A stochastic water-market pricing model for an emerging city in the case of South Africa

Abstract

Water scarcity in South-Africa is a major discussion point in most circles. The most recent drought in South Africa, especially in Cape Town and other emerging markets, emphasised the need for water in South Africa. Australia has recently opted for a water trading market and this has helped them to control the use of water and ensure that it is used more responsibly and efficiently.

Proposing pricing dynamics for water and establishing a market, will encourage people to use this resource more sparingly. It will provide financial benefits to all water users and municipalities and will allow municipalities the opportunity to manage water supply infrastructure under new dynamics that affect urban growing cities. We investigate, explicitly derive and simulate realistic pricing dynamics for water. We use the classical uniform method to simulate the L evy Process based on a Compound Poisson approximation to allow for jumps in water prices, with a Monte Carlo Simulation of the seasonal and mean-reverting Brownian motion. Seasonality and mean-reversion coefficients will be derived from South African fresh water supply data. The proposed water market is an incomplete market, and the restrictions on hedging mechanisms and arbitrage theory will be discussed.