Modeling and Pricing Rainfall Derivatives to HedgeWeather Risk in Kenya

Abstract

This study set out to price rainfall derivatives based on rainfall at a particular location in Kenya over a given period. We employ a Markovian-Gamma model to model the rainfall process. In addition, its parameters are determined via maximum likelihood estimation. We assume existence of a tradable asset whose performance is rainfall dependent. To compute the prices of the rainfall derivatives, we rely on the Esscher transform, an actuarial tool. We then compare the Esscher prices with the standard Black-Scholes prices. The results suggest a certain pattern of movement of the prices in which the derivative price decreases as the strike price increases in the Black-Scholes whereas they increase on considering the Esscher. The study is conducted using rainfall and stock market data in Kenya.