Rainfall Modeling and Simulation

The payout and price of a rainfall-based index insurance contract are both functions of rainfall, which is a random process. In order to design and price these contracts, therefore, the buyers and the sellers of the contracts must both have a satisfactory understanding of the rainfall process, and must be able to communicate their beliefs to each other in order to negotiate the design and price of the contract. Rather than base a contract design on the empirical (historical) distributions of various rainfall statistics, such as the 10th percentile of seasonal rainfall, or the length of the longest dry spell in the season, which can be sensitive to individual, unusual historical events and further limited by sparse or missing data, the designers of insurance contracts can use statistical models trained on historical data to more accurately estimate the distributions of various rainfall-based statistics. A statistical model for rainfall has at least two useful properties: (1) it can describe the relationship between rainfall at a given location and other weather-related variables, such as large-scale climate variables and rainfall observed at other nearby locations, in order to reduce the unexplained variation in rainfall amounts, and (2) it provides a principled way to quantify the uncertainty that accompanies rainfall processes, which is crucial to the efficient design of insurance contracts.