Essays on the Application and Computation of Real Options

Abstract

This dissertation presents a series of three essays that examine applications and computational issues associated with the use of stochastic optimal control modeling in the field of economics. In the first essay we examine the problem of valuing brownfield remediation and redevelopment projects amid regulatory and market uncertainty. A real options framework is developed to model the dynamic behavior of developers working with environmentally contaminated land in an investment environment with stochastic real estate prices and an uncertain entitlement process. In a case study of an actual brownfield regeneration project we examine the impact of entitlement risk on the value of the site and optimal developer behavior. The second essay presents a numerical method for solving optimal switching models combined with a stochastic control. For this class of hybrid control problems the value function and the optimal control policy are the solution to a Hamilton-Jacobi-Bellman quasi-variational inequality. We present a technique whereby approximating the value function using projection methods the Hamilton-Jacobi-Bellman quasi-variational inequality may be recast as extended vertical non-linear complementarity problem that may be solved using Newton's method. In the third essay we present a new method for estimating the parameters of stochastic differential equations using low observation frequency data. The technique utilizes a quasi-maximum likelihood framework with the assumption of a Gaussian conditional transition density for the process. In order to reduce the error associated with the normality assumption sub-intervals are incorporated and integrated out using the Chapman-Kolmogorov equation and multi-dimensional Gauss Hermite quadrature. Further improvements are made through the use of Richardson extrapolation and higher order approximations for the conditional mean and variance of the process, resulting in an algorithm that may easily produce third and fourth order approximations for the conditional transition density.