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Optimization Of Water Procurement Decisions In An Irrigation District: The Role Of Option Contracts

Congress: 2015
Author(s): Dolores Rey, Javier Calatrava, Alberto Garrido
Cranfield University / Technical University of Madrid1, Universidad Politecnica de Cartagena2, CEIGRAM, Technical University of Madrid3

Keyword(s): Sub-theme 9: Water allocation among competing uses and users,

Water supply instability is one of the main risks faced by water users. The optimization of water procurement decisions is essential to increase supply reliability and reduce costs. The resource to temporary water markets, such as spot purchases or water supply option contracts, can provide flexibility to this decision process. Previous works have demonstrated that a water planning portfolio that considers option contracts and/or spot purchases can reduce costs and risks (Michelsen and Young, 1993: Jenkis and Lund 2000; Gómez-Ramos and Garrido 2004; Calatrava and Garrido 2005 ; Characklis et al. 2006; Hollinshead and Lund 2006; Kirsch et al. 2009).

The aim of this work is to analyze the potential of an option contract to secure water supply for an irrigation district (ID) that has access to different water sources. Water option contracts give the holder the right (not the obligation) to buy or sell the underlying asset (Michelsen and Young, 1993: Williamson et al. 2008; Cui and Schreider 2009). They have a high risk-reduction potential in comparison with spot purchases and allow the holder to delay water purchase decisions until more information is available (Howitt 1998; Brown and Carriquiry 2007; Ranjan 2010).

We present an original two-stage stochastic recursive mathematical programming model that determines the optimal water procurement program of an ID in a context of water supply uncertainty. The analysis focuses on the decisions regarding the signing and exercising of the option contract, which interacts with other supply alternatives.


The model is applied to the Lorca ID (Southeast Spain), which has access to nine different water sources, including an inter-basin spot market that only functions during drought periods. Our initial database contains the annual ID's water availability from each water source for the period 1994-2012. This database has been processed to build data series that represent the current water availability situation for the district. To characterize water supply uncertainty, we consider each of the 19 years as a single state of the nature with equal probability of occurrence. Facing this set of possible scenarios (hydrological years), the ID managers will have to decide how much water to use and from which sources, taking into account the available water from stochastic sources and the price of the different water sources

The objective of the model is to minimize the ID's water procurement costs that meets the water requirements for irrigators, taking into account the different water sources availability and price. The model provides the optimal water acquisition strategy, including the possible signing of an option contract.

The option contract involves two steps: in the first one, the ID would have to decide whether to sign the contract to protect against the water supply uncertainty it is exposed to. In the second step, once supply uncertainty has disappeared and if the trigger condition of the contract is met, the ID would have to decide whether to exercise the previously signed option. Thus, it is a two-stage recursive stochastic model.

With this option contract, the ID could have access to the optioned volume at the maturity date paying the exercise price to the seller. For having the right to purchase this volume, the ID would have to pay the seller an annual premium (this type of trading mechanism does not currently exist in Spain).

The analysis is focused on the decisions related to the option contract: whether the ID would sign the contract in the first stage, whether the ID would exercise the option (if previously contracted), and the circumstances that determine both decisions. A wide range of parameters (premium, exercise price, optioned volume and trigger) has been used to assess the conditions that make the contract an attractive supply source for the district.

To assess the benefits derived from the existence of the option contract in the water source pool, we have also considered the case when the option contract for water is not available ('baseline scenario') to compare the costs and the water reliability with and without an option contract in the water sources pool.

The optimal solution has been obtained using GAMS.

Results and discussion

In the first stage, the ID has to make a decision about whether to sign the option contract The decision of signing the option contract (binary variable; 0,1) is analyzed through a logistic regression, using all the parameterizations. Depending on the values of the option contract's parameters, the ID would consider it an attractive option or not.

Table 1. Logistic regression results.

All variables, except for exercise price are statistically significant. The premium and the option volume determine the costs of signing the option contract, which explains the negative value of their coefficients. For high premium and optioned volume values, the ID would not sign the option contract. Besides, there is a trade-off between the optioned volume and the contract's annual premium.

In the second stage, our results show that, if the ID signed the option contract in the first stage, and if the trigger condition holds, the ID would always exercise the option contract. When the trigger is met and the ID exercises the option, the optioned volume is purchase in full in 99.46 per cent of the cases.

The next table reports the main statistics of the total costs and total water volume with and without the option contract.

Table 2. Comparison of water procurement costs and water volume, with and without the option contract (average values for all states of nature)

The major advantage of the option contract is its risk-reduction effect, as it reduces the variation coefficient of water availability and the probabilities of the left tails of the water availability probability distribution. Although the average effect is small, the impact is quite significant in scarcity situations.


Reducing water supply uncertainty improves farms' planning and promotes economic efficiency. Optimizing water procurement decisions can help IDs to reduce costs and water availability risks and help their growers be more efficient. Our model represents the water procurement decisions of an ID when different water sources are available, including water supply option contracts. This model can be applied to any other ID which relies on multiple water sources.

Results indicate that the ID would be willing to sign the proposed option contract in most cases, under realistic values of the option contract economic conditions.

The benefits of the option contract in terms of reduced risk exposure, at an average unitary cost of 0.01 EUR/m3, highlight its advantages for IDs in water-scarce areas. The potential benefits of water option contracts for more vulnerable district are thus likely to be much superior. 1. Brown, C. and Carriquiry, M. (2007). Managing hydroclimatological risk to water supply with option contracts and reservoir index insurance. Water Resources Research 43, W11423.
2. Calatrava, J. and Garrido, A. (2005b). Spot water markets and risk in water supply. Agricultural Economics 33, 131-143.
3. Characklis, G., Kirsch, B.R., Ramsey, J., Dillard, K. and Kelley, C.T. (2006). Developing portfolios of water supply transfers. Water Resources Research 42, W05403.
4. Gómez-Ramos, A. and Garrido, A. (2004). Formal risk-transfer mechanisms for allocating uncertain water resources: The case of option contracts, Water Resources Research 40, W12302.
5. Cui, J. and Schreider, S. (2009). Modelling of pricing and market impacts for water options. Journal of Hydrology 371, 31-41.
6. Hollinshead, S.L. and Lund, J.R. (2006). Optimization of Environmental Water Purchases with Uncertainty. Water Resources Research 42, W08403.
7. Howitt, R. E. (1998). Spot Prices, Option Prices, and Water Markets: An Analysis of Emerging Markets in California. Natural Resource Management and Policy 15,119-140.
8. Jenkins, M. W. and Lund, J.R. (2000). Integrating yield and shortage management under multiple uncertainties. Journal of Water Resources Planning and Management, 126(5), 288-297.
9. Kirsch, B.R., Characklis, G.W., Dillard, K. and Kelley, C.T. (2009). More efficient optimization of long-term water supply portfolios. Water Resources Research 45, W03414.
10. Michelsen A.M. and Young R.A. (1993). Optioning agricultural water rights for urban water supplies during drought. American Journal of Agricultural Economics, 75, 1010-1020. 11. Ranjan, R. (2010). Factors affecting Participation in Spot and Options Markets for Water. Journal of Water Resources Planning and Management 136 (4), 454-462.
12. Williamson, B., Villano, R. and Fleming, E. (2008). Structuring Exotic Option Contracts on Water to Improve the Efficiency of Resource Allocation in the Water Spot Water. AARES 52nd Annual Conference, February 2008.
2011 IWRA - International Water Resources Association - - Admin