Modelling and Pricing Rainfall Derivatives to Hedge on Weather Risk in Kenya

P. A. Okemwa, P. G. O. Weke, P. O. Ngare, J. M. Kihoro

Abstract: Weather risk is an unmitigated source of financial losses in developing economies. There is need to model this type risk in order to mitigate and reduce losses associated with the weather. In this article, we model the rainfall process at a particular location in Kenya using a markovian Gamma distribution whose parameters are estimated by way of maximum likelihood. The derivatives prices are estimated by making use of the Esscher transform. The obtained prices are adjusted by calibrating the market price of rainfall risk. The empirical analysis is conducted using Kenyan precipitation and stock market data.

Keywords: Esscher transform, Weather Derivatives, Markovian distribution, Equivalent Martingale, Market Price of Risk