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Step 3,they differ from C&A in recommending use of a
Smith: Alternative Approaches for Solving Real-Options Problems90 Decision Analysis 2(2), pp. 89–102, ©2005 INFORMSbinomial decision tree rather than a binomial lattice.Like earlier real-options work, the BDH andC&A approach can be interpreted as building on theanalogy with anoption on a stock: The first stepprovides an estimate of the value of the underlyingstock and the second step estimates the volatility
of this stock. Project cash flows are modeled as atime-varying dividend stream paid by the stock. Thenumerical methods in Step 3 of the process are quitesimilar to those used to value American or Bermudan
put-and-call options on a stock (those that allow earlyexercise), although BDH contemplate somewhat moregeneral kinds of options.
In this paper, I critique BDH’s approach and discusssome alternative approaches for solving real-optionsproblems. Although I focus on areas where I disagreewith BDH’s proposal, there are also many points of
agreement that should be emphasized. First, aboveall, we agree that it is important to model the resolutionof uncertainty over time, and options that canbe exercised as information is gathered. The values,
strategies, and insights derived from these dynamicmodels may be significantly different and richer thanthose generated by models that do not capture thesedynamics. Second, we agree that it is important to
recognize the relationship of the project to the marketand the implications this has for values and optimalstrategies. Again, the values and insights derivedfrom such analyses may be significantly different fromthose that use a constant corporate discount rate
and/or utility function to calculate expected NPVs orcertainty equivalents for all projects. Third, we agreethat the marriage of simulation, decision tree, and/ordynamic programming models with risk-neutral valuationtechniques provides a very fruitful approach formodeling dynamics and incorporating market informationinto project evaluations.My criticisms of BDH’s approach concern specific
implementation issues as well as more fundamentalissues. To be constructive as well as critical, I suggestalternative approaches that address these concerns.In §2, I consider the use of binomial lattices
in Step 3 of BDH’s procedure and compare the latticeapproach to BDH’s binomial tree representationusing BDH’s oil production problem as an example.In §3, I show that BDH’s (or C&A’s) proposed procedurefor calculating volatilities often overstates theactual uncertainty in the cash flows and, hence, willverstate the value of many options. In §4, I turno more fundamental issues and recommend usinga fully risk-neutral approach to value projects ratherthan using a mix of discounted cash flow and riskneutralmethods. The fully risk-neutral approach is,
I believe, better grounded in theory and leads toa single coherent valuation model that can be usedto value projects with and without options. In §5,I discuss the use of the value of the project without
options as the underlying uncertainty and arguethat, although this approach is potentially useful in
some cases, it is not broadly applicable. In this section,
I consider more general techniques that model the
underlying uncertainties directly, focusing on the use
of Monte Carlo methods (e.g., Longstaff and Schwartz
2001) for solving real-options problems. In §6, I summarize
and conclude.
BDH