where . The designer is to offer a product that pays ₹100 if the next realization of the index is below some trigger and ₹0 otherwise. Suppose that the designer aims to offer as much cover as possible for a pure premium of ₹10. Now, if the designer chooses for some small , at this trigger the product would have paid out twice in the past. An Historical Burn Analysis would lead to an estimate for the pure premium of . However, for the uniform distribution, we know that which is strictly greater than ₹10 for small enough .

Both ratemaking methodologies presented in this section would be vulnerable to this form of data mining. Both methodologies rely on either a raw or a smoothed historic burn cost approach and if this is biased downwards due to data mining in product design then average pure premium rates will also be biased downwards.

Products cannot be rated on an actuarially sound basis with this form of data mining. One could reduce the bias in rates by calculating historical burn costs for a particular product using weather data series from all nearby weather stations, and then charging a premium based on the average of the average burn costs for this product. However, this would involve cumbersome calculations and would introduce significant inefficiency in estimation; that is to say that premiums would often be either too high or too low, even if they were fair on average.

A way to guard against this form of data mining is to require that all products for a particular crop in a particular season differ only by a limited number of parameters. A standardized product could offer full cover for modeled crop loss above a specified deductible. The deductible parameter could be chosen by the insurer for each product, based on statistical principles, while the shape of the product would be determined by an agronomic model.

As another example, all Kharif maize products sold across India might include four phases of deficit rainfall cover, one phase of consecutive dry day cover, and one phase of excess rainfall cover. All such products would have identical exits, rates, maximum payments, periods, and trigger days. However, triggers for deficit rainfall cover could be uniformly increased or decreased for each maize product so that the calculated rate was within the required range. For example, if the triggers for the four phases of one maize product were {50, 70, 80, 40} then the triggers for any other maize product would be {50+X, 70+X, 80+X, 40+X} for some number of millimeters X, that could be positive or negative. X would be chosen for each product so that the Pure Premium Rate is within the target range. Such an approach would shield the design process from statistically insignificant features of historical weather data. Such dependence would not lead to data mining.

The suggested ratemaking procedure would allow insurers more flexibility in designing products based on agronomic principles. If the difference in rainfall for a group of weather stations in some Risk Collective was not statistically significant, then the same product could be sold in all stations at the same, or a very similar, price. This would have been difficult to justify under the existing ratemaking methodology.

Although the above discussion focuses on WBCIS, the importance of standardizing the shape of products, based on agronomic principles, and using historical data only to determine one or two key parameters is equally valid for any other types of products offered by insurers.

One might think of a weather insurance product as comprising a _shape_ of cover in addition to a _level_ of cover. The shape of cover should not be driven by individual weather data histories because, otherwise, products are likely to be underpriced. It might seem natural for the shape of cover to depend on agronomic fundamentals. In contrast, it is perfectly reasonable for the level of cover to depend on the individual weather data history. Such dependence would not lead to the form of data mining described above.

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