Multivariate real options valuation
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This dissertation research focuses on modeling and evaluating multivariate uncertainties and the dependency between the uncertainties. Managing risk and making strategic decisions under uncertainty is critically important for both individual and corporate success. In this dissertation research, we present two new methodologies, the implied binomial tree approach and the dependent decision tree approach, to modeling multivariate decision making problems with practical applications in real options valuation. First, we present the implied binomial tree approach to consolidate the representation of multiple sources of uncertainty into univariate uncertainty, while capturing the impact of these uncertainties on the project’s cash flows. This approach provides a nonparametric extension of the approaches in the literature by allowing the project value to follow a generalized diffusion process in which the volatility may vary with time and with the asset prices, therefore offering more modeling flexibility. This approach was motivated by the Implied Binomial Tree (IBT) approach that is widely used to value complex financial options. By constructing the implied recombining binomial tree in a way so as to be consistent with the simulated market information, we extended the finance-based IBT method for real options valuation — when the options are contingent on the value of one or more market related uncertainties that are not traded assets. Further, we present a general framework based on copulas for modeling dependent multivariate uncertainties through the use of a decision tree. The proposed dependent decision tree model allows multiple dependent uncertainties with arbitrary marginal distributions to be represented in a decision tree with a sequence of conditional probability distributions. This general framework could be naturally applied in decision analysis and real options valuations, as well as in more general applications of dependent probability trees. While this approach to modeling dependencies can be based on several popular copula families as we illustrate, we focus on the use of the normal copula and present an efficient computational method for multivariate decision and risk analysis that can be standardized for convenient application.