Moderators of pricing and willingness to pay for parametric weather risk mitigants in agriculture: An integrative review, conceptual framework, and research agenda

Figures & data

Figure 2. Year-wise publication of research articles on weather derivatives and parametric insurance in agriculture.

Figure 1. Inclusion and exclusion criteria for literature review.

Figure 3. Authors’ citation network.

Table 1. Influential authors, their top-cited publications, and citations

Sr No	Author (Year)	Top cited paper	Total Citation (Google Scholar)	Reference
1	Campbell and Diebold (2005)	Weather forecasting for weather derivatives.	583	Campbell and Diebold, (2005). Weather forecasting for weather derivatives. Journal of the American Statistical Association, 100(469), 6–16.
2	Alaton et al. (2002)	On modelling and pricing weather derivatives.	566	Alaton et al. (2002). On modelling and pricing weather derivatives. Applied mathematical finance, 9(1), 1–20.
3	Turvey (2001)	Weather derivatives for specific event risks in agriculture.	454	Turvey, C. G. (2001). Weather derivatives for specific event risks in agriculture. Applied Economic Perspectives and Policy, 23(2), 333–351.
4	Davis (2001)	Pricing weather derivatives by marginal value.	308	Davis, (2001). Pricing weather derivatives by marginal value. Quantitative Finance, 1(3), 305–308.
5	Benth and Benth, (2007)	Stochastic modelling of temperature variations with a view towards weather derivatives.	243	Benth, F. E., & Šaltytė‐Benth, J. (2005). Stochastic modelling of temperature variations with a view towards weather derivatives. Applied Mathematical Finance, 12(1), 53–85.
6	Stephen Jewson (2002)	Long memory in surface air temperature: detection, modeling, and application to weather derivative valuation.	148	Caballero, R., Jewson, S., & Brix, A. (2002). Long memory in surface air temperature: detection, modeling, and application to weather derivative valuation. Climate Research, 21(2), 127–140.
7	Martin Odening (2007)	Analysis of rainfall derivatives using daily precipitation models: Opportunities and pitfalls.	142	Odening, M., Mußhoff, O., & Xu, W. (2007). Analysis of rainfall derivatives using daily precipitation models: Opportunities and pitfalls. Agricultural Finance Review, 67(1), 135.
8	Musshoff et al. (2011)	Management of climate risks in agriculture–will weather derivatives permeate?	138	Musshoff et al. (2011). Management of climate risks in agriculture–will weather derivatives permeate? Applied economics, 43(9), 1067–1077.
9	Zapranis and Alexandridis (2008)	Modelling the Temperature Time‐dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing.	103	Zapranis and Alexandridis, (2008). Modelling the temperature time‐dependent speed of mean reversion in the context of weather derivatives pricing. Applied Mathematical Finance, 15(4), 355–386.
10	Wolfgang Karl Härdle (2012)	The Implied Market Price of Weather Risk.	93	Härdle, W. K., & Cabrera, B. L. (2012). The implied market price of weather risk. Applied Mathematical Finance, 19(1), 59–95.
11	Zapranis and Alexandridis (2009)	Weather derivatives pricing: Modeling the seasonal residual variance of an Ornstein–Uhlenbeck temperature process with neural networks.	78	Zapranis and Alexandridis, (2009). Weather derivatives pricing: Modeling the seasonal residual variance of an Ornstein–Uhlenbeck temperature process with neural networks. Neurocomputing, 73(1–3), 37–48.

Source: Prepared by authors.

Figure 4. Authors’ keywords analysis.

Figure 5. Models used in weather derivative and parametric insurance pricing and willingness to pay.

Figure 6. Thematic mapping of weather derivatives and parametric insurance landscape in the agriculture sector.

Figure 7. Moderators of pricing and willingness to pay for weather derivatives and index insurance in agriculture.

Table A1. Commonalities and differences between weather derivatives and index insurance

Attributes	Index-based insurance	Weather derivatives	Remarks
Type of risk mitigation	Pure or weather risk, reinsurance is a challenge if there is a co-variant risk	Pure, covariant, and market (price)/speculative risk	Pure risk is a peril or proximate cause of loss. In contrast, covariant risk arises from pure risk, for example, pest-disease infestation due to inclement weather events leading to crop damage and income loss.
Target users	Farmers or individuals or self-help groups or co-operatives	Farmers, large farms, processing entities, (re)insurance agencies, speculators (financial market participants)	For WII, the policyholder transfers the risk to a third party, an insurance company, or government agencies.
Type	Area-yield index insurance and Weather index insurance (WII)	Weather derivatives	Area-based (reference unit area) yield insurance An indemnity is paid if the actual yield is less than the threshold yield, irrespective of the actual yield of the policyholder. Weather Index Insurance Payment is based on deviation from a specific weather index from a predetermined trigger level. Weather Derivatives Payment is based on deviation from agreed contract weather parameters.
Risk management tool	Yes	Yes	Protect against specific adverse weather events and impact on assets.
Moral hazard	Reduces	Reduces	The indemnity does not depend on the individual producer’s realized yield.
Adverse selection	Reduces, but intertemporal adverse selection remains	Reduces but inter-temporal adverse selection may remain	Few informational asymmetries can be exploited as the indemnity is based on widely available information.
Basis risk	Yes	Yes	Index insurance is not an effective risk management tool without a sufficient correlation between the index and actual losses.
Weather index triggered pay-out	Yes	Yes	Pay-out based on predetermined weather parameters like temperature, rainfall, snowfall, hurricane, etc.
Threshold yield-linked pay-out	No (for traditional insurance)	No	Payment is based on the area average yield. All farmers are treated equally. Basis risk prevails.
Protection against losses	Yes	Yes	Index insurance compensates for actual losses, whereas derivatives provide a hedge against losses to the entire sector.
Weather events directly impact buyers.	Yes	Yes/No	Weather derivative allows the participation of market speculators with no direct asset loss attributed to adverse weather events.
Customization and Tailored terms	Yes	Yes	It can be for specific crops, areas, weather events, etc.
Point of sales: over-the-counter or the exchange-traded	No	Yes	Weather derivatives are treated as financial instruments and lie in the purview of financial market regulation.
Regulation	Yes	Yes	WII is offered by insurance agencies or the government and regulated by the insurance regulatory authorities. The securities exchange commission regulates weather derivatives that are exchange-traded.
Subsidies applicable	Yes	No	The government provides subsidies to farmers to adopt WII.
Pricing model	Historical Burn analysis	Deterministic and stochastic	Weather derivatives are dynamically priced based on demand.

Source: World Bank (2011), Rejda and McNamara (2014)

Annexure A.2.The process flow chart of working of index insurance and weather derivatives in the agriculture sector.

Campbell, S. D., & Diebold, F. X. (2005). Weather forecasting for weather derivatives. Journal of the American Statistical Association, 100(469), 6–16. https://doi.org/10.1198/016214504000001051

 Web of Science ®Google Scholar

Alaton, P., Djehiche, B., & Stillberger, D. (2002). On modeling and pricing weather derivatives. Applied Mathematical Finance, 9(1), 1–23. https://doi.org/10.1080/13504860210132897

 Google Scholar

Turvey, C. G. (2001). The pricing of degree‐day weather options. Agricultural Finance Review, 65(1), 59–85. https://doi.org/10.1108/00214660580001167

 Google Scholar

Turvey, C. G. (2001). Weather derivatives for specific event risks in agriculture. Applied Economic Perspectives and Policy, 23(2), 333–351. http://wiki.leg.ufpr.br/lib/exe/fetch.php/projetos:procad:turvey_2001.pdf

 Google Scholar

Davis, M. (2001). Pricing weather derivatives by marginal value. Quantitative Finance, 1(3), 305–308. https://doi.org/10.1080/713665730

 Google Scholar

Benth, F. E., & Benth, J. Š. (2007). The volatility of temperature and pricing of weather derivatives. Quantitative Finance, 7(5), 553–561. https://doi.org/10.1080/14697680601155334

 Web of Science ®Google Scholar

Benth, F. E., & Šaltytė‐Benth, J. (2005). Stochastic modelling of temperature variations with a view towards weather derivatives. Applied mathematical finance, 12(1), 53–85. https://www.duo.uio.no/bitstream/handle/10852/10324/1/stat-res-01-04.pdf

 Google Scholar

Caballero, R., Jewson, S., & Brix, A. (2002). Long memory in surface air temperature: detection, modeling, and application to weather derivative valuation. Climate Research, 21(2), 127–140. https://www.int-res.com/articles/cr2002/21/c021p127.pdf

 Web of Science ®Google Scholar

Odening, M., Mußhoff, O., & Xu, W. (2007). Analysis of rainfall derivatives using daily precipitation models: Opportunities and pitfalls. Agricultural Finance Review, 67(1), 135. https://www.researchgate.net/profile/Oliver-Musshoff/publication/227352509_Analysis_of_rainfall_derivatives_using_daily_precipitation_models_Opportunities_and_pitfalls/links/00b49521f7014eb3b0000000/Analysis-of-rainfall-derivatives-using-daily-precipitation-models-Opportunities-and-pitfalls.pdf

 Google Scholar

Musshoff, O., Odening, M., & Xu, W. (2011). Management of climate risks in agriculture–will weather derivatives permeate? Applied Economics, 43(9), 1067–1077. https://doi.org/10.1080/00036840802600210

 Web of Science ®Google Scholar

Zapranis, A., & Alexandridis, A. (2008). Modelling the temperature time‐dependent speed of mean reversion in the context of weather derivatives pricing. Applied Mathematical Finance, 15(4), 355–386. https://doi.org/10.1080/13504860802006065

 Google Scholar

Härdle, W. K., & Cabrera, B. L. (2012). The implied market price of weather risk. Applied mathematical finance, 19(1), 59–95. https://www.econstor.eu/bitstream/10419/25317/1/590227564.PDF

 Google Scholar

Zapranis, A., & Alexandridis, A. (2009). Weather derivatives pricing: Modeling the seasonal residual variance of an Ornstein–Uhlenbeck temperature process with neural networks. Neurocomputing, 73(1–3), 37–48. https://doi.org/10.1016/j.neucom.2009.01.018

 Web of Science ®Google Scholar

World Bank. (2011). Weather index insurance for agriculture: Guidance for development practitioners. Agriculture and rUral development discussion Paper 50, The World Bank. https://elibrary.worldbank.org/doi/abs/10.1596/26889.

 Google Scholar

Rejda, G. E., & McNamara, M. J. (2014). Principles of risk Management and insurance. Pearson Education.

 Google Scholar