We utilise several asset pricing models that allow for discontinuities in the returns and volatility time series in order to obtain estimates of Value-at-Risk (VaR). The first class of model that we use mixes a continuous diffusion process with discrete jumps at random points in time (Poisson Jump Diffusion Model). We also apply a purely discontinuous model that does not contain any continuous component at all in the underlying distribution (Variance Gamma Model). These models have been shown to have some success in capturing certain characteristics of return distributions, a few being leptokurtosis and skewness. Calibrating these models onto the returns of an index of Australian stocks (All Ordinaries Index), we then use the resulting parameters to obtain daily estimates of VaR. In order to obtain the VaR estimates for the Poisson Jump Diffusion Model and the Variance Gamma Model, we introduce the use of an innovation from option pricing techniques, which concentrates on the more tractable characteristic functions of the models. Having then obtained a series of VaR estimates, we then apply a variety of criteria to assess how each model performs and also evaluate these models against the traditional approaches to calculating VaR, such as that suggested by J.P. Morgan???s RiskMetrics. Our results show that whilst the Poisson Jump Diffusion model proved the most accurate at the 95% VaR level, neither the Poisson Jump Diffusion or Variance Gamma models were dominant in the other performance criteria examined. Overall, no model was clearly superior according to all the performance criteria analysed, and it seems that the extra computational time required to calibrate the Poisson Jump Diffusion and Variance Gamma models for the purposes of VaR estimation do not provide sufficient reward for the additional effort than that currently employed by Riskmetrics.

In this dissertation we develop and analyze numerical method to solve general elliptic boundary value problems with many scales. The numerical method presented is intended to capture the small scales effect on the large scale solution without resolving the small scale details, which is done through the construction of a multiscale map. The multiscale method is more effective when the coarse element size is larger than the small scale length. To guarantee a numerical conservation, a finite volume element method is used to construct the global problem. Analysis of the multiscale method is separately done for cases of linear and nonlinear coefficients. For linear coefficients, the multiscale finite volume element method is viewed as a perturbation of multiscale finite element method. The analysis uses substantially the existing finite element results and techniques. The multiscale method for nonlinear coefficients will be analyzed in the finite element sense. A class of correctors corresponding to the multiscale method will be discussed. In turn, the analysis will rely on approximation properties of this correctors. Several numerical experiments verifying the theoretical results will be given. Finally we will present several applications of the multiscale method in the flow in porous media. Problems that we will consider are multiphase immiscible flow, multicomponent miscible flow, and soil infiltration in saturated/unsaturated flow.

The influence of turbulence on the orientation state of a dilute suspension of stiff fibers at high Reynolds number in a planar contraction is investigated. High speed imaging and LDV techniques are used to quantify fiber orientation distribution and turbulent characteristics. A nearly homogenous, isotropic grid generated turbulent flow is introduced at the contraction inlet. Flow Reynolds number and inlet turbulent characteristics are varied in order to determine their effects on orientation distribution. The orientation anisotropy is shown to be accurately modelled by a Fokker-Planck type equation. Results show that rotational diffusion is highly influenced by inlet turbulent characteristics and decays exponentially with convergence ratio. Furthermore, the effect of turbulent energy production in the contraction is shown to be negligible. Also, the results show that the flow Reynolds number has negligible effect on the development of orientation anisotropy, and the influence of turbulence on fiber rotation is negligible for $mathrm{Pe_r}>$ 10. It was concluded that inertia induced fiber motion played a negligible role in the experiments.

High-frequency financial data are not only discretely sampled in time but the time separating successive observations is often random. We review the paper of Aït-Sahalia and Mykland (2003), that measure the effects of discreteness sampling and ignoring the randomness of the sampling for estimating the m.l.e of a continuous-time diffusion model. In that article, three different assumptions and restrict in one made on the sampling intervals, and the corresponding likelihood function, asymptotic normality, and covariance matrix are obtained. It is concluded that the effects due to discretely sampling are smaller than the effect of simply ignoring the sampling randomness. This study focuses on rechecking the results in the paper of A¡Lıt-Sahalia and Mykland (2003) including theory, simulation and application. We derive a different likelihood function expression from A¡Lıt-Sahalia and Mykland (2003)¡¦s result. However, the asymptotic covariance are consistent for both approaching in the O-U process. Furthermore, we conduct an empirical study on the high frequency transaction time data by using non-homogeneous Poisson Processes.

This dissertation investigates the volatility of the relationships between exchange rates and interest rates. The first part of the paper explores the transmission relationship between these two markets using a time-series model. Previous studies have assumed that covariance was constant in both markets. However, if the volatilities of the exchange rate and interest rate markets are correlated over time, the interaction and spillover effects between the two markets may be affected by time-varying covariance. Hence, this paper utilizes the BEKK-GARCH model developed by Engle and Kroner (1995) to capture the dynamic relationship between the exchange rates and interest rates. This study uses the returns data for G7 members¡¦ exchange rates and interest rates to test whether these markets exhibited volatilities spillover from 1978 to 2009. The results show bi-directional volatility spillovers in the markets of the UK, the Euro countries, and Canada, where the volatilities of the two markets were interrelated. The second part of the paper explores the relationship between exchange rates and interest rates using a jump diffusion model. Previous studies assumed that the dynamic processes of exchange rates and interest rates follow a diffusion process with a continuous time path, but an increasing number of empirical studies have shown that a continuous diffusion stochastic model does not capture the dynamic process of these variables. Thus, this paper investigates the discontinuous variables of exchange rates and interest rates and assumes that these variables follow a jump diffusion process. The UIRP model is employed to explore the relationship between both variables and to divide the systematic risk into systematic continuous risk and systematic jump risk. The returns data for G7 members¡¦ exchange rates and interest rates from 2005 to 2010 were analyzed to test whether the expected exchange rate is affected by jump components when the interest rate market experiences a jump. The results show that the jump diffusion model has more explanatory power than the pure diffusion model does, and, when the interest rate market experiences a jump risk, the systematic jump risk has a significant relationship with the expected exchange rates in some G7 countries.

In this study, we use the McKean's integral equation to evaluate the American option price for constant jump di

The study aims to explore some antecedents to products usage and its consequences in which a series of process of experiential evaluation is involved to center on the role of customer¡¦s experiential value after using personal computer. The conceptual model in this study is to extend the Use-Diffusion Model proposed by Shih and Venkatesh (2004) by including the framework of customer value based on Holbrook (1994). The survey method was employed in this study in which questionnaire was for data collection. The total sample size of 1114 was used in statistical analysis. According to the analytical results, we not only confirm the relationships suggested in the Use-Diffusion literature but also find the mediating effect of customer experiential value. That is, the evaluation of after-use experience leads to customer experiential value that in turn affects partially the customer intention of the sequential adoption of new technology. Besides contributing to the field of consumer research, the research findings in this study may provide insightful information that, we believe, helps managers to understand their incumbent customers.

In this dissertation we develop and analyze numerical method to solve general elliptic boundary value problems with many scales. The numerical method presented is intended to capture the small scales effect on the large scale solution without resolving the small scale details, which is done through the construction of a multiscale map. The multiscale method is more effective when the coarse element size is larger than the small scale length. To guarantee a numerical conservation, a finite volume element method is used to construct the global problem. Analysis of the multiscale method is separately done for cases of linear and nonlinear coefficients. For linear coefficients, the multiscale finite volume element method is viewed as a perturbation of multiscale finite element method. The analysis uses substantially the existing finite element results and techniques. The multiscale method for nonlinear coefficients will be analyzed in the finite element sense. A class of correctors corresponding to the multiscale method will be discussed. In turn, the analysis will rely on approximation properties of this correctors. Several numerical experiments verifying the theoretical results will be given. Finally we will present several applications of the multiscale method in the flow in porous media. Problems that we will consider are multiphase immiscible flow, multicomponent miscible flow, and soil infiltration in saturated/unsaturated flow.

Most of the derivative pricing models are developed in the jump diffusion models, and many literatures assume those jumps are diversifiable. However, we find many risk cannot be avoided through diversification. In this paper, we extend the Jarrow and Yildirim model to consider the existence of systematic jump risk in nominal interest rate, real interest rate and inflation rate to derive the no-arbitrage condition by using Esscher transformation. In addition, this study also derives the value of TIPS and TIPS European call option. Furthermore, we use the econometric theory to decompose TIPS market price volatility into a continuous component and a jump component. We find the jump component contribute most of the TIPS market price volatility. In addition, we also use the TIPS yield index to obtain the systematic jump component and systematic continuous component to find the systematic jump beta and the systematic continuous beta. The results show that the TIPS with shorter time to maturity are more vulnerable to systematic jump risk. In contrast, the individual TIPS with shorter time to maturity is more vulnerable to systematic jump. Finally, the sensitive analysis is conducted to detect the impacts of jumps risk on the value of TIPS European call option.

Solar photovoltaics have received government support in the form of rebates, tax credits and net metering tariff mechanisms. The intended goal of these incentives is to encourage innovation in the manufacturing and installation of these systems, which is expected to eventually help overcome the high cost barrier for the adoption of the technology. These systems have the advantages of abundant availability of the solar resource, low environmental footprint, and the possibility of onsite installation, reducing the need for additional generation and transmission capacity. Since millions of dollars have been invested in these incentive programs, there is an interest in tracking the progress in the cost and capacity installed. In the first part of this thesis, I analyzed the trends in costs and adoption of solar PV by residential and commercial customers in the city of Austin. This is accomplished by tabular and graphical analysis of data on PV installations from 2004, when Austin Energy’s rebate program started, to early 2010. In the second part of the thesis, I used technology diffusion models to analyze and forecast the diffusion of residential PV systems in Austin. Three types of models were used to model the adoption trends: Logistic growth model, Bass model without price effects and Bass model including price effects. In the final part of the thesis, I analyzed the net metering tariff mechanism in Austin and studied the difference between the current and an alternative tariff. The alternative tariff uses actual ‘grid usage’ to calculate the energy charge (cost of providing distribution service) instead of the ‘net energy consumed’ that is currently in use. Using simulated PV generation data and ERCOT load profile data, I calculated the difference in revenue for Austin Energy with the alternative tariff. The results indicate that the alternative tariff adds little revenue to Austin Energy’s energy charge revenues at the current level of penetration of solar PV. However, at a higher penetration level of PV, the alternative tariffs might result in significant additional revenue for the utility. The thesis concludes with a discussion on the possible rationale for the alternative tariff and directions for future research. / text