analyze underlying patterns/relationships. This is where dimension-reducing techniques come in, the most popular one being Principal Component Analysis. Hence, it is important to analyze exactly what makes PCA work and to study it and generalize it in order to leave room for more variants for differing fields and applications to grow. This paper examines PCA from a linear algebra perspective, particularly using module theory. We prove that PCA is an module homomorphism, and, when all principal components are kept, an module automorphism, meaning that it preserves structure and is invertible. We then look into what happens algebraically when only a subset of principal components are kept. The module homomorphism is then only an module epimorphism, not an isomorphism, still structure preserving but not invertible. Through these findings, we find that there are three essential, algebraic properties of Principal Component Analysis, namely (1) the transformation must be linear, (2) it must project the data onto a new orthonormal basis, and (3) it must diagonalize the covariance (or correlation) matrix of the centered dataset. With these properties, we get an algebraic definition of PCA: an module automorphism that diagonalizes the covariance structure of the original dataset via an orthogonal change of basis.
Co-Authors Sisilia Sylviani Yuningsih, Siti Hadiaty