This paper presents a modified version of Leland and Toft's (1996) structural credit risk model, together with a novel calibration methodology based on stock and CDS data: the firm asset value and volatility are consistently derived from equity prices; the default barrier is calibrated from CDS premia. It empirically shows that as long as the appropriate default barrier is selected, the model generates time series of stock market implied credit spreads which fit the times series of CDS spreads. Moreover, CDS implied default barriers prove to be consistent with stockholders' rationality, with predictions made by structural models with endogenous default, and with historical recovery rates.
This three-part book provides a comprehensive and systematic introduction to these challenging topics such as model calibration, parameter estimation, reliability assessment, and data collection design. Part 1 covers the classical inverse problem for parameter estimation in both deterministic and statistical frameworks, Part 2 is dedicated to system identification, hyperparameter estimation, and model dimension reduction, and Part 3 considers how to collect data and construct reliable models for prediction and decision-making. For the first time, topics such as multiscale inversion, stochastic field parameterization, level set method, machine learning, global sensitivity analysis, data assimilation, model uncertainty quantification, robust design, and goal-oriented modeling, are systematically described and summarized in a single book from the perspective of model inversion, and elucidated with numerical examples from environmental and water resources modeling. Readers of this book will not only learn basic concepts and methods for simple parameter estimation, but also get familiar with advanced methods for modeling complex systems. Algorithms for mathematical tools used in this book, such as numerical optimization, automatic differentiation, adaptive parameterization, hierarchical Bayesian, metamodeling, Markov chain Monte Carlo, are covered in details. This book can be used as a reference for graduate and upper level undergraduate students majoring in environmental engineering, hydrology, and geosciences. It also serves as an essential reference book for professionals such as petroleum engineers, mining engineers, chemists, mechanical engineers, biologists, biology and medical engineering, applied mathematicians, and others who perform mathematical modeling.
TRB’s National Cooperative Highway Research Program (NCHRP) Report 719: Calibration of Rutting Models for Structural and Mix Design highlights proposed revisions to the Mechanistic–Empirical Pavement Design Guide (MEPDG) and software to incorporate three alternative rut-depth prediction models that rely on repeated load (triaxial) permanent deformation or constant height testing to provide the requisite input data.
A new methodology for calibrating parameters when working with intractable, dynamic structural models is developed. A straight-forward extension also allows for formal estimation and hypothesis testing in a Generalized Method of Moment framework. The method is based on multigrid techniques used in many state of the art solvers from engineering applications. These techniques are adapted to solve Bellman and Euler-type equations and to handle subtleties arising from the interaction of statistical and numerical errors. The method works on a joint mode of analysis incorporating both statistical and numerical errors in the spirit of quot;forward-backwardquot; error analysis of Kubler and Schmedders (2005). Numerical results from example problems - and experience from thirty years of multigrid literature - support the papers main finding: a fully-identified model that is smooth in parameters can be calibrated and solved with only about three to five times the work required to solve the model and compute associated quot;momentsquot; for a single set of parameters. As with other multigrid methods, the solvers can be efficiently and naturally implemented on parallel processors. This work also shows that the size of numerical error can be less important than the qualitative type of error when parameters are fitted to a numerically solved model subject to discretization error. An example is presented in which a popular, consistent discretization of a portfolio problem with endogenous retirement produces an ill-posed, unstable calibration problem. This example and subsequent analysis show greater care must be taken when discretizing a model for a calibration or estimation problem: To avoid corrupting sensitivity analysis, identification, and inference, it is important to perform a joint error analysis that includes both discretization and statistical errors.
Published by the American Geophysical Union as part of the Water Science and Application Series, Volume 6. During the past four decades, computer-based mathematical models of watershed hydrology have been widely used for a variety of applications including hydrologic forecasting, hydrologic design, and water resources management. These models are based on general mathematical descriptions of the watershed processes that transform natural forcing (e.g., rainfall over the landscape) into response (e.g., runoff in the rivers). The user of a watershed hydrology model must specify the model parameters before the model is able to properly simulate the watershed behavior.
Achieving market consistency can be challenging, even for the most established finance practitioners. In Market Consistency: Model Calibration in Imperfect Markets, leading expert Malcolm Kemp shows readers how they can best incorporate market consistency across all disciplines. Building on the author's experience as a practitioner, writer and speaker on the topic, the book explores how risk management and related disciplines might develop as fair valuation principles become more entrenched in finance and regulatory practice. This is the only text that clearly illustrates how to calibrate risk, pricing and portfolio construction models to a market consistent level, carefully explaining in a logical sequence when and how market consistency should be used, what it means for different financial disciplines and how it can be achieved for both liquid and illiquid positions. It explains why market consistency is intrinsically difficult to achieve with certainty in some types of activities, including computation of hedging parameters, and provides solutions to even the most complex problems. The book also shows how to best mark-to-market illiquid assets and liabilities and to incorporate these valuations into solvency and other types of financial analysis; it indicates how to define and identify risk-free interest rates, even when the creditworthiness of governments is no longer undoubted; and it explores when practitioners should focus most on market consistency and when their clients or employers might have less desire for such an emphasis. Finally, the book analyses the intrinsic role of regulation and risk management within different parts of the financial services industry, identifying how and why market consistency is key to these topics, and highlights why ideal regulatory solvency approaches for long term investors like insurers and pension funds may not be the same as for other financial market participants such as banks and asset managers.
In this fast growing world, where technological advancements are influenced by more efficient and less expensive designs, there is a significant need of adopting methods and techniques that can support this thought process. To address this requirement, finite element (FE) modeling techniques were introduced as a viable solution. Specifically in case of mechanical structures, where prototype building and physical testing requires a lot of time and involves huge costs, developing an FE model that can predict its dynamic characteristics accurately is key to address the issue. However, with more reliance on FE models as a true representative of physical structures, there is a significant need to evaluate such models. This evaluation involves comparing the results obtained from simulating FE models with the results achieved from mathematical models and real world test data. In other words, such models need to undergo "verification" and "validation" before they can be used to predict reliable results for the future. In this research, a model verification, calibration, and validation case study is performed on a rectangular steel plate structure. The case study was based on a systematic approach that was used in an attempt to follow the guidelines for verification and validation (V\ & V) published recently by the American Society of Mechanical Engineers (ASME) and the American Institute of Aeronautics and Astronautics (AIAA). The accuracy of the model and the validation process was confirmed by modal correlation when the structure and the calibrated model were subjected to perturbed mass and constrained boundary conditions. The validation criteria were achieved using the calibrated model and the results obtained through validation criterion helped quantify the accuracy of the developed model under different boundary conditions.
