James E. Smith

Options in the Real World: Lessons Learned in Evaluating Oil and Gas Investments

Many firms in the oil and gas business have long used decision analysis techniques to evaluate exploration and development opportunities and have looked at recent development in option pricing theory as potentially offering improvements over the decision analysis approach. Unfortunately, it is difficult to discern the benefits of the options approach from the literature on the topic: Most of the published examples greatly oversimplify the kinds of projects encountered in practice, and comparisons are typically made to traditional discounted cash flow analysis, which, unlike the option pricing and decision analytic approaches, does not explicitly consider the uncertainty in project cash flows. In this paper, we provide a tutorial introduction to option pricing methods, focusing on how they relate to and can be integrated with decision analysis methods, and describe some lessons learned in using these methods to evaluate some real oil and gas investments.

Valuing Oil Properties: Integrating Option Pricing and Decision Analysis Approaches

There are two major competing procedures for evaluating risky projects where managerial flexibility plays an important role: one is decision analytic, based on stochastic dynamic programming, and the other is option pricing theory (or contingent claims analysis), based on the no-arbitrage theory of financial markets. In this paper, we show how these two approaches can be profitably integrated to evaluate oil properties. We develop and analyze a model of an oil property-either a developed property or a proven but undeveloped reserve-where production rates and oil prices both vary stochastically over time and, at any time, the decision maker may terminate production or accelerate production by drilling additional wells. The decision maker is assumed to be risk averse and can hedge price risks by trading oil futures contracts. We also describe extensions of this model that incorporate additional uncertainties and options, discuss its use in exploration decisions and in evaluating a portfolio of properties rather than a single property, and briefly describe other potential applications of this integrated methodology.

Information Relaxations and Duality in Stochastic Dynamic Programs

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a “penalty” that punishes violations of nonanticipativity. In applications, the hope is that this relaxed version of the problem will be simpler to solve than the original dynamic program. The upper bounds provided by this dual approach complement lower bounds on values that may be found by simulating with heuristic policies. We describe the theory underlying this dual approach and establish weak duality, strong duality, and complementary slackness results that are analogous to the duality results of linear programming. We also study properties of good penalties. Finally, we demonstrate the use of this dual approach in an adaptive inventory control problem with an unknown and changing demand distribution and in valuing options with stochastic volatilities and interest rates. These are complex problems of significant practical interest that are quite difficult to solve to optimality. In these examples, our dual approach requires relatively little additional computation and leads to tight bounds on the optimal values.

Structuring conditional relationships in influence diagrams

An influence diagram is a graphical representation of a decision problem that is at once a formal description of a decision problem that can be treated by computers and a representation that is easily understood by decision makers who may be unskilled in the art of complex probabilistic modeling. The power of an influence diagram, both as an analysis tool and a communication tool, lies in its ability to concisely summarize the structure of a decision problem. However, when confronted with highly asymmetric problems in which particular acts or events lead to very different possibilities, many analysts prefer decision trees to influence diagrams. In this paper, we extend the definition of an influence diagram by introducing a new representation for its conditional probability distributions. This extended influence diagram representation, combining elements of the decision tree and influence diagram representations, allows one to clearly and efficiently represent asymmetric decision problems and provides an attractive alternative to both the decision tree and conventional influence diagram representations.

Dynamic Portfolio Optimization with Transaction Costs: Heuristics and Dual Bounds

We consider the problem of dynamic portfolio optimization in a discrete-time, finite-horizon setting. Our general model considers risk aversion, portfolio constraints (e.g., no short positions), return predictability, and transaction costs. This problem is naturally formulated as a stochastic dynamic program. Unfortunately, with nonzero transaction costs, the dimension of the state space is at least as large as the number of assets, and the problem is very difficult to solve with more than one or two assets. In this paper, we consider several easy-to-compute heuristic trading strategies that are based on optimizing simpler models. We complement these heuristics with upper bounds on the performance with an optimal trading strategy. These bounds are based on the dual approach developed in Brown et al. (Brown, D. B., J. E. Smith, P. Sun. 2009. Information relaxations and duality in stochastic dynamic programs. Oper. Res. 58(4) 785--801). In this context, these bounds are given by considering an investor who has access to perfect information about future returns but is penalized for using this advance information. These heuristic strategies and bounds can be evaluated using Monte Carlo simulation. We evaluate these heuristics and bounds in numerical experiments with a risk-free asset and 3 or 10 risky assets. In many cases, the performance of the heuristic strategy is very close to the upper bound, indicating that the heuristic strategies are very nearly optimal. This paper was accepted by Dimitris Bertsimas, optimization.

Alternative Approaches for Solving Real-Options Problems: (Comment on Brandão et al. 2005)

Brandao et al. (2005) describe an approach for using traditional decision analysis tools to solve real-option valuation problems. Their approach calls for a mix of discounted cash flow analysis and risk-neutral valuation methods and is implemented using Monte Carlo simulation and binomial decision trees. In this note, I critique their approach and discuss some alternative approaches for solving these kinds of problems. My criticisms and suggestions concern implementation issues as well as more fundamental issues. On implementation, I discuss the use of binomial lattices instead of trees, and alternative methods for estimating volatilities. More fundamentally, I discuss alternative approaches that rely entirely on risk-neutral valuation and model the uncertainties in the problem more directly.

Anniversary Article: Decision Analysis in Management Science

As part of the 50th anniversary ofManagement Science, the journal is publishing articles that reflect on the past, present, and future of the various subfields the journal represents. In this article, we consider decision analysis research as it has appeared inManagement Science. After reviewing the foundations of decision analysis and the history of the journals decision analysis department, we review a number of key developments in decision analysis research that have appeared inManagement Science and offer some comments on the current state of the field.

A Multimethod Approach for Creating New Business Models: The General Motors OnStar Project

We developed a multimethod modeling approach to evaluate strategic alternatives for GMs OnStar communications system. We used dynamic modeling to address some decisions GM faced in 1997, such as the companys choice between incremental and aggressive marketing strategies for OnStar. We used an integrated simulation model for analyzing the new telematics industry, consisting of six sectors: customer acquisition, customer choice, alliances, customer service, financial dynamics, and dealer behavior. The modeling effort had important financial, organizational, and societal results. The OnStar business now has two million subscribers, an 80 percent market share of the emerging telematics market, and has been valued at between

Evaluation of Installation Stock Based (R, Q)-Policies Fortwo-Level Inventory Systems with Poisson Demands

4 and

The Optimizers Curse: Skepticism and Postdecision Surprise in Decision Analysis

10 billion. The OnStar project set the stage for a broader GM initiative in service businesses that ultimately could yield billions in incremental earnings. Most important, OnStar has saved many lives that otherwise would have been lost in vehicle accidents.