Contingency estimating using option pricing theory: closing the gap between theory and practice

Abstract

Valuation of contingency budgets for construction projects considering technical and market uncertainties as well as the time it takes to execute the project can be estimated using option pricing theory. Although option pricing theory provides an attractive framework for calculation of contingency budgets, it typically results in complex highly non-linear partial differential equations that require the use of numerical algorithms and computer intensive techniques, thus making it difficult for practitioners to adopt this valuation technique. An attempt to bridge the gap between theory and practice is made by proposing an equivalent linear stochastic process to model the complex non-linear random variation with time of the technical and market uncertainty for projects. The approximation allows estimation of contingency budgets using either closed-form solutions for pricing options, or the intuitive binomial approach. To validate the proposed equivalent linear solution, its results were compared to the solution to the non-linear partial differential equation that governs the pricing of contingency budgets solved by Monte Carlo simulations. A parametric study of the error shows that the proposed approximation to estimate contingency budgets compares well with the results obtained from simulation. The main advantages of the proposed solution are its simplicity and straightforward implementation.

Keywords:

• Real options
• contingency cost
• decision analysis

Notes

aUnit prices were established by competitive bidding and corresponded to the low bidder.

bThe total construction cost was obtained by multiplying the unit cost times the corresponding quantities.

cThe average construction cost (Q) was obtained assuming a triangular distribution using the bid, min and max quantities.

1. The terms ‘option’ and ‘derivative’ are used interchangeably in this paper.

2. A European option refers to derivatives that can only be exercised (executed) at the end of the contract period not earlier. The term ‘American option’ is used to refer to derivatives that can be exercised at any time during the contract period. Many contract terms can be linked to these features.

3. The project convenience yield corresponds to the economic output that the project would generate after completion. For instance, if a project that consists of building a commercial development at the cost of $10 million is estimated to generate $800 000 per year, then the convenience yield would be 8%.

4. PVDs are typically used at sites with soft compressible saturated foundations. The site under consideration was located in Delaware, USA, at the confluence of two rivers. The site was reclaimed from the river and was a former dredge disposal facility used by the US Army Corps of Engineers. In order to build a 1.5 km long 20 m high reinforced beam, the foundation needed to be improved.