Download or read book Haar Wavelets Based Approach for Quantifying Credit Portfolio Losses written by Josep Masdemont and published by . This book was released on 2013 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelet basis functions and calculate the coefficients of the approximation by inverting its Laplace transform. The Wavelet Approximation (WA) method is particularly suitable for non-smooth distributions, often arising in small or concentrated portfolios, when the hypothesis of the Basel II formulas are violated. To test the methodology we consider the Vasicek one-factor portfolio credit loss model as our model framework. WA is an accurate, robust and fast method, allowing to estimate VaR much more quickly than with a Monte Carlo (MC) method at the same level of accuracy and reliability.
Download or read book Haar Wavelets based Methods for Credit Risk Portfolio Modeling written by Luis Ortiz Gracia and published by . This book was released on 2014 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation we have investigated the credit risk measurement of a credit portfolio by means of the wavelets theory. Banks became subject to regulatory capital requirements under Basel Accords and also to the supervisory review process of capital adequacy, this is the economic capital. Concentration risks in credit portfolios arise from an unequal distribution of loans to single borrowers (name concentration) or different industry or regional sectors (sector concentration) and may lead banks to face bankruptcy. The Merton model is the basis of the Basel II approach, it is a Gaussian one-factor model such that default events are driven by a latent common factor that is assumed to follow the Gaussian distribution. Under this model, loss only occurs when an obligor defaults in a fixed time horizon. If we assume certain homogeneity conditions, this one-factor model leads to a simple analytical asymptotic approximation of the loss distribution function and VaR. The VaR value at a high confidence level is the measure chosen in Basel II to calculate regulatory capital. This approximation, usually called Asymptotic Single Risk Factor model (ASRF), works well for a large number of small exposures but can underestimates risks in the presence of exposure concentrations. Then, the ASRF model does not provide an appropriate quantitative framework for the computation of economic capital. Monte Carlo simulation is a standard method for measuring credit portfolio risk in order to deal with concentration risks. However, this method is very time consuming when the size of the portfolio increases, making the computation unworkable in many situations. In summary, credit risk managers are interested in how can concentration risk be quantified in short times and how can the contributions of individual transactions to the total risk be computed. Since the loss variable can take only a finite number of discrete values, the cumulative distribution function (CDF) is discontinuous and then the Haar wavelets are particularly well-suited for this stepped-shape functions. For this reason, we have developed a new method for numerically inverting the Laplace transform of the density function, once we have approximated the CDF by a finite sum of Haar wavelet basis functions. Wavelets are used in mathematical analysis to denote a kind of orthonormal basis with remarkable approximation properties. The difference between the usual sine wave and a wavelet may be described by the localization property, while the sine wave is localized in frequency domain but not in time domain, a wavelet is localized in both, frequency and time domain. Once the CDF has been computed, we are able to calculate the VaR at a high loss level. Furthermore, we have computed also the Expected Shortfall (ES), since VaR is not a coherent risk measure in the sense that it is not sub-additive. We have shown that, in a wide variety of portfolios, these measures are fast and accurately computed with a relative error lower than 1% when compared with Monte Carlo. We have also extended this methodology to the estimation of the risk contributions to the VaR and the ES, by taking partial derivatives with respect to the exposures, obtaining again high accuracy. Some technical improvements have also been implemented in the computation of the Gauss-Hermite integration formula in order to get the coefficients of the approximation, making the method faster while the accuracy remains. Finally, we have extended the wavelet approximation method to the multi-factor setting by means of Monte Carlo and quasi-Monte Carlo methods.
Download or read book Haar Wavelets based Methods for Credit Risk Portfolio Modeling written by Luis Ortiz Gracia and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Risk Analysis and Portfolio Modelling written by Elisa Luciano and published by MDPI. This book was released on 2019-10-16 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial Risk Measurement is a challenging task, because both the types of risk and the techniques evolve very quickly. This book collects a number of novel contributions to the measurement of financial risk, which address either non-fully explored risks or risk takers, and does so in a wide variety of empirical contexts.
Download or read book Wavelets written by Gordon Erlebacher and published by Oxford University Press. This book was released on 1996-01-04 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets are spatially localized functions whose amplitude drops off exponentially outside a small "window". They are used to magnify experimental or numerical data and have become powerful tools in signal processing and other computational sciences. This book gives scientists and engineers a practical understanding of wavelets--their origins, their purpose, their use, and their prospects. It covers the applications of wavelets as a diagnostic tool and the use of wavelet basis functions to solve differential equations. Each chapter was written by one of five lecturers of a course sponsored by the Institute of Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center. Not only does this book treat the latest advances on the subject, but it also attempts to impart practical knowledge to allow scientists and engineers to evaluate objectively where these tools stand in relation to their needs.
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Download or read book Concentration Risk in Credit Portfolios written by Eva Lütkebohmert and published by Springer Science & Business Media. This book was released on 2008-09-30 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and management of credit risk are the main topics within banks and other lending institutions. Historical experience shows that, in particular, concentration of risk in credit portfolios has been one of the major causes of bank distress. Therefore, concentration risk is highly relevant to anyone who wants to go beyond the very basic portfolio credit risk models. The book gives an introduction to credit risk modeling with the aim to measure concentration risks in credit portfolios. Taking the basic principles of credit risk in general as a starting point, several industry models are studied. These allow banks to compute a probability distribution of credit losses at the portfolio level. Besides these industry models the Internal Ratings Based model, on which Basel II is based, is treated. On the basis of these models various methods for the quantification of name and sector concentration risk and the treatment of default contagion are discussed. The book reflects current research in these areas from both an academic and a supervisory perspective
Download or read book Bayesian Networks written by Olivier Pourret and published by John Wiley & Sons. This book was released on 2008-04-30 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Networks, the result of the convergence of artificial intelligence with statistics, are growing in popularity. Their versatility and modelling power is now employed across a variety of fields for the purposes of analysis, simulation, prediction and diagnosis. This book provides a general introduction to Bayesian networks, defining and illustrating the basic concepts with pedagogical examples and twenty real-life case studies drawn from a range of fields including medicine, computing, natural sciences and engineering. Designed to help analysts, engineers, scientists and professionals taking part in complex decision processes to successfully implement Bayesian networks, this book equips readers with proven methods to generate, calibrate, evaluate and validate Bayesian networks. The book: Provides the tools to overcome common practical challenges such as the treatment of missing input data, interaction with experts and decision makers, determination of the optimal granularity and size of the model. Highlights the strengths of Bayesian networks whilst also presenting a discussion of their limitations. Compares Bayesian networks with other modelling techniques such as neural networks, fuzzy logic and fault trees. Describes, for ease of comparison, the main features of the major Bayesian network software packages: Netica, Hugin, Elvira and Discoverer, from the point of view of the user. Offers a historical perspective on the subject and analyses future directions for research. Written by leading experts with practical experience of applying Bayesian networks in finance, banking, medicine, robotics, civil engineering, geology, geography, genetics, forensic science, ecology, and industry, the book has much to offer both practitioners and researchers involved in statistical analysis or modelling in any of these fields.
Download or read book An Introduction to Wavelets and Other Filtering Methods in Finance and Economics written by Ramazan Gençay and published by Elsevier. This book was released on 2001-10-12 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Wavelets and Other Filtering Methods in Finance and Economics presents a unified view of filtering techniques with a special focus on wavelet analysis in finance and economics. It emphasizes the methods and explanations of the theory that underlies them. It also concentrates on exactly what wavelet analysis (and filtering methods in general) can reveal about a time series. It offers testing issues which can be performed with wavelets in conjunction with the multi-resolution analysis. The descriptive focus of the book avoids proofs and provides easy access to a wide spectrum of parametric and nonparametric filtering methods. Examples and empirical applications will show readers the capabilities, advantages, and disadvantages of each method. The first book to present a unified view of filtering techniques Concentrates on exactly what wavelets analysis and filtering methods in general can reveal about a time series Provides easy access to a wide spectrum of parametric and non-parametric filtering methods
Download or read book Nonparametric Econometric Methods and Application written by Thanasis Stengos and published by MDPI. This book was released on 2019-05-20 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present Special Issue collects a number of new contributions both at the theoretical level and in terms of applications in the areas of nonparametric and semiparametric econometric methods. In particular, this collection of papers that cover areas such as developments in local smoothing techniques, splines, series estimators, and wavelets will add to the existing rich literature on these subjects and enhance our ability to use data to test economic hypotheses in a variety of fields, such as financial economics, microeconomics, macroeconomics, labor economics, and economic growth, to name a few.
Download or read book Pattern Recognition and Machine Learning written by Christopher M. Bishop and published by Springer. This book was released on 2016-08-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are not feasible. It uses graphical models to describe probability distributions when no other books apply graphical models to machine learning. No previous knowledge of pattern recognition or machine learning concepts is assumed. Familiarity with multivariate calculus and basic linear algebra is required, and some experience in the use of probabilities would be helpful though not essential as the book includes a self-contained introduction to basic probability theory.
Download or read book How can I get started Investing in the Stock Market written by Lokesh Badolia and published by Educreation Publishing. This book was released on 2016-10-27 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is well-researched by the author, in which he has shared the experience and knowledge of some very much experienced and renowned entities from stock market. We want that everybody should have the knowledge regarding the different aspects of stock market, which would encourage people to invest and earn without any fear. This book is just a step forward toward the knowledge of market.
Download or read book Quantitative Finance written by Maria C. Mariani and published by John Wiley & Sons. This book was released on 2019-11-06 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a multitude of topics relevant to the quantitative finance community by combining the best of the theory with the usefulness of applications Written by accomplished teachers and researchers in the field, this book presents quantitative finance theory through applications to specific practical problems and comes with accompanying coding techniques in R and MATLAB, and some generic pseudo-algorithms to modern finance. It also offers over 300 examples and exercises that are appropriate for the beginning student as well as the practitioner in the field. The Quantitative Finance book is divided into four parts. Part One begins by providing readers with the theoretical backdrop needed from probability and stochastic processes. We also present some useful finance concepts used throughout the book. In part two of the book we present the classical Black-Scholes-Merton model in a uniquely accessible and understandable way. Implied volatility as well as local volatility surfaces are also discussed. Next, solutions to Partial Differential Equations (PDE), wavelets and Fourier transforms are presented. Several methodologies for pricing options namely, tree methods, finite difference method and Monte Carlo simulation methods are also discussed. We conclude this part with a discussion on stochastic differential equations (SDE’s). In the third part of this book, several new and advanced models from current literature such as general Lvy processes, nonlinear PDE's for stochastic volatility models in a transaction fee market, PDE's in a jump-diffusion with stochastic volatility models and factor and copulas models are discussed. In part four of the book, we conclude with a solid presentation of the typical topics in fixed income securities and derivatives. We discuss models for pricing bonds market, marketable securities, credit default swaps (CDS) and securitizations. Classroom-tested over a three-year period with the input of students and experienced practitioners Emphasizes the volatility of financial analyses and interpretations Weaves theory with application throughout the book Utilizes R and MATLAB software programs Presents pseudo-algorithms for readers who do not have access to any particular programming system Supplemented with extensive author-maintained web site that includes helpful teaching hints, data sets, software programs, and additional content Quantitative Finance is an ideal textbook for upper-undergraduate and beginning graduate students in statistics, financial engineering, quantitative finance, and mathematical finance programs. It will also appeal to practitioners in the same fields.
Download or read book Wavelet Theory written by David K. Ruch and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained, elementary introduction to wavelet theory and applications Exploring the growing relevance of wavelets in the field of mathematics, Wavelet Theory: An Elementary Approach with Applications provides an introduction to the topic, detailing the fundamental concepts and presenting its major impacts in the world beyond academia. Drawing on concepts from calculus and linear algebra, this book helps readers sharpen their mathematical proof writing and reading skills through interesting, real-world applications. The book begins with a brief introduction to the fundamentals of complex numbers and the space of square-integrable functions. Next, Fourier series and the Fourier transform are presented as tools for understanding wavelet analysis and the study of wavelets in the transform domain. Subsequent chapters provide a comprehensive treatment of various types of wavelets and their related concepts, such as Haar spaces, multiresolution analysis, Daubechies wavelets, and biorthogonal wavelets. In addition, the authors include two chapters that carefully detail the transition from wavelet theory to the discrete wavelet transformations. To illustrate the relevance of wavelet theory in the digital age, the book includes two in-depth sections on current applications: the FBI Wavelet Scalar Quantization Standard and image segmentation. In order to facilitate mastery of the content, the book features more than 400 exercises that range from theoretical to computational in nature and are structured in a multi-part format in order to assist readers with the correct proof or solution. These problems provide an opportunity for readers to further investigate various applications of wavelets. All problems are compatible with software packages and computer labs that are available on the book's related Web site, allowing readers to perform various imaging/audio tasks, explore computer wavelet transformations and their inverses, and visualize the applications discussed throughout the book. Requiring only a prerequisite knowledge of linear algebra and calculus, Wavelet Theory is an excellent book for courses in mathematics, engineering, and physics at the upper-undergraduate level. It is also a valuable resource for mathematicians, engineers, and scientists who wish to learn about wavelet theory on an elementary level.
Download or read book Advances in Soft Computing and Machine Learning in Image Processing written by Aboul Ella Hassanien and published by Springer. This book was released on 2017-10-13 with total page 711 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of the latest applications of methods from soft computing and machine learning in image processing. It explores different areas ranging from image segmentation to the object recognition using complex approaches, and includes the theory of the methodologies used to provide an overview of the application of these tools in image processing. The material has been compiled from a scientific perspective, and the book is primarily intended for undergraduate and postgraduate science, engineering, and computational mathematics students. It can also be used for courses on artificial intelligence, advanced image processing, and computational intelligence, and is a valuable resource for researchers in the evolutionary computation, artificial intelligence and image processing communities.
Download or read book Deep Learning written by Ian Goodfellow and published by MIT Press. This book was released on 2016-11-10 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to a broad range of topics in deep learning, covering mathematical and conceptual background, deep learning techniques used in industry, and research perspectives. “Written by three experts in the field, Deep Learning is the only comprehensive book on the subject.” —Elon Musk, cochair of OpenAI; cofounder and CEO of Tesla and SpaceX Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.
Download or read book A Wavelet Tour of Signal Processing written by Stephane Mallat and published by Elsevier. This book was released on 1999-09-14 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris. Provides a broad perspective on the principles and applications of transient signal processing with wavelets Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition Optical flow calculation and video compression algorithms Image models with bounded variation functions Bayes and Minimax theories for signal estimation 200 pages rewritten and most illustrations redrawn More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics
