Copula statistical models for analyzing stochastic dependencies of systemic drought risk and potential adaptation strategies

  • Thong Nguyen-Huy
  • Ravinesh C. DeoEmail author
  • Shahbaz Mushtaq
  • Jarrod Kath
  • Shahjahan Khan
Original Paper


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.


Joint insurance losses Clustering C-vine copulas Index-based insurance Weather systemic risk Diversification 



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.

Supplementary material

477_2019_1662_MOESM1_ESM.docx (6.6 mb)
Supplementary material 1 (DOCX 6750 kb)


  1. Aas K, Czado C, Frigessi A, Bakken H (2009) Pair-copula constructions of multiple dependence. Insur Math Econ 44:182–198. CrossRefGoogle Scholar
  2. 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. CrossRefGoogle Scholar
  3. 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 332:220–224CrossRefGoogle Scholar
  4. Bedford T, Cooke RM (2001) Probability density decomposition for conditionally dependent random variables modeled by vines. Ann Math Artif Intell 32:245–268. CrossRefGoogle Scholar
  5. Bedford T, Cooke RM (2002) Vines: a new graphical model for dependent random variables. Ann Stat. Google Scholar
  6. 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. CrossRefGoogle Scholar
  7. Brechmann EC, Hendrich K, Czado C (2013) Conditional copula simulation for systemic risk stress testing. Insur Math Econ 53:722–732. CrossRefGoogle Scholar
  8. 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 30:1591–1612CrossRefGoogle Scholar
  9. Coumou D, Rahmstorf S (2012) A decade of weather extremes. Nat Clim Change 2:491. CrossRefGoogle Scholar
  10. 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. CrossRefGoogle Scholar
  11. Duncan J, Myers RJ (2000) Crop insurance under catastrophic risk. Am J Agr Econ 82:842–855. CrossRefGoogle Scholar
  12. Duong T (2016a) ks: kernel smoothing, r package version 1.10. 4Google Scholar
  13. 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. CrossRefGoogle Scholar
  14. Embrechts P, McNeil A, Straumann D (2002) Correlation and dependence in risk management: properties and pitfalls. Risk Manag Value Risk Beyond 1:176–223CrossRefGoogle Scholar
  15. FAO (2015) The impact of natural hazards and disasters on agriculture and food and nutrition security—a call for action to build resilient livelihoods.
  16. Frey R, McNeil AJ (2003) Dependent defaults in models of portfolio credit risk. J Risk 6:59–92. CrossRefGoogle Scholar
  17. Frey R, McNeil AJ, Nyfeler M (2001) Copulas and credit models. Risk October 2001:111–114Google Scholar
  18. 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. CrossRefGoogle Scholar
  19. Goodwin BK (2001) Problems with market insurance in agriculture. Am J Agr Econ 83:643–649. CrossRefGoogle Scholar
  20. 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. CrossRefGoogle Scholar
  21. Kim G, Silvapulle MJ, Silvapulle P (2007) Comparison of semiparametric and parametric methods for estimating copulas. Comput Stat Data Anal 51:2836–2850. CrossRefGoogle Scholar
  22. 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. CrossRefGoogle Scholar
  23. Kraus D, Czado C (2017) D-vine copula based quantile regression. Comput Stat Data Anal 110:1–18. CrossRefGoogle Scholar
  24. Kurowicka D (2005) Distribution-free continuous bayesian belief. Mod Stat Math Methods Reliab 10:309CrossRefGoogle Scholar
  25. Kurowicka D, Cooke RM (2007) Sampling algorithms for generating joint uniform distributions using the vine-copula method. Comput Stat Data Anal 51:2889–2906. CrossRefGoogle Scholar
  26. Lesk C, Rowhani P, Ramankutty N (2016) Influence of extreme weather disasters on global crop production. Nature 529:84. CrossRefGoogle Scholar
  27. Mahul O (1999) Optimum area yield crop insurance. Am J Agr Econ 81:75–82. CrossRefGoogle Scholar
  28. Martin SW, Barnett BJ, Coble KH (2001) Developing and pricing precipitation insurance. J Agric Resour Econ 26:261–274Google Scholar
  29. McNeil A, Frey R, Paul E (2005) Quantitative risk management: concepts, techniques and tools. Princeton University Press, PrincetonGoogle Scholar
  30. Miranda MJ, Glauber JW (1997) Systemic risk, reinsurance, and the failure of crop insurance markets. Am J Agr Econ 79:206–215. CrossRefGoogle Scholar
  31. Musafer GN, Thompson MH (2017) Non-linear optimal multivariate spatial design using spatial vine copulas. Stoch Environ Res Risk Assess 31:551–570CrossRefGoogle Scholar
  32. Musshoff O, Odening M, Xu W (2011) Management of climate risks in agriculture–will weather derivatives permeate? Appl Econ 43:1067–1077. CrossRefGoogle Scholar
  33. 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. CrossRefGoogle Scholar
  34. 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. CrossRefGoogle Scholar
  35. 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 21:76–89CrossRefGoogle Scholar
  36. Noh H, Ghouch AE, Bouezmarni T (2013) Copula-based regression estimation and inference. J Am Stat Assoc 108:676–688. CrossRefGoogle Scholar
  37. Odening M, Shen Z (2014) Challenges of insuring weather risk in agriculture. Agric Finance Rev 74:188–199. CrossRefGoogle Scholar
  38. Odening M, Mußhoff O, Xu W (2007) Analysis of rainfall derivatives using daily precipitation models: opportunities and pitfalls. Agric Finance Rev 67:135–156. CrossRefGoogle Scholar
  39. Okhrin O, Odening M, Xu W (2013) Systemic weather risk and crop insurance: the case of China. J Risk Insur 80:351–372. CrossRefGoogle Scholar
  40. Osipenko M, Shen Z, Odening M (2015) Is there a demand for multi-year crop insurance? Agric Finance Rev 75:92–102. CrossRefGoogle Scholar
  41. Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33:1065–1076. CrossRefGoogle Scholar
  42. 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 30:2197–2214CrossRefGoogle Scholar
  43. Reddy MJ, Singh VP (2014) Multivariate modeling of droughts using copulas and meta-heuristic methods. Stoch Environ Res Risk Assess 28:475–489CrossRefGoogle Scholar
  44. Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J Bank Finance 26:1443–1471. CrossRefGoogle Scholar
  45. Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat 23:470–472. CrossRefGoogle Scholar
  46. 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 31:2607–2616CrossRefGoogle Scholar
  47. 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.
  48. 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.
  49. Serinaldi F (2009) Copula-based mixed models for bivariate rainfall data: an empirical study in regression perspective. Stoch Environ Res Risk Assess 23:677–693CrossRefGoogle Scholar
  50. Shen Z, Odening M (2013) Coping with systemic risk in index-based crop insurance. Agric Econom 44(1):1–3. CrossRefGoogle Scholar
  51. Skees JR, Barnett BJ (1999) Conceptual and practical considerations for sharing catastrophic/systemic risks. Rev Agric Econ 21:424–441. Google Scholar
  52. 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 89:1255–1261CrossRefGoogle Scholar
  53. Sklar M (1959) Fonctions de répartition à n dimensions et leurs marges. Université Paris 8Google Scholar
  54. Song S, Singh VP (2010) Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stoch Environ Res Risk Assess 24:425–444CrossRefGoogle Scholar
  55. Tankov P (2011) Improved Fréchet bounds and model-free pricing of multi-asset options. J Appl Probab 48:389–403CrossRefGoogle Scholar
  56. Van Den Goorbergh RW, Genest C, Werker BJ (2005) Bivariate option pricing using dynamic copula models. Insur Math Econ 37:101–114. CrossRefGoogle Scholar
  57. Vedenov D (2008) Application of copulas to estimation of joint crop yield distributions. In: American Agricultural Economics Association annual meeting, Orlando, FL, pp 27–29Google Scholar
  58. Vedenov DV, Barnett BJ (2004) Efficiency of weather derivatives as primary crop insurance instruments. J Agric Resour Econ 1:387–403. Google Scholar
  59. Wang SS (2000) A class of distortion operators for pricing financial and insurance risks. J Risk Insur. Google Scholar
  60. Woodard JD, Garcia P (2008) Basis risk and weather hedging effectiveness. Agric Finance Rev 68:99–117. CrossRefGoogle Scholar
  61. Xu W, Filler G, Odening M, Okhrin O (2010) On the systemic nature of weather risk. Agric Finance Rev 70:267–284. CrossRefGoogle Scholar
  62. Xu Y, Huang G, Fan Y (2017) Multivariate flood risk analysis for Wei River. Stoch Environ Res Risk Assess 31:225–242CrossRefGoogle Scholar
  63. 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. CrossRefGoogle Scholar
  64. 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 27:1397–1406CrossRefGoogle Scholar
  65. 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 27–29Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Agricultural, Computational and Environmental SciencesToowoombaAustralia
  2. 2.Centre for Applied Climate Sciences (CACS)ToowoombaAustralia
  3. 3.Institute of Agriculture and Environment (IAg&E)University of Southern QueenslandToowoombaAustralia
  4. 4.Vietnam National Space Center (VNSC)Vietnam Academy of Science and Technology (VAST)HanoiVietnam

Personalised recommendations