Abstract
Development and implementation of advanced statistical models for analyzing stochastic dependencies of systemic weather risk can help farmers, agricultural policy-makers and financial agents to address potential risk adaptation strategies and mitigation of threats to the agricultural industry. This study develops copula-based statistical models to provide a better understanding of systemic weather risks with agricultural and weather event data from Australia. In particular, we adopt a C-vine approach to model the joint insurance losses caused by drought events occurring simultaneously across different locations, and consecutively in different growing seasons. This modelling approach is enriched by a clustering analysis process through the multidimensional Kruskal–Shephard scaling method. Daily rainfall data (1889–2012) recorded in sixteen meteorological stations across Australia’s wheat belt spanning different climatic conditions are employed. On a regional scale, droughts occurring in the west are more scattered during the October–December period and for April–June and October–December in the eastern, south-eastern and southern regions. On a national scale, drought events in the east are likely to spread out to the south-east and the south but not to the west. The results also reveal that the drought events in different seasons may not be perfectly correlated. Therefore, we conclude that spatial and temporal diversification strategies are likely to feasibly reduce the systemic weather risk in Australia. In particular, the average risk-reducing effect of the entire insured area across regional, national and temporal scales ranges between 0.62–0.94, 0.48–0.76, and 0.25–0.33, corresponding to 5%- (extreme drought) and 25%-quantiles (moderate drought). The findings suggest that diversifying risks over time is potentially more effective than spatial diversification. The outcomes may also act as an efficient tool for agricultural risk reduction, but simultaneously, it may also provide immensely useful information for suitable pricing of weather index-based insurance products.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aas K, Czado C, Frigessi A, Bakken H (2009) Pair-copula constructions of multiple dependence. Insur Math Econ 44:182–198. https://doi.org/10.1016/j.insmatheco.2007.02.001
AghaKouchak A, Cheng L, Mazdiyasni O, Farahmand A (2014) Global warming and changes in risk of concurrent climate extremes: Insights from the California drought. Geophys Res Lett 41:8847–8852. https://doi.org/10.1002/2014GL062308
Barriopedro D, Fischer EM, Luterbacher J, Trigo RM, García-Herrera R (2011) The hot summer of 2010: redrawing the temperature record map of Europe. Science 332:220–224
Bedford T, Cooke RM (2001) Probability density decomposition for conditionally dependent random variables modeled by vines. Ann Math Artif Intell 32:245–268. https://doi.org/10.1023/A:1016725902970
Bedford T, Cooke RM (2002) Vines: a new graphical model for dependent random variables. Ann Stat. https://doi.org/10.1214/aos/1031689016
Botzen WW, de Boer J, Terpstra T (2013) Framing of risk and preferences for annual and multi-year flood insurance. J Econ Psychol 39:357–375. https://doi.org/10.1016/j.joep.2013.05.007
Brechmann EC, Hendrich K, Czado C (2013) Conditional copula simulation for systemic risk stress testing. Insur Math Econ 53:722–732. https://doi.org/10.1016/j.insmatheco.2013.09.009
Carreau J, Bouvier C (2016) Multivariate density model comparison for multi-site flood-risk rainfall in the French Mediterranean area. Stoch Environ Res Risk Assess 30:1591–1612
Coumou D, Rahmstorf S (2012) A decade of weather extremes. Nat Clim Change 2:491. https://doi.org/10.1038/nclimate1452
Dissmann J, Brechmann EC, Czado C, Kurowicka D (2013) Selecting and estimating regular vine copulae and application to financial returns. Comput Stat Data Anal 59:52–69. https://doi.org/10.1016/j.csda.2012.08.010
Duncan J, Myers RJ (2000) Crop insurance under catastrophic risk. Am J Agr Econ 82:842–855. https://doi.org/10.1111/0002-9092.00085
Duong T (2016a) ks: kernel smoothing, r package version 1.10. 4
Duong T (2016b) Non-parametric smoothed estimation of multivariate cumulative distribution and survival functions, and receiver operating characteristic curves. J Korean Stat Soc 45:33–50. https://doi.org/10.1016/j.jkss.2015.06.002
Embrechts P, McNeil A, Straumann D (2002) Correlation and dependence in risk management: properties and pitfalls. Risk Manag Value Risk Beyond 1:176–223
FAO (2015) The impact of natural hazards and disasters on agriculture and food and nutrition security—a call for action to build resilient livelihoods. http://www.fao.org/3/a-i4434e.pdf
Frey R, McNeil AJ (2003) Dependent defaults in models of portfolio credit risk. J Risk 6:59–92. https://doi.org/10.21314/JOR.2003.089
Frey R, McNeil AJ, Nyfeler M (2001) Copulas and credit models. Risk October 2001:111–114
Glauber JW, Collins KJ, Barry PJ (2002) Crop insurance, disaster assistance, and the role of the federal government in providing catastrophic risk protection. Agric Finance Rev 62:81–101. https://doi.org/10.1108/00214900280001131
Goodwin BK (2001) Problems with market insurance in agriculture. Am J Agr Econ 83:643–649. https://doi.org/10.1111/0002-9092.00184
Holly Wang H, Zhang H (2003) On the possibility of a private crop insurance market: a spatial statistics approach. J Risk Insur 70:111–124. https://doi.org/10.1111/1539-6975.00051
Kim G, Silvapulle MJ, Silvapulle P (2007) Comparison of semiparametric and parametric methods for estimating copulas. Comput Stat Data Anal 51:2836–2850. https://doi.org/10.1016/j.csda.2006.10.009
Kleindorfer PR, Kunreuther H, Ou-Yang C (2012) Single-year and multi-year insurance policies in a competitive market. J Risk Uncertain 45:51–78. https://doi.org/10.1007/s11166-012-9148-2
Kraus D, Czado C (2017) D-vine copula based quantile regression. Comput Stat Data Anal 110:1–18. https://doi.org/10.1016/j.csda.2016.12.009
Kurowicka D (2005) Distribution-free continuous bayesian belief. Mod Stat Math Methods Reliab 10:309
Kurowicka D, Cooke RM (2007) Sampling algorithms for generating joint uniform distributions using the vine-copula method. Comput Stat Data Anal 51:2889–2906. https://doi.org/10.1016/j.csda.2006.11.043
Lesk C, Rowhani P, Ramankutty N (2016) Influence of extreme weather disasters on global crop production. Nature 529:84. https://doi.org/10.1038/nature16467
Mahul O (1999) Optimum area yield crop insurance. Am J Agr Econ 81:75–82. https://doi.org/10.2307/1244451
Martin SW, Barnett BJ, Coble KH (2001) Developing and pricing precipitation insurance. J Agric Resour Econ 26:261–274
McNeil A, Frey R, Paul E (2005) Quantitative risk management: concepts, techniques and tools. Princeton University Press, Princeton
Miranda MJ, Glauber JW (1997) Systemic risk, reinsurance, and the failure of crop insurance markets. Am J Agr Econ 79:206–215. https://doi.org/10.2307/1243954
Musafer GN, Thompson MH (2017) Non-linear optimal multivariate spatial design using spatial vine copulas. Stoch Environ Res Risk Assess 31:551–570
Musshoff O, Odening M, Xu W (2011) Management of climate risks in agriculture–will weather derivatives permeate? Appl Econ 43:1067–1077. https://doi.org/10.1080/00036840802600210
Nguyen-Huy T, Deo RC, An-Vo D-A, Mushtaq S, Khan S (2017) Copula-statistical precipitation forecasting model in Australia’s agro-ecological zones. Agric Water Manag 191:153–172. https://doi.org/10.1016/j.agwat.2017.06.010
Nguyen-Huy T, Deo RC, Mushtaq S, An-Vo D-A, Khan S (2018a) Modeling the joint influence of multiple synoptic-scale, climate mode indices on Australian wheat yield using a vine copula-based approach. Eur J Agron 98:65–81. https://doi.org/10.1016/j.eja.2018.05.006
Nguyen-Huy T, Deo RC, Mushtaq S, Kath J, Khan S (2018b) Copula-based agricultural conditional value-at-risk modelling for geographical diversifications in wheat farming portfolio management. Weather Clim Extrem 21:76–89
Noh H, Ghouch AE, Bouezmarni T (2013) Copula-based regression estimation and inference. J Am Stat Assoc 108:676–688. https://doi.org/10.1080/01621459.2013.783842
Odening M, Shen Z (2014) Challenges of insuring weather risk in agriculture. Agric Finance Rev 74:188–199. https://doi.org/10.1108/AFR-11-2013-0039
Odening M, Mußhoff O, Xu W (2007) Analysis of rainfall derivatives using daily precipitation models: opportunities and pitfalls. Agric Finance Rev 67:135–156. https://doi.org/10.1108/00214660780001202
Okhrin O, Odening M, Xu W (2013) Systemic weather risk and crop insurance: the case of China. J Risk Insur 80:351–372. https://doi.org/10.1111/j.1539-6975.2012.01476.x
Osipenko M, Shen Z, Odening M (2015) Is there a demand for multi-year crop insurance? Agric Finance Rev 75:92–102. https://doi.org/10.1108/AFR-12-2014-0043
Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33:1065–1076. https://doi.org/10.1214/aoms/1177704472
Pham MT, Vernieuwe H, De Baets B, Willems P, Verhoest N (2016) Stochastic simulation of precipitation-consistent daily reference evapotranspiration using vine copulas. Stoch Environ Res Risk Assess 30:2197–2214
Reddy MJ, Singh VP (2014) Multivariate modeling of droughts using copulas and meta-heuristic methods. Stoch Environ Res Risk Assess 28:475–489
Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J Bank Finance 26:1443–1471. https://doi.org/10.1016/S0378-4266(02)00271-6
Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat 23:470–472. https://doi.org/10.1214/aoms/1177729394
Sak H, Yang G, Li B, Li W (2017) A copula-based model for air pollution portfolio risk and its efficient simulation. Stoch Environ Res Risk Assess 31:2607–2616
Schepsmeier U, Stoeber J, Brechmann EC, Graeler B, Nagler T, Erhardt T, Almeida C, Min A, Czado C, Hofmann M, Killiches M (2018) Package ‘VineCopula’. R package version. https://github.com/tnagler/VineCopula
Schoelzel C, Friederichs P (2008) Multivariate non-normally distributed random variables in climate research–introduction to the copula approach. Nonlinear Process Geophys 15:761–772. https://doi.org/10.5194/npg-15-761-2008
Serinaldi F (2009) Copula-based mixed models for bivariate rainfall data: an empirical study in regression perspective. Stoch Environ Res Risk Assess 23:677–693
Shen Z, Odening M (2013) Coping with systemic risk in index-based crop insurance. Agric Econom 44(1):1–3. https://doi.org/10.1111/j.1574-0862.2012.00625.x
Skees JR, Barnett BJ (1999) Conceptual and practical considerations for sharing catastrophic/systemic risks. Rev Agric Econ 21:424–441. https://doi.org/10.2307/1349889
Skees JR, Hartell J, Murphy AG (2007) Using index-based risk transfer products to facilitate micro lending in Peru and Vietnam. Am J Agr Econ 89:1255–1261
Sklar M (1959) Fonctions de répartition à n dimensions et leurs marges. Université Paris 8
Song S, Singh VP (2010) Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stoch Environ Res Risk Assess 24:425–444
Tankov P (2011) Improved Fréchet bounds and model-free pricing of multi-asset options. J Appl Probab 48:389–403
Van Den Goorbergh RW, Genest C, Werker BJ (2005) Bivariate option pricing using dynamic copula models. Insur Math Econ 37:101–114. https://doi.org/10.1016/j.insmatheco.2005.01.008
Vedenov D (2008) Application of copulas to estimation of joint crop yield distributions. In: American Agricultural Economics Association annual meeting, Orlando, FL, pp 27–29
Vedenov DV, Barnett BJ (2004) Efficiency of weather derivatives as primary crop insurance instruments. J Agric Resour Econ 1:387–403. http://www.jstor.org/stable/40987240
Wang SS (2000) A class of distortion operators for pricing financial and insurance risks. J Risk Insur. https://doi.org/10.2307/253675
Woodard JD, Garcia P (2008) Basis risk and weather hedging effectiveness. Agric Finance Rev 68:99–117. https://doi.org/10.1108/00214660880001221
Xu W, Filler G, Odening M, Okhrin O (2010) On the systemic nature of weather risk. Agric Finance Rev 70:267–284. https://doi.org/10.1108/00021461011065283
Xu Y, Huang G, Fan Y (2017) Multivariate flood risk analysis for Wei River. Stoch Environ Res Risk Assess 31:225–242
Zhang L, Yang B, Guo A, Huang D, Huo Z (2018) Multivariate probabilistic estimates of heat stress for rice across China. Stoch Environ Res Risk Assess 32(11):3137–3150. https://doi.org/10.1007/s00477-018-1572-7
Zhang Q, Xiao M, Singh VP, Chen X (2013) Copula-based risk evaluation of hydrological droughts in the East River basin China. Stoch Environ Res Risk Assess 27:1397–1406
Zhu Y, Ghosh SK, Goodwin BK (2008) Modeling dependence in the design of whole farm insurance contract,| A copula-based model approach. In: Selected paper prepared for presentation at the American Agricultural Economics Association Annual Meeting, Orlando, July, pp 27–29
Acknowledgements
The project was financed by the University of Southern Queensland Post Graduate Research Scholarship (USQPRS 2015–2018); School of Agricultural, Computational and Environmental Sciences and the Drought and Climate Adaptation (DCAP) Project (Producing Enhanced Crop Insurance Systems and Associated Financial Decision Support Tools). The authors would like to acknowledge constructive comments from the reviewers.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Nguyen-Huy, T., Deo, R.C., Mushtaq, S. et al. Copula statistical models for analyzing stochastic dependencies of systemic drought risk and potential adaptation strategies. Stoch Environ Res Risk Assess 33, 779–799 (2019). https://doi.org/10.1007/s00477-019-01662-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-019-01662-6