Stochastic volatility

Given the importance of return volatility on a number of practical financial management decisions, the efforts to provide good real- time estimates and forecasts of current and future volatility have been extensive. The main framework used in this context involves stochastic volatility models. In a broad sense, this model class includes GARCH, but we focus on a narrower set of specifications in which volatility follows its own random process, as is common in models originating within financial economics. The distinguishing feature of these specifications is that volatility, being inherently unobservable and subject to independent random shocks, is not measurable with respect to observable information. In what follows, we refer to these models as genuine stochastic volatility models. Much modern asset pricing theory is built on continuous- time models. The natural concept of volatility within this setting is that of genuine stochastic volatility. For example, stochastic-volatility (jump-) diffusions have provided a useful tool for a wide range of applications, including the pricing of options and other derivatives, the modeling of the term structure of risk-free interest rates, and the pricing of foreign currencies and defaultable bonds. The increased use of intraday transaction data for construction of so-called realized volatility measures provides additional impetus for considering genuine stochastic volatility models. As we demonstrate below, the realized volatility approach is closely associated with the continuous-time stochastic volatility framework of financial economics. There are some unique challenges in dealing with genuine stochastic volatility models. For example, volatility is truly latent and this feature complicates estimation and inference. Further, the presence of an additional state variable - volatility - renders the model less tractable from an analytic perspective. We examine how such challenges have been addressed through development of new estimation methods and imposition of model restrictions allowing for closed-form solutions while remaining consistent with the dominant empirical features of the data.Stochastic analysis

Parametric Soil-Structure Modeling for Rapid Climatic Disaster Response

Title from PDF of title page, viewed on July 15, 2015Thesis advisor: ZhiQiang ChenVitaIncludes bibliographic references (pages 124-128)Thesis (M.S.)--School of Computing and Engineering. University of Missouri--Kansas City, 2014Global climate changes have seemly caused acerbating impacts on coastal environments in terms of severe meteorological hazards, such as hurricanes and their induced storm surges, flooding, and heavy precipitation. Recent disasters of these types, such as HurricaneSandy, have afflicted millions in coastal communities and resulted in billion dollars of losses. Given disasters at such scales, field-based reconnaissance has become ever demanding than before. In the context of structural and geotechnical damage inspection, it calls for efficient tools that can analyze coastal structures that take a system modeling approach. Such a system approach should consider structuresthat are subjected to a combination of extreme forces and changes of boundary conditions, which may include hydrodynamic wave effects, hydraulic buoyancy, debris impact, and foundation scour. The objective of this thesis to develop a rapid tool for assessing the vulnerability of coastal structures subjected to climatic impacts. Similar tools have been widely used in Structural and Earthquake Engineering for design and loss assessment, such as the use of a fixed oscillator model characterized by a single parameter of Tn (the natural period of the structure). The direct hazardous impacts considered in this thesis are extreme hydraulic forces and local foundation scouring that may ultimately cause failure of coastal structures (i.e. collapse). The criteria of success of this tool emphasize that it should be as simple as the oscillator model in Earthquake Engineering and is parametric in terms of a few key (intrinsic) parameters to model the nonlinear behavior of a structure subjected to hydraulic storm surges and foundations scour. To precede, two research components are conducted. The first is a hypothesis-driven physical modeling experiment, in which a flume-based modeling is conducted to prove that storm surges can attack a structure by simultaneous surging and scouring. In the hydraulic flume, a generic foundation-structure system is placed and is subjected to forced vibration for probing the dynamic properties of the structure model. Test result successfully revealed the formation of foundation scour, the failure of structure, and the progressively modified dynamic characteristics of the soil-structure system. The second, based on the above flume-based evidence, is to computationally model such the failure of building systems in a reduced order subjected to the combined hazards of storm surges and foundation scour. In this thesis, Ibuild afinite-element (FE) based model using Abaqus software. In this model, the structural system response has been resolved from prototype models to simplified dimensionless model consisting of a single degree of freedom (SDOF) oscillator founded on a square foundation. The footing is embedded in near-field soil modeled using inelastic soil under an undrained condition. The two primary intrinsic parameters identified in this thesis. The first is theratio of the vertical foundation load N in comparison with the ultimate vertical capacity Nu, expressed through the ratio χ = N/Nu. The second is defined as ao = ω H / vswhere ω is the circular frequency of the fixed base structure, H is the height of superstructure and vs is the shear wave velocity. Rocking response of the (SDOF) system on nonlinear soil is examined through the general-purpose finite element software Abaqus to perform the parametric analysis, and to establish the failure mechanism of the system. Lightly loaded oscillators tend to uplift from the supporting soil whereas heavily loaded oscillators tend to accumulate settlement and soil yielding is intense. The structural response corresponding to moment-rotation settlement under monotonic loading at the mass center, under loading has been designed to output. The Python-based Abaqus scripting interface is used to realize a client-based model input, which is an extension of the Python object-oriented programming language.Impact of climate on changes in civil infrastructure -- Literature review -- Physical modeling methodology and system identification -- Soil material modeling and verification -- Parametric soil-structure modeling using Abaqus CAE -- Conclusions and future work -- Appendix A. -- Appendix

Smart Classifiers and Bayesian Inference for Evaluating River Sensitivity to Natural and Human Disturbances: A Data Science Approach

Excessive rates of channel adjustment and riverine sediment export represent societal challenges; impacts include: degraded water quality and ecological integrity, erosion hazards to infrastructure, and compromised public safety. The nonlinear nature of sediment erosion and deposition within a watershed and the variable patterns in riverine sediment export over a defined timeframe of interest are governed by many interrelated factors, including geology, climate and hydrology, vegetation, and land use. Human disturbances to the landscape and river networks have further altered these patterns of water and sediment routing. An enhanced understanding of river sediment sources and dynamics is important for stakeholders, and will become more critical under a nonstationary climate, as sediment yields are expected to increase in regions of the world that will experience increased frequency, persistence, and intensity of storm events. Practical tools are needed to predict sediment erosion, transport and deposition and to characterize sediment sources within a reasonable measure of uncertainty. Water resource scientists and engineers use multidimensional data sets of varying types and quality to answer management-related questions, and the temporal and spatial resolution of these data are growing exponentially with the advent of automated samplers and in situ sensors (i.e., “big data”). Data-driven statistics and classifiers have great utility for representing system complexity and can often be more readily implemented in an adaptive management context than process-based models. Parametric statistics are often of limited efficacy when applied to data of varying quality, mixed types (continuous, ordinal, nominal), censored or sparse data, or when model residuals do not conform to Gaussian distributions. Data-driven machine-learning algorithms and Bayesian statistics have advantages over Frequentist approaches for data reduction and visualization; they allow for non-normal distribution of residuals and greater robustness to outliers. This research applied machine-learning classifiers and Bayesian statistical techniques to multidimensional data sets to characterize sediment source and flux at basin, catchment, and reach scales. These data-driven tools enabled better understanding of: (1) basin-scale spatial variability in concentration-discharge patterns of instream suspended sediment and nutrients; (2) catchment-scale sourcing of suspended sediments; and (3) reach-scale sediment process domains. The developed tools have broad management application and provide insights into landscape drivers of channel dynamics and riverine solute and sediment export

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Hot flow anomalies at earth's bow shock and their magnetospheric-ionospheric signatures

Thesis (Ph.D.) University of Alaska Fairbanks, 2017Hot flow anomalies (HFAs) are typically observed upstream of bow shocks. They are characterized by a significant increase in particle temperature and substantial flow deflection from the solar wind flow direction coinciding with a decrease in density. HFAs are important to study and understand because they may play an important role in solar wind-magnetosphere coupling. They may drive magnetopause motion, boundary waves, and flux transfer events. They can excite ultra low frequency waves in the magnetosphere, drive magnetic impulse events in the ionosphere, and trigger aurora brightening or dimming. Studying HFAs will aid in the understanding of fundamental processes that operate throughout the heliosphere such as particle energization and shocks. This dissertation presents statistical and case studies of hot flow anomalies identified in Time History of Events and Macroscale Interactions During Substorms (THEMIS) satellite data from 2007-2009. The characteristics and occurrence of HFAs, their dependence on solar wind/interplanetary magnetic field (IMF) conditions and location, and their magnetospheric-ionospheric signatures, have been investigated using in-situ spacecraft observations and ground based observations. THEMIS observations show that HFAs span a wide range of magnetic local times (MLTs) from approximately 7 to 16.5 MLT. HFAs were observed up to 6.3 Earth radii (RE) upstream from the bow shock. It has been found that the HFA occurrence rate depends on solar wind and interplanetary magnetic field (IMF) conditions as well as distance from the bow shock. HFA occurrence decreases with distance upstream from the bow shock. HFAs are more prevalent when there is an approximately radial interplanetary magnetic field. No HFAs were observed when the Mach number was less than 5, suggesting there is a minimum threshold Mach number for HFAs to form. HFAs occur most preferentially for solar wind speeds from 550-600 km/s. Multiple THEMIS spacecraft observations of the same HFA provide an excellent opportunity to perform a spatial and temporal analysis of an HFA. The leading edge, tangential discontinuity inside the HFA, and trailing shock boundaries for the event were identified. The boundaries' orientations and motion through space were characterized. The HFA expansion against the solar wind was 283 km/s. The spatial structure of the HFA was deduced from multiple spacecraft observations. The HFA is thicker closer to the bow shock. The magnetospheric-ionospheric signatures of an HFA have been investigated using in-situ spacecraft observations and ground based observations. Magnetic field perturbations were observed by three GOES spacecraft at geostationary orbit and high-latitude ground magnetometers in both hemispheres. Observations from magnetometers located at different MLTs showed that the perturbation propagates tailward at 0.32°/s or 9 km/s (1.27°/s or 21 km/s) for the northern (southern) hemisphere, which is consistent with an HFA propagating tailward along the dawn flank. SuperDARN radar observations showed a change in plasma velocity shortly after the HFA was observed by THEMIS

Volatility forecasting

Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1