Abstract
Rainfall is considered to be one of the major factors affecting the yield of farmers and the production of hydroelectric energy generators. On the other hand snowfall affects the revenues of ski industry. Rainfall and snowfall can be accounted as a form of precipitation. The aim of this chapter is to analyze the dynamics of the precipitation process and present a modeling procedure for precipitation. Precipitation modeling is separated in two components. The first step is to model the frequency process of precipitation and the second to model the magnitude process. In this chapter the dynamics of the precipitation generating process are modeled using a Markov chain model that define the frequency process and with a gamma distribution for the magnitude process. Our model is validated in Berlin, and the basis risk in the context of precipitation is also examined. Finally, we provide the pricing framework for rainfall futures.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
References
Akaike H (1974) New look at statistical-model identification. IEEE Trans Automat Contr AC19(6):716–723
Brockett PL, Wang M, Yang C, Zou H (2006) Portfolio effects and valuation of weather derivatives. Financ Rev 41:55–76
Campbell SD, Diebold FX (2005) Weather forecasting for weather derivatives. J Am Stat Assoc 100:6–16
Cao M, Li A, Wei J (2004) Precipitation modeling and contract valuation: a frontier in weather derivatives. J Altern Invest 7(2):92–99
Carmona R, Diko P (2005) Pricing precipitation based derivatives. Int J Theor Appl Finance 8(7):959–988
Carr P, Geman H, Madan DB (2001) Pricing and hedging in incomplete markets. J Financ Econ 62:131–167
Coles S, Pericchi LR, Sisson S (2003) A fully probabilistic approach to extreme rainfall modeling. J Hydrol 273:35–50
Dischel B (2000) Seeding a rain market. Environ Finance (September):2–4
Dubrovsky M, Buchtele J, Zalud Z (2004) High-frequency and low-frequency variability in stochastic daily weather generator and its effect on agricultural and hydrologic modelling. Clim Change 63:145–179
Edwards M, Simmons P (2004) Preliminary results for the measurement of willingness to pay for climate derivatives. In: 48 annual conference of the Australian Agricultural & Resource Economics Society, Melbourne, Australia, February 2004
Feng Y, Kitzmiller D (2006) A short-range quantitative precipitation forecast algorithm using back-propagation neural network approach. Adv Atmos Sci 23(3):405–414. doi:10.1007/s00376-006-0405-7
Goncu A (2011) Modeling and pricing precipitation-based weather derivatives. Financ Math Appl 1(1):9–18
Leobacher G, Ngare P (2010) On modelling and pricing rainfall derivatives with seasonality. Appl Math Finance 18(1):71–91
Little MA, McSharry PE, Taylor JW (2009) Generalized linear models for site-specific density forecasting of U.K. daily rainfall. Mon Weather Rev 137(3):1029–1045. doi:10.1175/2008mwr2614.1
Martin WS, Barnett JB, Coble HK (2001) Developing and pricing precipitation insurance. J Agric Resour Econ 26(1):261–274
Moreno M (2002) Rain risk. Speedwell Weather Derivatives, London
Musshoff O, Odening M, Xu W (2006) Modeling and hedging rain risk. In: American Agricultural Economics Association annual meeting, Long Beach, California, 23–26 July 2006
Odening M, Musshoff O, Xu W (2007) Analysis of rainfall derivatives using daily precipitation models: opportunities and pitfalls. Agric Finance Rev 67:135–156
Oetomo T, Stevenson M (2005) Hot or cold? A comparison of different approaches to the pricing of weather derivatives. J Emerg Mark Finance 4(2):101–133
Richards TJ, Manfredo MR, Sanders DR (2004) Pricing weather derivatives. Am J Agric Econ 4(86):1005–1017
Schoof JT, Pryor SC (2008) On the proper order of Markov chain model for daily precipitation occurrence in the contiguous United States. J Appl Meteorol Climatol 47(9):2477–2486. doi:10.1175/2008jamc1840.1
Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464
Simmons P, Edwards M, Byrne J (2007) Willingness to pay for weather derivatives by Australian wheat farmers. In: European Association of Agricultural Economists, 101st seminar, Berlin, 5–6 July 2007
Stowasser M (2012) Modelling rain risk: a multi-order Markov chain model approach. J Risk Finance 13(1):45–60
Valverde Ramírez MC, de Campos Velho HF, Ferreira NJ (2005) Artificial neural network technique for rainfall forecasting applied to the São Paulo region. J Hydrol 301(1–4):146–162. doi:10.1016/j.jhydrol.2004.06.028
Vedenov DV, Miranda MJ (2001) Rainfall insurance for midwest crop production. American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association)
Wilks DS (1998) Multisite generalization of a daily stochastic precipitation generation model. J Hydrol 210(1–4):178–191. doi:10.1016/s0022-1694(98)00186-3
Wilks DS (1999) Multisite downscaling of daily precipitation with a stochastic weather generator. Clim Res 11:125–136
Wilks DS (2011) Statistical methods in the atmospheric sciences, vol 100, 3rd edn, International geophysics series. Academic, Oxford, UK
Williams PM (1998) Modelling seasonality and trends in daily rainfall data. Paper presented at the proceedings of the 1997 conference on advances in neural information processing systems, vol 10, Denver
Xu W, Odening M, Musshof O (2008) Indifference pricing of weather derivatives. Am J Agric Econ 90(4):979–993
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Alexandridis, A.K., Zapranis, A.D. (2013). Precipitation Derivatives. In: Weather Derivatives. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6071-8_10
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6071-8_10
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-6070-1
Online ISBN: 978-1-4614-6071-8
eBook Packages: Business and EconomicsEconomics and Finance (R0)