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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON DATA SCIENCE AND OFFICIAL STATISTICS
Thalita, Bella Cindy
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Computer Science & IT Mathematics

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Pricing Double Barrier Options with Time-Varying Interest using Standard, Antithetic, and Control Variate Monte Carlo Thalita, Bella Cindy; Darti, Isnani
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.37010

Abstract

This study develops an integrated framework for pricing double barrier options under time-varying interest rates by combining ARIMA-based forecasting with Monte Carlo simulations. Monthly U.S. Treasury Bill rates from 2019–2025 are modeled using the ARIMA(2,2,0) process to generate dynamic risk-free rates, which are incorporated into three Monte Carlo approaches standard, antithetic variate, and control variate. Tesla Inc. stock prices are used as the underlying asset modeled through Geometric Brownian Motion. The integration of ARIMA-based dynamic rates within the Monte Carlo framework enables more realistic pathwise discounting and improves simulation convergence. The results show that the control variate method provides the most accurate and stable estimates for knock-in call options, whereas the antithetic variate technique yields superior accuracy for knock-in put, knock-out call, and knock-out put options. Overall, the combined use of ARIMA-forecasted interest rates and variance-reduction techniques enhances the precision and stability of double barrier option valuation under dynamic financial conditions.
Mapping Regional Economic Resilience of Indonesian Provinces Through PCA and K-Means Analysis to Support Regional Development Policy Optimization Thalita, Bella Cindy; A'la, Kevina Alal
Proceedings of The International Conference on Data Science and Official Statistics Vol. 2025 No. 1 (2025): Proceedings of 2025 International Conference on Data Science and Official St
Publisher : Politeknik Statistika STIS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34123/icdsos.v2025i1.430

Abstract

In Indonesia’s post-decentralization era, assessing regional economic resilience is critical to promoting inclusive development. This study constructs a composite resilience index using seven indicators Human Development Index (HDI), Open Unemployment Rate, GRDP per capita, Gini Ratio, Economic Growth, Capital Expenditure, and Own-Source Revenue (OSR) across 34 provinces from 2020–2024. Principal Component Analysis (PCA) and K-Means clustering are applied to identify resilience patterns and classify provinces into high, moderate, and low resilience categories. The findings reveal significant interprovincial disparities. Provinces such as DKI Jakarta (HDI: 81.65), Bali (HDI: 76.54), and DI Yogyakarta (HDI: 80.22) consistently demonstrate high resilience, supported by low unemployment (e.g., Jakarta: 5.78%) and robust fiscal capacity (e.g., OSR share: Jakarta 58.29%). In contrast, Papua and West Papua exhibit lower resilience scores, characterized by HDI below 65, limited OSR below 15%, and economic growth volatility. Correlation analysis indicates a strong positive association between HDI and fiscal indicators (r = 0.82), while OLS regression confirms OSR and Capital Expenditure as significant predictors of resilience (p < 0.05). Spatial mapping highlights geographic clustering of resilience, with Western Indonesia outperforming the Eastern region— underscoring persistent spatial inequalities. These findings reinforce the necessity for regionally differentiated policies. The study recommends enhancing fiscal autonomy, investing in human capital, and integrating Fintech-based financial inclusion, especially for lagging regions. The study recommends boosting fiscal autonomy, investing in human capital, and leveraging Fintech for inclusive growth. This framework supports evidence-based policies aligned with Indonesia’s SDG and post-2024 development goals.
Co-Authors A'la, Kevina Alal Isnani Darti