A Stochastic Weather Model for Drought Derivatives in Arid Regions: A Case Study in Qatar

Abstract

In this paper, we propose a stochastic weather model consisting of temperature, humidity, and precipitation, which is used to calculate a reconnaissance drought index (RDI) in Qatar. The temperature and humidity models include stochastic differential equations and utilize an adjusted Ornstein–Uhlenbeck (O–U) process. For the precipitation model, a first-order Markov chain is used to differentiate between wet and dry days and the precipitation amount on wet days is determined by a probability distribution. Five different probability distributions were statistically tested to obtain an appropriate precipitation amount. The evapotranspiration used in the RDI calculation incorporates crop coefficient values, depends on the growth stages of the crops, and provides a crop-specific and more realistic representation of the drought conditions. Five different evapotranspiration formulations were investigated in order to obtain the most accurate RDI values. The calculated RDI was used to assess the intensity of drought in Doha, Qatar, and could be used for the pricing of financial drought derivatives, a form of weather derivative. These derivatives could be used by agricultural producers to hedge against the economic effects of droughts.

Keywords

• stochastic differential equations (SDEs)
• reconnaissance drought index (<i>RDI</i>)
• Ornstein–Uhlenbeck (O–U) processes
• Markov chains