A weather product based on normal seasonal rainfall is a special case of a weighted rainfall index, where all the weights are chosen to be the same. In general, a weighted rainfall index may be defined as where denote the weights, denotes realized rainfall and is typically chosen to be the average historical rainfall. Products based on such indices have been sold by ICICI Lombard in Kharif 2003 and AICI and IFFCO Tokio in Kharif 2004 and 2005 (see Table 4).

Weighted rainfall indices offer more flexibility to a designer than indices based on total seasonal rainfall, but suffer from similar limitations. In particular, a weighted rainfall index provided scope for cross-subsidization across different rainfall periods. For example, a large volume of rainfall in a period of low significance (weight) could compensate for poor rainfall in a period of high significance (weight). Application of daily caps (ceilings) for rainfall volume could partly address this constraint at the cost of further complicating the index.

# <u>Multiple phase weather index</u>

In response to the farmer feedback collected after the first pilot, ICICI Lombard developed a rainfall index with multiple phases for the Kharif 2004 season, described in Giné et al (2010). For such an index the growing season is divided into sequential phases of varying duration, typically chosen to correspond to the crop-growth stages as defined by crop calendars and other reference sources for agronomy. For each phase, the schedule of payments is typically piecewise linear in the total rainfall in the phase, reflecting the water requirements of the crop in that phase, and with payments only if the total rainfall in the phase is sufficiently low (or high).

For example, Table 5 provides an example of a product for which payments are triggered if the total rainfall in the phase is below the rainfall trigger , linearly increasing to the maximum payment of for . Such a schedule would lead to a claim payment as follows: This design could be more intuitive to potential policyholders by clearly associating each critical crop-growth phase with a distinct rainfall insurance structure, and provides scope for interim payouts instead of having to wait till the completion of policy period. However, multiple-phase rainfall insurance index may not capture long dry spells, particularly for phases with durations exceeding a fortnight.

Perhaps more importantly multiple-phase rainfall indices do not fully capture the conditional impact on rainfall in different phases on yields, instead implicitly assuming that the crop productivity in a particular phase is independent of the crop health and rainfall in the previous phase(s). For example, if the index defined in equation (2) is used to determine claim payments, a farmer will only ever receive the maximum claim payment of if there is sufficiently low rainfall in _all_ phases; complete crop loss in one phase is not sufficient to trigger a maximum claim payment even if it is sufficient to destroy an entire crop.

Designers have experimented with two ways of introducing conditionality between phases. First, products usually include a maximum claim payment for the policy which is smaller than the sum of maximum claim payments for each phase. A maximum claim payment may therefore be triggered by exceptionally poor weather in one or a small number of phases. Second, a product may allow 6