Pricing of Rainfall Derivatives Using Generalized Linear Models of the Daily Rainfall Process

Abstract

The structure of a typical rainfall insurance is complex; insurance payoffs are based on many parameters such as the rainfall volume, the rainfall distribution (the number of consecutive dry days), the number of days with excess rainfall etc. Such a complex insurance structure is essential to minimize the basis risk and to amply compensate a farmer for the loss of the crop yield due to the rainfall weather event. A rainfall derivative could always be brokered as a rainfall insurance or a traded option. To price complex rainfall insurances or to trade complex financial instrument based on the rainfall index on the capital markets, the underlying daily rainfall process needs to be modelled. The daily rainfall modelling is essential because the trading of any financial instrument based on the rainfall index requires the pricing of the instrument contingent on the daily rainfall information as it becomes available. In this work, we price a rainfall derivative by modelling the underlying daily rainfall process using generalized linear models (GLMs). The rainfall occurrence process is modelled using a binomial GLM and the rainfall intensity process is modelled using a quasi-likelihood GLM with the gamma, the Pareto and the lognormal distribution assumptions. Our models estimate the average annual monsoon rainfall correctly but overestimate the standard deviation, the skewness and the excess kurtosis of the annual monsoon rainfall distribution. The expected total derivative payoff obtained using only the models with the gamma distribution assumption is comparable to that obtained from Burn analysis. There was no significant gain from using a model with two auto-regressive rainfall intensity terms.