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 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 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 Portfolio Credit Risk written by Guillermo Navas Palencia and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this thesis is the study of portfolio credit risk models and the numerical methods applied for their computation. The Vasicek one-factor model will provide a point of departure, allowing us to study its generalization and the development of a numerical method for its computation. Subsequently, we present the large portfolio approximation and its generalization. These methodologies and especially their generalizations will require the use of advanced numerical methods whose implementation will be explained in detail. Furthermore, we include other more sophisticated methodologies, such as the Fourier transform method or the Haar wavelet approximation, which consider portfolios with exposure concentrations and loss given default. A detailed study of their respective implementations will be presented for both methodologies. Finally, we present a comparative study of methods in order to identify the most appropriate method for each type of portfolio.

Download or read book A Fast Wavelet Expansion Technique for Evaluation of Portfolio Credit Risk Under the Vasicek Multi Factor Model written by Kensuke Ishitani and published by . This book was released on 2014 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a new methodology to compute value at risk (VaR) and the marginal VaR contribution (VaRC) in the Vasicek multi-factor model of portfolio credit loss. The wavelet approximation method can be useful to compute non-smooth distributions, often arising in small or concentrated portfolios. This paper contributes to this technique by extending the wavelet approximation method for the Vasicek one-factor model to the multi-factor model. Key features of the new algorithm presented in this paper are (i) a finite series expansion of the wavelet scaling coefficients, (ii) fast calculation methods to accelerate convergence of those series and (iii) an efficient spline interpolation method to calculate the Laplace transforms. This paper also illustrates the effectiveness of the algorithm through numerical examples.

Download or read book Quantifying Credit Portfolio Losses Under Multi Factor Models written by Gemma Colldeforns-Papiol and published by . This book was released on 2017 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, we investigate the challenging problem of estimating credit risk measures of portfolios with exposure concentration under the multi-factor Gaussian and multi-factor t-copula models. It is well-known that Monte Carlo (MC) methods are highly demanding from the computational point of view in the aforementioned situations. We present efficient and robust numerical techniques based on the Haar wavelets theory for recovering the cumulative distribution function (CDF) of the loss variable from its characteristic function. To the best of our knowledge, this is the first time that multi-factor t-copula models are considered outside the MC framework. The analysis of the approximation error and the results obtained in the numerical experiments section show a reliable and useful machinery for credit risk capital measurement purposes in line with Pillar II of the Basel Accords.

Download or read book Introduction To Wavelet Theory In Finance An A Wavelet Multiscale Approach written by Francis Haeuck In and published by World Scientific. This book was released on 2012-09-28 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to wavelet theory and provides the essence of wavelet analysis — including Fourier analysis and spectral analysis; the maximum overlap discrete wavelet transform; wavelet variance, covariance, and correlation — in a unified and friendly manner. It aims to bridge the gap between theory and practice by presenting substantial applications of wavelets in economics and finance.This book is the first to provide a comprehensive application of wavelet analysis to financial markets, covering new frontier issues in empirical finance and economics. The first chapter of this unique text starts with a description of the key features and applications of wavelets. After an overview of wavelet analysis, successive chapters rigorously examine the various economic and financial topics and issues that stimulate academic and professional research, including equity, interest swaps, hedges and futures, foreign exchanges, financial asset pricing, and mutual fund markets.This detail-oriented text is descriptive and designed purely for academic researchers and financial practitioners. It assumes no prior knowledge of econometrics and covers important topics such as portfolio asset allocation, asset pricing, hedging strategies, new risk measures, and mutual fund performance. Its accessible presentation is also suitable for post-graduates in a variety of disciplines — applied economics, financial engineering, international finance, financial econometrics, and fund management. To facilitate the subject of wavelets, sophisticated proofs and mathematics are avoided as much as possible when applying the wavelet multiscaling method. To enhance the reader's understanding in practical applications of the wavelet multiscaling method, this book provides sample programming instruction backed by Matlab wavelet code.

Download or read book Entropy Based Models of Portfolio Credit Risk written by Seung Won Yang and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Modeling and Calibration Errors in Measures of Portfolio Credit Risk written by Nikola A. Tarashev and published by . This book was released on 2013 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops an empirical procedure for analyzing the impact of model misspecification and calibration errors on measures of portfolio credit risk. When applied to large simulated portfolios with realistic characteristics, this procedure reveals that violations of key assumptions of the well-known Asymptotic Single-Risk Factor (ASRF) model are virtually inconsequential. By contrast, flaws in the calibrated inter-dependence of credit risk across exposures, which are driven by plausible small-sample estimation errors or popular rule-of-thumb values of asset return correlations, can lead to significant inaccuracies in measures of portfolio credit risk. Similar inaccuracies arise under erroneous, albeit standard, assumptions regarding the tails of the distribution of asset returns.

Download or read book Journal of analysis and its applications written by and published by . This book was released on 2008 with total page 540 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 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 Modelling Financial Time Series written by Stephen J. Taylor and published by World Scientific. This book was released on 2008 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains several innovative models for the prices of financial assets. First published in 1986, it is a classic text in the area of financial econometrics. It presents ARCH and stochastic volatility models that are often used and cited in academic research and are applied by quantitative analysts in many banks. Another often-cited contribution of the first edition is the documentation of statistical characteristics of financial returns, which are referred to as stylized facts. This second edition takes into account the remarkable progress made by empirical researchers during the past two decades from 1986 to 2006. In the new Preface, the author summarizes this progress in two key areas: firstly, measuring, modelling and forecasting volatility; and secondly, detecting and exploiting price trends. Sample Chapter(s). Chapter 1: Introduction (1,134 KB). Contents: Features of Financial Returns; Modelling Price Volatility; Forecasting Standard Deviations; The Accuracy of Autocorrelation Estimates; Testing the Random Walk Hypothesis; Forecasting Trends in Prices; Evidence Against the Efficiency of Futures Markets; Valuing Options; Appendix: A Computer Program for Modelling Financial Time Series. Readership: Academic researchers in finance & economics; quantitative analysts.

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 Empirical Asset Pricing written by Wayne Ferson and published by MIT Press. This book was released on 2019-03-12 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory and methods of empirical asset pricing, integrating classical foundations with recent developments. This book offers a comprehensive advanced introduction to asset pricing, the study of models for the prices and returns of various securities. The focus is empirical, emphasizing how the models relate to the data. The book offers a uniquely integrated treatment, combining classical foundations with more recent developments in the literature and relating some of the material to applications in investment management. It covers the theory of empirical asset pricing, the main empirical methods, and a range of applied topics. The book introduces the theory of empirical asset pricing through three main paradigms: mean variance analysis, stochastic discount factors, and beta pricing models. It describes empirical methods, beginning with the generalized method of moments (GMM) and viewing other methods as special cases of GMM; offers a comprehensive review of fund performance evaluation; and presents selected applied topics, including a substantial chapter on predictability in asset markets that covers predicting the level of returns, volatility and higher moments, and predicting cross-sectional differences in returns. Other chapters cover production-based asset pricing, long-run risk models, the Campbell-Shiller approximation, the debate on covariance versus characteristics, and the relation of volatility to the cross-section of stock returns. An extensive reference section captures the current state of the field. The book is intended for use by graduate students in finance and economics; it can also serve as a reference for professionals.