Abstract
This article approaches some of the current rainfall derivatives pricing and operational challenges through an empirical application to Comunidad Valenciana, Spain. Regarding the former, two different issues are addressed. First, we examine the rightness of suggesting the Gamma distribution to price rainfall contracts, which is the alternative chosen by previous authors applying the Index Value Simulation technique. This is done for the purpose of determining whether the consideration and comparison of other alternatives may lead to more accurate valuation results. Concretely, two different distributions, in addition to the Gamma, are proposed: the exponential and the mixed exponential, whose fits are assessed through the Kolmogorov–Smirnov/Lilliefors test and graphical analyses. The outcomes attained indicate that this selection process leads indeed to a precise generation of the rainfall index’s moments. Next, we examine the viability of using a unique distribution to model the rainfall risk of regions located nearby, since this would considerably decrease valuation complexity. Our analysis shows that the most convenient choice depends on the period and location considered, although the mixed exponential appears as a reasonable option in most cases. Finally, a relevant operational challenge related to geographical basis risk is approached. Concretely, an evaluation of this type of risk among the locations studied is conducted. The results attained indicate that, given the insufficient degree of correlation between nearby locations, rainfall risk hedging measures may rely on compound derivatives referred to several neighbor stations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The KS test requires that the parameters of the theoretical distribution have not been estimated from the same bunch of data used to apply this test (Blain 2014, p. 193). As in this case this requirement is not fulfilled, the probability of accepting a false H0 becomes high and a change in the original KS test needs to be implemented. The corrected test is called KS/Lilliefors and relies on Monte Carlo simulations to attain more accurate p-values. First, many samples (in this case, 4999) of the same size than the observed sample are generated. For that purpose, the MLE parameters of the observed sample are used. After that, the MLE parameters of the distribution of each of the random samples are estimated. Then, the KS test is applied to each of the samples, using their estimated parameters. Finally, the p-value is computed as the proportion of test statistics D equal or higher than the test statistic obtained from the KS test applied to the observed sample. A value of one is included in numerator and denominator to allow the observed sample to be represented within the null distribution (Manly 2007, pp. 4–9).
References
Agroseguro (2019). Agroseguro: Introducción y objetivos. Retrieved March 30, 2019, from https://agroseguro.es/agroseguro/quienes-somos/introduccion-y-objetivos.
Alaton, P., Djehiche, B., & Stillberger, D. (2002). On modelling and pricing weather derivatives. Applied Mathematical Finance,9(1), 1–20. https://doi.org/10.1080/13504860210132897.
Alexandridis, A. K., & Zapranis, A. D. (2013). Weather derivatives: Modeling and pricing weather-related risk. New York: Springer.
Black, E., Greatrex, H., Young, M., & Maidment, R. (2016a). Incorporating satellite data into weather index insurance. Bulletin of the American Meteorological Society. https://doi.org/10.1175/bams-d-16-0148.1.
Black, E., Tarnavsky, E., Maidment, R., Greatrex, H., Mookerjee, A., Quaife, T., et al. (2016b). The use of remotely sensed rainfall for managing drought risk: A case study of weather index insurance in Zambia. Remote Sensing. https://doi.org/10.3390/rs8040342.
Blain, G. C. (2014). Revisiting the critical values of the Lilliefors test: Towards the correct agrometeorological use of the Kolmogorov–Smirnov framework. Bragantia,73(2), 192–202. https://doi.org/10.1590/brag.2014.015.
Bohm, G., & Zech, G. (2010). Introduction to statistics and data analysis for physicists. Hamburg: Verl. Dt. Elektronen-Synchrotron.
Bokusheva, R., Kogan, F., Vitkovskaya, I., Conradt, S., & Batyrbayeva, M. (2016). Satellite-based vegetation health indices as a criteria for insuring against drought-related yield losses. Agricultural and Forest Meteorology,220, 200–206. https://doi.org/10.1016/j.agrformet.2015.12.066.
Brockett, P. L., Wang, M., & Yang, C. (2005). Weather derivatives and weather risk management. Risk Management Insurance Review,8(1), 127–140. https://doi.org/10.1111/j.1540-6296.2005.00052.x.
Cabrera, B. L., Odening, M., & Ritter, M. (2013). Pricing rainfall derivatives at the CME (SFB 649 discussion paper 2013-005). Retrieved October 12, 2017 from Humboldt-Universität zu Berlin website https://edoc.hu-berlin.de/bitstream/handle/18452/5097/5.pdf?sequence=1&isAllowed=y.
Cao, M., Li, A., & Wei, J. Z. (2003). Weather derivatives: A new class of financial instruments. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.1016123.
Cao, M., Li, A., & Wei, J. Z. (2004). Precipitation modeling and contract valuation: A frontier in weather derivatives. The Journal of Alternative Investments,7(2), 93–99. https://doi.org/10.3905/jai.2004.439656.
Cao, M., & Wei, J. (2004). Weather derivatives valuation and market price of weather risk. Journal of Futures Markets,24(11), 1065–1089. https://doi.org/10.1002/fut.20122.
Chicago Mercantile Exchange (CME). (2005). An introduction to CME weather products. Retrieved September 15, 2017 from http://www.levow.com/wp-content/uploads/SG/%20Commodities/CME%20Weather%20products.pdf.
Coble, K. H., Knight, T. O., Pope, R. D., & Williams, J. R. (1997). An expected-indemnity approach to the measurement of moral hazard in crop insurance. American Journal of Agricultural Economics,79(1), 216–226. https://doi.org/10.2307/1243955.
Consellería do Mar. (2009). Orden del 21 de Octubre del 2009 pola que se convoca concurso de selección dunha entidade aseguradora que ofreza un seguro de indemnización diaria en caso de paralización e perda da produción por condicións climatolóxicas adversas no sector pesqueiro e marisqueiro de Galicia, así como as axudas para a súa subscrición. Diario Oficial de Galicia, October 29, 2009, 212, 16826–16836. Retrieved November 21, 2018 from https://www.xunta.gal/dog/Publicados/2009/20091029/Anuncio339B6_es.html.
Forbes, C., Evans, M., Hastings, N., & Peacock, B. (2011). Statistical distributions. Hoboken: Wiley.
Giné, X., Menand, L., Townsend, R. W., & Vickery, J. (2012). Microinsurance: A case study of the Indian rainfall index insurance market. Oxford Handbooks Online. https://doi.org/10.1093/oxfordhb/9780199734580.013.0006.
Hess, U., Richter, K., & Stoppa, A. (2002). Weather risk management for agriculture and agri-business in developing countries. In R. S. Dischel (Ed.), Climate risk and the weather market: Financial risk management with weather hedges (pp. 295–310). London: Risk Books.
Huang, H., Shiu, Y., & Lin, P. (2008). HDD and CDD option pricing with market price of weather risk for Taiwan. Journal of Futures Markets,28(8), 790–814. https://doi.org/10.1002/fut.20337.
Leobacher, G., & Ngare, P. (2011). On modelling and pricing rainfall derivatives with seasonality. Applied Mathematical Finance,18(1), 71–91. https://doi.org/10.1080/13504861003795167.
Makaudze, E. M., & Miranda, M. J. (2010). Catastrophic drought insurance based on the remotely sensed normalised difference vegetation index for smallholder farmers in Zimbabwe. Agrekon,49(4), 418–432. https://doi.org/10.1080/03031853.2010.526690.
Manfredo, M. R., & Richards, T. J. (2009). Hedging with weather derivatives: A role for options in reducing basis risk. Applied Financial Economics,19(2), 87–97. https://doi.org/10.1080/09603100701765166.
Manly, B. F. (2007). Randomization, bootstrap and Monte Carlo methods in biology. Boca Raton: Chapman & Hall/CRC.
Dirección General de Industria y de la PYME. Ministerio de Economía, Industria y Competitividad. (2018). Cifras PYME enero 2018. Retrieved March 5, 2018 from http://www.ipyme.org/es-ES/ApWeb/EstadisticasPYME/Documents/CifrasPYME-enero2018.pdf.
Möllmann, J., Buchholz, M., & Musshoff, O. (2019). Comparing the hedging effectiveness of weather derivatives based on remotely sensed vegetation health indices and meteorological indices. Weather, Climate, and Society,11(1), 33–48. https://doi.org/10.1175/wcas-d-17-0127.1.
Norton, M. T., Turvey, C., & Osgood, D. (2012). Quantifying spatial basis risk for weather index insurance. The Journal of Risk Finance,14(1), 20–34. https://doi.org/10.1108/15265941311288086.
Odening, M., Musshoff, O., & Xu, W. (2007). Analysis of rainfall derivatives using daily precipitation models: Opportunities and pitfalls. Agricultural Finance Review,67(1), 135–156. https://doi.org/10.1108/00214660780001202.
Pérez-González, F., & Yun, H. (2013). Risk management and firm value: Evidence from weather derivatives. The Journal of Finance,68(5), 2143–2176. https://doi.org/10.1111/jofi.12061.
Porth, C. B., Porth, L., Zhu, W., Boyd, M. S., Tan, K. S., & Liu, K. (2018). Remote sensing applications for insurance: A predictive model for pasture yield in the presence of systemic weather. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3195389.
Quiggin, J. C., Karagiannis, G., & Stanton, J. (1993). Crop insurance and crop production: An empirical study of moral hazard and adverse selection. Australian Journal of Agricultural Economics,37(2), 95–113. https://doi.org/10.1111/j.1467-8489.1993.tb00531.x.
Reboredo, J. C. (2011). How do crude oil prices co-move? A copula approach. Energy Economics,33(5), 948–955. https://doi.org/10.1016/j.eneco.2011.04.006.
Richards, T. J., Manfredo, M. R., & Sanders, D. R. (2004). Pricing weather derivatives. American Journal of Agricultural Economics,86(4), 1005–1017. https://doi.org/10.1111/j.0002-9092.2004.00649.x.
Ritter, M., Mußhoff, O., & Odening, M. (2013). Minimizing geographical basis risk of weather derivatives using a multi-site rainfall model. Computational Economics,44(1), 67–86. https://doi.org/10.1007/s10614-013-9410-y.
Rohrer, M. B. (2004). The relevance of basis risk in the weather derivatives market. In M. Constantino & C. A. Brebbia (Eds.), Computational finance and its applications (pp. 67–76). Southampton: WIT Press.
Roustant, O., Laurent, J.-P., Bay, X., & Carraro, L. (2003). Model risk in the pricing of weather derivatives. Villeurbanne: Ecole des Mines, Saint- Etienne and Ecole ISFA.
SCOR Global P&C. (2012). The transfer of weather risk faced with the challenges of the future. Retrieved December 10, 2017 from https://www.scor.com/images/stories/PDF/library/newsletter/pc_nl_cata_naturelles_en.PDF.
Shah, A. (2017). Pricing of rainfall derivatives by modelling multivariate monsoon rainfall distribution using Gaussian and t copulas. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2778577.
Skees, J. R., & Reed, M. R. (1986). Rate making for farm-level crop insurance: Implications for adverse selection. American Journal of Agricultural Economics,68(3), 653–659. https://doi.org/10.2307/1241549.
Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut Statistique de l’Université de Paris,8, 229–231.
Smith, V. H., & Goodwin, B. K. (1996). Crop insurance, moral hazard, and agricultural chemical use. American Journal of Agricultural Economics,78(2), 428–438. https://doi.org/10.2307/1243714.
Turvey, C. G. (2001). Weather derivatives for specific event risks in agriculture. Review of Agricultural Economics,23(2), 333–351. https://doi.org/10.1111/1467-9353.00065.
Weber, C., & Stöttner, R. (2011). Insurance linked securities: The role of the banks. Wiesbaden: Gabler Verlag.
Wilks, D. S. (1990). Maximum likelihood estimation for the Gamma distribution using data containing zeros. Journal of Climate,3(12), 1495–1501. https://doi.org/10.1175/1520-0442(1990)0032.0.co;2.
Wilks, D. S., & Wilby, R. L. (1999). The weather generation game: A review of stochastic weather models. Progress in Physical Geography,23(3), 329–357. https://doi.org/10.1177/030913339902300302.
Woodard, J. D., & Garcia, P. (2008). Basis risk and weather hedging effectiveness. Agricultural Finance Review,68(1), 99–117. https://doi.org/10.1108/00214660880001221.
Woolhiser, D. A., & Pegram, G. G. (1979). Maximum likelihood estimation of Fourier coefficients to describe seasonal variations of parameters in stochastic daily precipitation models. Journal of Applied Meteorology,18(1), 34–42. https://doi.org/10.1175/1520-0450(1979)0182.0.co;2.
Young, V. R. (2004). Premium principles. Encyclopedia of Actuarial Science. https://doi.org/10.1002/9780470012505.tap027.
Acknowledgements
The Project which has generated these results has been supported by a grant of Fundación Bancaria “la Caixa” (ID 100010434), whose code is LCF/BQ/ES16/11570002. The authors are thankful to Professor Joan Montllor-i-Serrats (UAB) for interesting insights on previous stages of this research. They are also grateful to the anonymous referee and Gurdip Bakshi (the editor) for providing helpful comments.
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
Martínez Salgueiro, A., Tarrazon-Rodon, MA. Approaching rainfall-based weather derivatives pricing and operational challenges. Rev Deriv Res 23, 163–190 (2020). https://doi.org/10.1007/s11147-019-09161-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11147-019-09161-0