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

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.