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This paper (SPE 57894) was revised for publication from paper 52949, originally presented at the 1999 SPE Hydrocarbon Economics and Evaluation Symposium held in Dallas, 20–23 March. Original manuscript received 3 January 1999. This paper has not been peer reviewed. Summary Option pricing, decision trees, and Monte Carlo simulations are three methods used to evaluate projects. In this paper, we compare their similarities and differences from three points of view—how they handle uncertainty in the values of key parameters, such as reserves, oil price, and costs; how they incorporate the time value of money; and whether they allow for managerial flexibility. We show that, despite their obvious differences, they are in fact different facets of a general project-evaluation framework that has the static base-case scenario as its simplest form. Compromises have to be made when modeling the complexity of the real world. These three approaches can be obtained from the general framework by focusing on certainty aspects. Introduction Option pricing, decision trees, and Monte Carlo simulations are three methods for evaluating oil projects that seem at first radically different. Option pricing comes from the world of finance. In its most common form, it incorporates the Black and Scholes1 model for spot prices and expresses the value of the project as a stochastic differential equation. Decision trees, which come from operations research and games theory, neglect the time variations in prices but concentrate on estimating the probabilities of possible values of the project, sometimes with Bayes theorem and pre- and post-probabilities (see Ref. 2). In their simplest form, Monte Carlo simulations merely require the user to specify the marginal distributions of all the parameters appearing in the equation for the net present value (NPV) of the project. All three approaches seek to determine the expected value (or maximum expected value) of the project and possibly the histogram of project values; however, they make different assumptions about the underlying distributions, the variation with time of input variables, and the correlations between these variables. Another important difference is the way they handle the time value of money. Decision trees and Monte Carlo simulations use the traditional discount rate; option pricing makes use of the financial concept of risk-neutral probabilities. One of the difficulties in estimating the value of a project is that it usually is a nonlinear function of the input variables (for example, tax is treated differently in years with a profit than in years with a loss). Starting out from the NPV calculated on the base case, this paper shows how Monte Carlo simulations and decision trees build uncertainty and managerial flexibility into the evaluation method. Option pricing starts out by defining the options available to management and then models the uncertainty in key parameters. The three approaches are, in fact, different facets of a general framework. They can be obtained from this framework by focusing on certain aspects and simplifying or ignoring others. First Step-NPV for the base case The first step in evaluating any project is to set up a base-case scenario and to calculate its NPV with the parameter values that have been agreed upon. This assumes that the values of the input parameters are known: original oil in place, decline rate, oil prices for each year, costs for each year, discount rate, and tax structure, among others. It further assumes that the scenario and the project life are fixed and that management will not intervene because of changes in the oil price, new technological developments, and other such factors. In the real world, the values of the variables are uncertain and management does react to changing situations, so it is vital to incorporate these two factors into the evaluation procedure. Ideally, distributions of all the variables should be modeled together with the correlations over time and the complex links between variables should be modeled for a wide variety of management scenarios. However, as Smith and McCardle3 demonstrated, this rapidly becomes very unwieldy and the sheer complexity of the situation forces compromise. Monte Carlo simulations, decision trees, and option pricing address this problem in different ways; each focuses on certain aspects and simplifies or ignores others. We show how these methods build up from the NPV equation in the base case incorporating uncertainty in the input variables for all three methods and incorporating managerial flexibility for decision trees and option pricing.
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