Browsing by Author "Paul Fackler, Committee Chair"

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    Affine Diffusion Modeling of Commodity Futures Price Term Structure
    (2003-07-28) Tian, Yanjun; Nick Piggott, Committee Member; Peter Bloomfield, Committee Member; John Seater, Committee Member; Paul Fackler, Committee Chair
    Diffusion modeling of commodity price behavior is important for commodity risk management. This research seeks to improve upon the existing commodity diffusion models by incorporating stochastic volatility and seasonality through the affine diffusion framework. In particular, it evaluates affine diffusion models' performance at modeling commodity futures price term structure. Six affine diffusion models are studied in this research. They are one, two, three-factor Gaussian model and one, two, three-factor stochastic volatility model with a single stochastic volatility factor. Seasonality is modeled by allowing the forcing terms of the instantaneous drift and the instantaneous covariance to be seasonal. Model estimation is done through Q-MLE, for which the state variables are filtered through the Kalman Filter. To build the connection between affine diffusion models and known market regularities, affine state variables are interpreted. Factor interpretations used include the log of the spot price, a spot drift factor, and a spot variance factor. Empirical analysis covers models' performance at fitting and predicting futures price term structures; behavior of the interpretable models; and model stability. Empirical studies are applied to the corn and the unleaded gasoline markets. The following conclusions can be drawn from both markets: 1. For the purpose of modeling futures price dynamics alone, stochastic volatility models have no advantage over Gaussian models; 2. At least two factors are needed to adequately model commodity futures price term structures; the advantage of three-factor models, which is better capturing the curvature of the term structures, become evident under extreme market conditions; 3. State independent seasonality modeling is effective under most market conditions, but under extreme market conditions, seasonality can be mis-represented and it is the source of big measurement errors and prediction errors. 4. Two and three-factor affine diffusion models are able to generate model behavior that is consistent with known market regularities.
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    Essays on the Application and Computation of Real Options
    (2009-06-22) Marten, Alex Lennart; Roger von Haefen, Committee Member; Paul Fackler, Committee Chair; Denis Pelletier, Committee Member; John Seater, Committee Member
    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.