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Although globally used in option pricing, the Black-Scholes model has not been able to reflect the evolution of stocks in the real world. A regime-switching model which allows jumps in the underlying asset prices and the parameters of the corresponding stochastic process is more accurate. We evaluate the analytical solution for pricing of European options under a two-state regime switching model. Both the convergence of the analytical solution and the feature of implied volatility are investigated through numerical examples. We develop a number of techniques for pricing American options by solving the system of partial differential equations in a general \mathcal{K}-state regime-switching model. The linear complementarity problem is replaced by either the penalty or the direct control formulations. With an implicit discretization, we compare a number of iterative procedures (full policy iteration, fixed point-policy iteration, and local American iteration) for the associated nonlinear algebraic equations. Specifically, a linear system appears in the full policy iteration which can be solved directly or iteratively. Numerical tests indicate that the fixed point-policy iteration and the full-policy iteration (using a simple iteration for the linear system), both coupled with a penalty formulation, results in an efficient method. In addition, using a direct solution method to solve the linear system appearing in the full policy iteration is usually computationally very expensive depending on the jump parameters. A Fourier transform is applied to the system of partial differential equations for pricing American options to obtain a linear system of ordinary differential equations that can be solved explicitly at each timestep. We develop the Fourier space timestepping algorithm which incorporates a timestepping scheme in the frequency domain, in which the frequency domain prices are obtained by applying the discrete Fourier transform to the spatial domain. Close to quadratic convergence in time and space is observed for all regimes when using a second order Crank-Nicolson scheme for approximation of the explicit solution of the ordinary differential equation.

This thesis explores option pricing and hedging in a discrete time regime-switching environment. If the regime risk cannot be hedged away, then we cannot ignore this risk and use the Black-Scholes pricing and hedging framework to generate a unique pricing and hedging measure. We develop a risk neutral pricing measure by applying an Esscher Transform to the real world asset price process, with the focus on the issue of incompleteness of the market. The Esscher transform turns out to be a convenient and effective tool for option pricing under the discrete time regime switching models. We apply the pricing measure to both single variate European options and multivariate options. To better understand the effect of the pricing method, we also compared the results with those generated from two other risk neutral methods: the Black-Scholes model, and the natural equivalent martingale method. We further investigate the difference in hedging associated with different pricing measures. This is of interest when the choice of pricing method is uncertain under regime switching models. We compare four hedging strategies: delta hedging for the three risk neutral pricing methods under study, and mean variance hedging. We also develop a more general tool of tail ordering for hedging analysis in a general incomplete market with the uncertainty of the risk neutral measures. As a result of the analysis, we propose that pricing and hedging using the Esscher transform may be an effective strategy for a market where the regime switching process brings uncertainty.

In this dissertation, a hydrologic classification approach was tested using the shape factor of hydrographs to represent variation in streamflow regimes across Alberta. Hydrograph shape factor was effective at separating the forested landbase into 6 spatially distinct regions. Further statistical analysis of hydrometric data showed each region to have unique streamflow characteristics. Differences in physiography between regions were evident and strong associations were found between physical catchment characteristics and hydrologic variables describing streamflow magnitude and timing. In a case study, findings were used to define the regional natural range of hydrologic variation and applied into a watershed assessment tool evaluating the potential changes to streamflow regimes as a result of forest disturbance. This analysis showed that because of hydrologic variability among regions, spatial variation in sensitivity to harvest likely exists within the forested landbase, highlighting the need for development of regional criteria and indicators for sustainable management of water resources. / Forest Biology and Management

Secondary salinisation has affected large areas of inland southwestern Australia, and in particular, low lying aquatic areas; causing the loss of freshwater submerged macrophyte communities and their replacement by salt-tolerant species. At high salinities, the salt-tolerant macrophyte-dominated ecological regime may be replaced by a regime dominated by benthic microbial communities, further reducing the structural and functional diversity of salinised wetland ecosystems. There is little prospect of restoring salinised systems to a freshwater state, meaning that saline macrophyte dominated wetlands have a heightened structural and functional importance in this landscape. Prior to this study, little was known about the drivers for change from one ecological regime to another in salinising wetlands or about rates of ecosystem response to these drivers. This study used experimental and observational data from seven saline wetlands in order to identify some of the potential mechanisms for the transition between the salt tolerant submerged macrophyte-dominated regime and the benthic microbial community-dominated regime. The applicability of existing conceptual models for ecological regime shifts was then tested against these data. Some of the mechanisms responsible for the formation and maintenance of the macrophyte-dominated regime were explored by examining the effects of salinity on germination and flowering in a series of salt-tolerant submerged macrophytes. The initiation and dominance of benthic microbial communities over a range of salinity and wetting regimes was also examined. The results suggested that macrophyte communities are unlikely to develop in seasonally-drying wetlands at high salinities (>45 ppt), but will usually germinate and establish well at lower salinities. It was also predicted that although benthic microbial communities can survive and grow across a wide range of salinities, they are likely to be outcompeted at low salinities by macrophytes or by phytoplankton blooms if water column nutrient levels are high. However, water permanence may facilitate benthic microbial community dominance. Existing conceptual models of ecological regime transitions, such as the alternative regimes model, did not account for the effect of water regime on the dynamics of seasonally-drying systems. Therefore, a new conceptual model incorporating the interaction between hydrology and salinity in seasonally-drying wetlands was proposed.

Thesis (Ph. D.)--Duke University, 2007.

Thesis (M.A.)--State University of New York at Binghamton, Department of Political Science, 2009. / Includes bibliographical references (leaves 43-44).

Diss.