Study title

This project used historical data on rainfall in Kenya. The economic problem we seek to address is the design of a specific-event weather insurance product that can be embedded into a credit product to provide relief to farm borrowers in time of drought, reduce risk-rationing and increase demand for credit, and provide at least a partial substitute for collateral and reduce financial risk and exposure to lenders, who are reluctant to lend to agriculture because of the very weather risks we seek to insure. To address the phenological problem we develop in what we refer to as a dynamic trigger. This trigger establishes an indemnity if the accumulated rainfall in any 21-day period is below 60% of the historical average rainfall in that same 21-day period for a given year. More on this later, but when we examined the ‘average’ path of overlapping 21-day measures and took the deviation of each year’s equivalent measure we found the distribution of the difference to be non-normal! Indeed we find it to be close to a lognormal distribution with the probability that below-normal rainfall in our study region was approximately 50% more likely than above normal rainfall. The failure of normality suggest also a failure in the Gauss-Markov assumption normally assumed in a first-guess approach to statistical assumption. But this also comes with a possible failure in the independence assumption and Brownian presumption of the historical time-path of our data series – as limited as it is. As Mandelbrot and Wallis (1968) point out the failure to recognize the non-Markov possibilities would greatly underestimate the duration and intensity of the longest drought. Exploring further, we deployed the within-year variance-ratio measure of the Hurst coefficient and found that a) when taken as an average (1983-2017) the within-year Hurst coefficient is approximately H=0.8, b) the within-year Hurst coefficient varies widely from a low of 0.137, a high of 0.687; and c) an average H of...