RAINFALL MODELLING IN EAST JAVA USING A MODIFIED ORNSTEIN-UHLENBECK MODEL
DOI:
https://doi.org/10.25077/jmua.14.1.46-61.2025Keywords:
Ornstein-Uhlenbeck, rainfall, weather derivativesAbstract
One of the current global issues is climate change and weather variability. This phenomenon has real impacts on various regions, including East Java Province. East Java is experiencing increased rainfall intensity as one of the effects of climate change. High and continuous rainfall intensity can trigger disasters such as flooding, which has the potential to cause significant financial losses for the community. Therefore, effective risk management becomes crucial. One possible solution to address these risks is through the use of financial derivatives. The initial step in risk management involves modeling the behavior of rainfall. It is assumed that the rainfall pattern follows a mean-reverting process, specifically the Ornstein-Uhlenbeck process. The existing Ornstein-Uhlenbeck model is then modified to ensure that the resulting model accurately reflects the rainfall conditions in East Java. To validate the modified model, simulations of the Ornstein-Uhlenbeck process were conducted using estimated parameter values. The Ornstein-Uhlenbeck simulation achieved a minimum MSE score that approaches zero. This MSE score indicate that the proposed modified Ornstein-Uhlenbeck model is accurate in representing the rainfall patterns in East Java.
References
Susilokarti, D., Arif, S. S., Susanto, S., Sutiarso, L., 2015, Identifikasi Perubahan Iklim Berdasarkan Data Curah Hujan di Wilayah Selatan Jatiluhur Kabupaten Subang, Jawa Barat, Agritech, Vol. 35(1): 98 – 105
Chou, C., Neelin, J. D., Chen, C. A., Tu J. Y., 2009, Evaluating the “Rich-Get-Richer†Mechanism in Tropical Precipitation Change under Global Warming, Journal of Climate, Vol. 22(8): 1982 – 2005
Rosyida, A., Aziz, M., Firmansyah, Y., Setiawan, T., Pangesti, K. P., Kakanur, F., 2024, Buku Data Bencana Indonesia 2023, Volume 3, Badan Nasional Penanggulangan Bencana (BNPB) Indonesia, Jakarta
Stulec, I., Petljak, K., Bakovic, T., 2016, Effectiveness of Weather Derivatives As a Hedge against the Weather Risk in Agriculture, Agric. Econ., Vol. 62(8): 356 – 362
Cramer, S., Kampouridis, M., Freitas, A. A., Alexandridis, A. K., 2017, An Extensive Evaluation of Seven Machine Learning Methods for Rainfall Prediction in Weather Derivatives, Expert Systems With Applications, Vol. 85: 169 – 181
Cao, M., Li, A., Wei, J. Z., 2004, Precipitation Modeling and Contract Valuation: A Frontier in Weather Derivatives, Journal of Alternative Investments, Vol. 7(2): 93 – 99
Leobacher, G., Ngare, P., 2011, On Modelling and Pricing Rainfall Derivatives with Seasonality, Applied Mathematical Finance, Vol. 18(1): 71 – 91
Shah, A., 2017, Pricing of Rainfall Derivatives Using Generalized Linear Modelling of Daily Rainfall Process, International Agricultural Risk, Finance and Insurance Conference (IARFIC) 2017 Paris Meetings Paper, 1 – 22
Li, P., 2018, Pricing Weather Derivatives with Partial Differential Equations of the Ornstein–Uhlenbeck Process, Computers and Mathematics with Applications, Vol. 75(3): 1044 – 1059
Jewson, S., Brix, A., Ziehmann, C., 2005, Weather Derivative Valuation, Cambridge University Press, United States of America
Øksendal, B., 1995, Stochastic Differential Equations, Springer Berlin Heidelberg, Berlin
Nhangumbe, C., Sousa, E., 2024, Numerical Solutions of An Option Pricing Rainfall Weather Derivatives Model, Computers and Mathematics with Applications, Vol. 153: 43 – 55
Bibby, B. M., Sørensen, M., 1995, Martingale Estimation Functions for Discretely Observed Diffusion Processes, Bernoulli, Vol. 1(1/2): 17 – 39
Emmerich, C. V., 2005, Modelling and Simulating of Rain Derivatives, University of Wuppertal, Wuppertal
Chapra, S. C., Canale, R. P., 2010, Numerical Methods for Engineers, Edisi ke-6, McGraw-Hill, New York
Downloads
Published
Issue
Section
License
All articles published in Jurnal Matematika UNAND (JMUA) are open access and licensed under the Creative Commons Attribution-ShareAlike (CC BY-SA) license. This ensures that the content is freely available to all users and can be shared and adapted, provided appropriate credit is given and any adaptations are distributed under the same license.
Copyright Holder
The copyright of all articles published in Jurnal Matematika UNAND is held by the Departemen Matematika dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Andalas (UNAND). This applies to all published versions, including the HTML and PDF formats of the articles.
Author Rights
While the Departemen Matematika dan Sains Data FMIPA UNAND holds the copyright for all published content, authors retain important rights under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA). This license grants authors and users the following rights:
- Reuse: Authors can reuse and distribute their work for any lawful purpose, including sharing on personal websites, institutional repositories, or in subsequent publications.
- Attribution and Adaptation: Authors and others may remix, adapt, and build upon the published work for any purpose, even commercially, as long as proper credit is given to the original authors, and any derivative works are distributed under the same CC BY-SA license.
Creative Commons License (CC BY-SA)
Under the terms of the CC BY-SA license, users are free to:
- Share: Copy and redistribute the material in any medium or format.
- Adapt: Remix, transform, and build upon the material for any purpose, even commercially.
However, the following conditions apply:
- Attribution: Users must give appropriate credit to the original author(s) and Departemen Matematika dan Sains Data FMIPA UNAND, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author or the journal.
- ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same license as the original.
For more information about the CC BY-SA license, please visit the Creative Commons website.
Third-Party Content
If authors include third-party material (such as figures, tables, or images) that is not covered by a Creative Commons license, they must obtain the necessary permissions for reuse and provide proper attribution. Authors are required to ensure that any third-party content complies with open-access licensing requirements or includes permissions for redistribution under similar terms.
Copyright and Licensing Information Display
The copyright and licensing terms will be clearly displayed on each article's landing page, as well as within the full-text versions (HTML and PDF) of all published articles.
No "All Rights Reserved"
As an open-access journal, JMUA does not use "All Rights Reserved" policies. Instead, the CC BY-SA license ensures that the works remain accessible and reusable for a wide audience while still protecting both the authors' and the copyright holder's rights.
Â
