Pricing of Rainfall Derivatives by Modelling Multivariate Monsoon Rainfall Distribution using Gaussian and t Copulas

Abstract

Low income households, especially in the developing countries could suffer losses due to weather related events such as drought, hurricanes, floods etc. Such losses could cast a household into a chronic poverty cycle - a poverty trap from which the household may find it difficult to re-emerge. Rainfall derivatives are the insurance contracts that compensate a household based on the weather outcome rather than the actual crop yield. Traditional methods for pricing rainfall derivatives include burn analysis, index value simulation and daily rainfall simulation. In this work, we price the rainfall derivatives using a different method that uses the Gaussian and t copulas to capture the dependence between the monthly rainfalls in the monsoon season in India. We find that the premium, the standard deviation and Value at Risk “VaR” of the insurance payoffs computed using burn analysis is lower than those calculated using our methodology. Therefore, in practice, the actuarial pricing of the rainfall insurance contract using burn analysis would be lower than that calculated using our proposed method. The burn analysis could result in an underestimation of the actuarial risk and thus could lower the regulatory capital requirement of the insurers. Furthermore, as observed from the t copula fit, our method could find applicability in regions with extreme rainfalls where burn analysis may prove to be inappropriate, especially due to limited data.

Keywords: Weather derivatives, rainfall insurance in India, pricing in incomplete markets, Gaussian and t Copulas, agriculture yields, Monte Carlo simulations

JEL Classification: Q14, G13, G17, G22