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AbstractClimate risk financing programs in agriculture have caught the attention of researchers and policy makers over the last decade. Weather index insurance has emerged as a promising market-based risk financing mechanism. However, to develop a suitable weather index insurance mechanism it is essential to incorporate the distribution of underlying weather and climate risks to a specific event model that can minimize intraseasonal basis risk. In this paper we investigate the erratic nature of rainfall patterns in Kenya using Climate Hazards Group Infrared Precipitation with Station Data (CHIRPS) rainfall data from 1983 to 2017. We find that the patterns of rainfall are fractional, both erratic and persistent, which is consistent with the Noah and Joseph effects that are well known in mathematics. The erratic nature of rainfall emerges from the breakdown of the convergence to a normal distribution. Instead we find that the distribution about the average is approximately lognormal, with an almost 50% higher chance of deficit rainfall below the mean than adequate rainfall above the mean. We find that the rainfall patterns obey the Hurst law and that the measured Hurst coefficients for seasonal rainfall pattern across all years range from a low of 0.137 to a high above 0.685. To incorporate the erratic and persistent nature of seasonal rainfall, we develop a new approach to weather index insurance based upon the accumulated rainfall in any 21-day period falling below 60% of the long-term average for that same 21-day period. We argue that this approach is more satisfactory to matching drought conditions within and between various phenological stages of growth.

Abstract
Weather index insurance (WII) has been a promising innovation that protects smallholder farmers against drought risks and provides resilience against adverse rainfall conditions. However, the uptake of WII has been hampered by high spatial and intraseasonal basis risk. To minimize intraseasonal basis risk, the standard approaches to designing WII based on seasonal cumulative rainfall have been shown to be ineffective in some cases because they do not incorporate different water requirements across each phenological stage of crop growth. One of the challenges in incorporating crop phenology in insurance design is to determine the water requirement in crop growth stages. Borrowing from agronomy, crop science, and agrometeorology, we adopt evapotranspiration methods in determining water requirements for a crop to survive in each stage that can be used as a trigger level for a WII product. Using daily rainfall and evapotranspiration data, we illustrate the use of Monte Carlo risk modeling to price an operational WII and WII-linked credit product. The risk modeling approach that we develop includes incorporation of correlation between rainfall and evapotranspiration indices that can minimize significant intertemporal basis risk in WII.

Global insurance markets are vast and diverse, and may offer many opportunities for remote sensing. To date, however, few operational applications of remote sensing for insurance exist. Papers claiming potential application of remote sensing typically stress the technical possibilities, without considering its contribution to customer value for the insured or to the profitability of the insurance industry. Based on a systematic search of available literature, this review investigates the potential and actual support of remote sensing to the insurance industry. The review reveals that research on remote sensing in classical claim-based insurance described in the literature revolve around crop damage and flood and fire risk assessment. Surprisingly, the use of remote sensing in claim-based insurance appears to be instigated by government rather than the insurance industry. In contrast, insurance companies are offering various index insurance products that are based on remote sensing. For example, remotely sensed index insurance for rangelands and livestock are operational, while various applications in crop index insurance are being considered or under development. The paper discusses these differences and concludes that there is particular scope for application of remote sensing by the insurance industry in index insurance because (1) indices can be constructed that correlate well with what is insured; (2) these indices can be delivered at low cost; and (3) it opens up new markets that are not served by claim-based insurance. The paper finally suggests that limited adoption of remote sensing in insurance results from a lack of mutual understanding and calls for greater cooperation between the insurance industry and the remote sensing community.

Global insurance markets are vast and diverse, and may offer many opportunities for remote sensing. To date, however, few operational applications of remote sensing for insurance exist. Papers claiming potential application of remote sensing typically stress the technical possibilities, without considering its contribution to customer value for the insured or to the profitability of the insurance industry. Based on a systematic search of available literature, this review investigates the potential and actual support of remote sensing to the insurance industry. The review reveals that research on remote sensing in classical claim-based insurance described in the literature revolve around crop damage and flood and fire risk assessment. Surprisingly, the use of remote sensing in claim-based insurance appears to be instigated by government rather than the insurance industry. In contrast, insurance companies are offering various index insurance products that are based on remote sensing. For example, remotely sensed index insurance for rangelands and livestock are operational, while various applications in crop index insurance are being considered or under development. The paper discusses these differences and concludes that there is particular scope for application of remote sensing by the insurance industry in index insurance because (1) indices can be constructed that correlate well with what is insured; (2) these indices can be delivered at low cost; and (3) it opens up new markets that are not served by claim-based insurance. The paper finally suggests that limited adoption of remote sensing in insurance results from a lack of mutual understanding and calls for greater cooperation between the insurance industry and the remote sensing community.