Suchergebnisse

Two-factor stochastic processes have been developed to more accurately describe the intertemporal dynamics of variables such as commodity prices. In this paper we develop an approach for modeling these types of stochastic processes in discrete time as two-dimensional binomial sequences. This approach facilitates the numerical solution of dynamic optimization problems such as investment decision making under uncertainty and option valuation related to commodities. We implement this approach in a two-dimensional lattice format, apply it to two hypothetical valuation problems discussed by Schwartz and Smith, and compare the results to those from simulation- and dynamic-programming-based methods.

In this note, we respond to Smith's (2005) discussion of the approach outlined in our paper (Brandão et al. 2005) on using traditional decision analysis methods to solve real-options problems. Our response addresses several areas where we largely agree with Smith, but have different views on modeling preferences or on the practicality of implementing alternative modeling approaches. We view the issue raised by Smith on the estimation of process volatility to be a valid concern and propose a modification to our method to address this problem.

Traditional decision analysis methods can provide an intuitive approach to valuing projects with managerial flexibility or real options. The discrete-time approach to real-option valuation has typically been implemented in the finance literature using a binomial lattice framework. Instead, we use a binomial decision tree with risk-neutral probabilities to approximate the uncertainty associated with the changes in the value of a project over time. Both methods are based on the same principles, but we use dynamic programming to solve the binomial decision tree, thereby providing a computationally intensive but simpler and more intuitive solution. This approach also provides greater flexibility in the modeling of problems, including the ability to include multiple underlying uncertainties and concurrent options with complex payoff characteristics.