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Book Asset Return Correlation and Non Normality

Download or read book Asset Return Correlation and Non Normality written by Michael Tschan and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The non-normal behaviour of stock returns of the S&P 500 index as well as of a vast majority of its components - as shown based on several statistical normality tests - entails the risk of shrinking Pearson correlation bounds. By means of maximum likelihood estimations (MLE), we identified a superior fit of the normal-inverse Gaussian (NIG) distribution compared to other distributions for most cases of univariate daily, weekly and monthly stock returns. Using the parameters for the marginal distributions estimated by MLE and applying Monte Carlo methods to model the Fréchet-Hoeffding bounds, we found in case of monthly - but not for daily - stock returns evidence for shrinking correlation intervals. In particular, a group of seven stocks indicated in a majority of simulations the anomaly of diminished attainable correlation ranges, caused by - a few - extreme historical return realisations. An analysis of the bivariate copulas using the Akaike information criterion (AIC) determined with the t-copula a representative of the elliptical copula family as the most appropriate instrument to describe the dependence structure between two stock returns. In 87% percent of the analysed stock combinations, the AIC affirms a better relative goodness of fit for this specific copula with MLE estimated parameters compared to 39 other copula families. Furthermore, two goodness of fit tests - albeit for a smaller subsample - provide evidence that assuming Gaussian copulas to describe the dependence structures between stock returns is much less problematic than the normality assumption for the marginal distributions. While we conclude that shrinking correlation bounds are of rather minor importance for stock returns, a simulation of distributions with higher skewness and kurtosis indicates the existence of this risk in other multivariate distributions, in particular in cases with marginal distributions which are only supported on semi-infinite in.

Book Fat Tailed and Skewed Asset Return Distributions

Download or read book Fat Tailed and Skewed Asset Return Distributions written by Svetlozar T. Rachev and published by John Wiley & Sons. This book was released on 2005-09-15 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: While mainstream financial theories and applications assume that asset returns are normally distributed, overwhelming empirical evidence shows otherwise. Yet many professionals don’t appreciate the highly statistical models that take this empirical evidence into consideration. Fat-Tailed and Skewed Asset Return Distributions examines this dilemma and offers readers a less technical look at how portfolio selection, risk management, and option pricing modeling should and can be undertaken when the assumption of a non-normal distribution for asset returns is violated. Topics covered in this comprehensive book include an extensive discussion of probability distributions, estimating probability distributions, portfolio selection, alternative risk measures, and much more. Fat-Tailed and Skewed Asset Return Distributions provides a bridge between the highly technical theory of statistical distributional analysis, stochastic processes, and econometrics of financial returns and real-world risk management and investments.

Book Asset Allocation

Download or read book Asset Allocation written by William Kinlaw and published by John Wiley & Sons. This book was released on 2021-07-27 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover a masterful exploration of the fallacies and challenges of asset allocation In Asset Allocation: From Theory to Practice and Beyond—the newly and substantially revised Second Edition of A Practitioner’s Guide to Asset Allocation—accomplished finance professionals William Kinlaw, Mark P. Kritzman, and David Turkington deliver a robust and insightful exploration of the core tenets of asset allocation. Drawing on their experience working with hundreds of the world’s largest and most sophisticated investors, the authors review foundational concepts, debunk fallacies, and address cutting-edge themes like factor investing and scenario analysis. The new edition also includes references to related topics at the end of each chapter and a summary of key takeaways to help readers rapidly locate material of interest. The book also incorporates discussions of: The characteristics that define an asset class, including stability, investability, and similarity The fundamentals of asset allocation, including definitions of expected return, portfolio risk, and diversification Advanced topics like factor investing, asymmetric diversification, fat tails, long-term investing, and enhanced scenario analysis as well as tools to address challenges such as liquidity, rebalancing, constraints, and within-horizon risk. Perfect for client-facing practitioners as well as scholars who seek to understand practical techniques, Asset Allocation: From Theory to Practice and Beyond is a must-read resource from an author team of distinguished finance experts and a forward by Nobel prize winner Harry Markowitz.

Book Financial Modeling Under Non Gaussian Distributions

Download or read book Financial Modeling Under Non Gaussian Distributions written by Eric Jondeau and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines non-Gaussian distributions. It addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series.

Book Measuring Market Risk

Download or read book Measuring Market Risk written by Kevin Dowd and published by John Wiley & Sons. This book was released on 2007-01-11 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully revised and restructured, Measuring Market Risk, Second Edition includes a new chapter on options risk management, as well as substantial new information on parametric risk, non-parametric measurements and liquidity risks, more practical information to help with specific calculations, and new examples including Q&A’s and case studies.

Book Multifractal Volatility

Download or read book Multifractal Volatility written by Laurent E. Calvet and published by Academic Press. This book was released on 2008-10-13 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calvet and Fisher present a powerful, new technique for volatility forecasting that draws on insights from the use of multifractals in the natural sciences and mathematics and provides a unified treatment of the use of multifractal techniques in finance. A large existing literature (e.g., Engle, 1982; Rossi, 1995) models volatility as an average of past shocks, possibly with a noise component. This approach often has difficulty capturing sharp discontinuities and large changes in financial volatility. Their research has shown the advantages of modelling volatility as subject to abrupt regime changes of heterogeneous durations. Using the intuition that some economic phenomena are long-lasting while others are more transient, they permit regimes to have varying degrees of persistence. By drawing on insights from the use of multifractals in the natural sciences and mathematics, they show how to construct high-dimensional regime-switching models that are easy to estimate, and substantially outperform some of the best traditional forecasting models such as GARCH. The goal of Multifractal Volatility is to popularize the approach by presenting these exciting new developments to a wider audience. They emphasize both theoretical and empirical applications, beginning with a style that is easily accessible and intuitive in early chapters, and extending to the most rigorous continuous-time and equilibrium pricing formulations in final chapters. Presents a powerful new technique for forecasting volatility Leads the reader intuitively from existing volatility techniques to the frontier of research in this field by top scholars at major universities The first comprehensive book on multifractal techniques in finance, a cutting-edge field of research

Book Multi moment Asset Allocation and Pricing Models

Download or read book Multi moment Asset Allocation and Pricing Models written by Emmanuel Jurczenko and published by John Wiley & Sons. This book was released on 2006-10-02 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: While mainstream financial theories and applications assume that asset returns are normally distributed and individual preferences are quadratic, the overwhelming empirical evidence shows otherwise. Indeed, most of the asset returns exhibit “fat-tails” distributions and investors exhibit asymmetric preferences. These empirical findings lead to the development of a new area of research dedicated to the introduction of higher order moments in portfolio theory and asset pricing models. Multi-moment asset pricing is a revolutionary new way of modeling time series in finance which allows various degrees of long-term memory to be generated. It allows risk and prices of risk to vary through time enabling the accurate valuation of long-lived assets. This book presents the state-of-the art in multi-moment asset allocation and pricing models and provides many new developments in a single volume, collecting in a unified framework theoretical results and applications previously scattered throughout the financial literature. The topics covered in this comprehensive volume include: four-moment individual risk preferences, mathematics of the multi-moment efficient frontier, coherent asymmetric risks measures, hedge funds asset allocation under higher moments, time-varying specifications of (co)moments and multi-moment asset pricing models with homogeneous and heterogeneous agents. Written by leading academics, Multi-moment Asset Allocation and Pricing Models offers a unique opportunity to explore the latest findings in this new field of research.

Book Asset Allocation  Performance Measurement and Downside Risk

Download or read book Asset Allocation Performance Measurement and Downside Risk written by Alexandra Elisabeth Janovsky and published by diplom.de. This book was released on 2001-03-26 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inhaltsangabe:Abstract: Investors should not and in fact do not hold a single asset, they hold groups or portfolios of assets. An important aspect in portfolio theory is that the risk of a portfolio is more complex than the risk of its components. It depends on how much the assets represented in the portfolio move together, that is, on the correlation between the single assets. In portfolio theory, there are several definitions of risk: First of all, the Capital Asset Pricing Model (CAPM) relies on the beta factor of an asset relative to the market as a measure for the asset s risk. On the other hand, also downside risk can be used in order to determine a portfolio s risk. The kind of risk in question is market risk, which is the risk of losses arising from adverse movements in market prices or rates. Market risk can be subdivided into interest rate risk, equity price risk, exchange rate risk and commodity price risk. For many investment decisions, there is a minimum return that has to be reached in order to meet different criteria. Returns above this minimum acceptable return ensure that these goals are reached and thus are not considered risky. Standard deviation captures the risk associated with achieving the mean, while downside risk assumes that only those returns that fall below the minimal acceptable return incur risk. One has to distinguish between good and bad volatility. Good volatility is dispersion above the minimal acceptable return, the farther above the minimal acceptable return, the better it is. One way of measuring downside risk is to consider the shortfall probability or chances of falling below the minimal acceptable return. Another possibility is measuring downside variance, i.e. variance of the returns falling below the minimal acceptable return. As a consequence, downside variance is very sensitive to the estimate of the mean of the return function, while standard deviation does not suffer from this problem. Thus the calculation of downside deviation is more difficult than the calculation of standard deviation. The quality of the calculation also depends on the choice of differencing interval of the time series. The calculation of downside risk assumes that financial time series follow either a normal or lognormal distribution. Finally, there is no universal risk measure for the many broad categories of risk. For example, standard deviation captures the risk of not achieving the mean, beta captures the risk of investing [...]

Book Cryptofinance and Mechanisms of Exchange

Download or read book Cryptofinance and Mechanisms of Exchange written by Stéphane Goutte and published by Springer Nature. This book was released on 2020-01-03 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes how the rapid advancement in encryption and network computing gave birth to new tools and products that have influenced the local and global economy alike. One recent and notable example is the emergence of virtual currencies (such as Bitcoin) also known as cryptocurrencies. Virtual currencies introduced a fundamental transformation that affected the way goods, services and assets are exchanged. As a result of its distributed ledgers based on blockchain, cryptocurrencies not only offer some unique advantages to the economy, investors, and consumers, but also pose considerable risks to users and challenges for regulators when fitting the new technology into the old legal framework. The core of this proposed book is to present and discuss the evidence on financial asset capabilities of virtual currencies. The contributors of this volume analyze several interesting and timely issues such as the particularities of virtual currencies and their statistical characteristics; the diversification benefits of virtual currencies; the behavior and dependence structure between virtual currencies and the financial markets; the economic implications of virtual currencies, their effects, their price risk, and contagion spillovers in a unified and comprehensive framework; the future of virtual currencies and their distributed ledgers technology.

Book Alternative Investments and Strategies

Download or read book Alternative Investments and Strategies written by Rüdiger Kiesel and published by World Scientific. This book was released on 2010 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines academic research and practical expertise on alternative assets and trading strategies in a unique way. The asset classes that are discussed include : credit risk, cross-asset derivatives, energy, private equity, freight agreements, alternative real assets (ARA), and socially responsible investments (SRI). The coverage on trading and investment strategies are directed at portfolio insurance, especially constant proportion portfolio insurance (CPPI) and constant proportion debt obligation (CPDO) strategies, robust portfolio optimization, and hedging strategies for exotic options.

Book Understanding Investments

Download or read book Understanding Investments written by Nikiforos T. Laopodis and published by Routledge. This book was released on 2020-06-03 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and fully expanded edition of Understanding Investments continues to incorporate the elements of traditional textbooks on investments, but goes further in that the material is presented from an intuitive, practical point of view, and the supplementary material included in each chapter lends itself to both class discussion and further reading by students. It provides the essential tools to navigate complex, global financial markets and instruments including relevant (and classic) academic research and market perspectives. The author has developed a number of key innovative features. One unique feature is its economic angle, whereby each chapter includes a section dedicated to the economic analysis of that chapter’s material. Additionally, all chapters contain sections on strategies that investors can apply in specific situations and the pros and cons of each are also discussed. The book provides further clarification of some of the concepts discussed in the previous edition, thereby offering a more detailed analysis and discussion, with more real-world examples. The author has added new, shorter text boxes, labeled "Market Flash" to highlight the use of, or changes in current practices in the field; updates on strategies as applied by professionals; provision of useful information for an investor; updates on regulations; and anything else that might be relevant in discussing and applying a concept. This second edition also includes new sections on core issues in the field of investments, such as alternative investments, disruptive technologies, and future trends in investment management. This textbook is intended for undergraduate students majoring or minoring in finance and also for students in economics and related disciplines who wish to take an elective course in finance or investments.

Book Portfolio Management in Practice  Volume 2

Download or read book Portfolio Management in Practice Volume 2 written by CFA Institute and published by John Wiley & Sons. This book was released on 2020-12-10 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the latest essential resource on asset allocation for students and investment professionals. Part of the CFA Institute’s three-volume Portfolio Management in Practice series, Asset Allocation offers a deep, comprehensive treatment of the asset allocation process and the underlying theories and markets that support it. As the second volume in the series, Asset Allocation meets the needs of both graduate-level students focused on finance and industry professionals looking to become more dynamic investors. Filled with the insights and industry knowledge of the CFA Institute’s subject matter experts, Asset Allocation effectively blends theory and practice while helping the reader expand their skillsets in key areas of interest. This volume provides complete coverage on the following topics: Setting capital market expectations to support the asset allocation process Principles and processes in the asset allocation process, including handling ESG-integration and client-specific constraints Allocation beyond the traditional asset classes to include allocation to alternative investments The role of exchange-traded funds can play in implementing investment strategies An integrative case study in portfolio management involving a university endowment To further enhance your understanding of tools and techniques explored in Asset Allocation, don’t forget to pick up the Portfolio Management in Practice, Volume 2: Asset Allocation Workbook. The workbook is the perfect companion resource containing learning outcomes, summary overview sections, and challenging practice questions that align chapter-by-chapter with the main text.

Book Alternative Investments

Download or read book Alternative Investments written by CFA Institute and published by John Wiley & Sons. This book was released on 2021-11-04 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: The complete guide to alternative investments, from experts working with CFA Institute Alternative Investments is the definitive guide to understanding non-traditional asset classes. Alternatives are a disparate group of investments that are distinguished from long-only, publicly traded investments in stocks, bonds, and cash (often referred to as traditional investments). Alternative investments include real estate, commodities, infrastructure, and other non-traditional investments such as private equity or debt and hedge funds. They are attractive to investors because of the potential for portfolio diversification resulting in a higher risk-adjusted return for the portfolio. Alternative Investments and its accompanying workbook (sold separately) lead students and investment professionals through the many characteristics of non-traditional assets, including: Narrow specialization of the investment managers Relatively low correlation of returns with those of traditional investments Less regulation and less transparency than traditional investments Limited historical risk and return data Unique legal and tax considerations Higher fees, often including performance or incentive fees Concentrated portfolios Restrictions on redemptions (i.e. “lockups” and “gates”) CFA Institute is the world's premier association for investment professionals, and the governing body for the CFA® Program, CIPM® Program, CFA Institute ESG Investing Certificate, and Investment Foundations® Program. Those seeking a deeper understanding of the markets, mechanisms, and use of alternatives will value the level of expertise CFA Institute brings to the discussion, providing a clear, comprehensive resource for students and professionals alike. Whether used alone or in conjunction with the companion workbook, Alternative Investments offers a complete course in alternative investments and their role in investment management.

Book International Investments in Private Equity

Download or read book International Investments in Private Equity written by Peter Klaus Cornelius and published by Academic Press. This book was released on 2011-02-17 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can private equity investors exploit investment opportunities in foreign markets? Peter Cornelius uses a proprietary database to investigate and describe private equity markets worldwide, revealing their levels of integration, their risks, and the ways that investors can mitigate those risks. In three major sections that concentrate on the risk and return profile of private equity, the growth dynamics of discrete markets and geographies, and opportunities for private equity investments, he offers hard-to-find analyses that fill knowledge gaps about foreign markets. Observing that despite the progressive dismantling of barriers investors are still home-biased, he demonstrates that a methodical approach to understanding foreign private equity markets can take advantage of the macroeconomic and structural factors that drive supply and demand dynamics in individual markets. Foreword by Josh Lerner Teaches readers how to investigate and analyze foreign private equity markets Forecasts private equity investment opportunities via macroeconomic and structural factors in individual markets Draws on data from a proprietary database covering 250 buyout and VC funds and 7,000 portfolio companies

Book Integrated Market and Credit Portfolio Models

Download or read book Integrated Market and Credit Portfolio Models written by Peter Grundke and published by Springer Science & Business Media. This book was released on 2008-08-15 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to their business activities, banks are exposed to many different risk types. Peter Grundke shows how various risk exposures can be aggregated to a comprehensive risk position. Furthermore, computational problems of determining a loss distribution that comprises various risk types are analyzed.

Book Asset Management at Central Banks and Monetary Authorities

Download or read book Asset Management at Central Banks and Monetary Authorities written by Jacob Bjorheim and published by Springer Nature. This book was released on 2020-09-07 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: In response to the Global Financial Crisis and the COVID-19 pandemic, central banks have used all available instruments in their monetary policy tool-kit to avoid financial market disruptions and a collapse in real economic activities. These actions have expanded the size of their balance sheets and altered the composition of the asset-side. This edited book highlights how these assets are managed, providing an intellectual and practical contribution to an under-researched field of central bank responsibilities. It first reviews the sources and uses of domestic and international assets and how they complement—or possibly conflict with—the implementation of monetary policy goals. Next, the book examines the asset management mandate in a balance sheet context before turning to the investment decision-making process from strategic and tactical asset allocation to investment strategies, risk management, governance, reporting and control. Finally, it presents new developments in the field of managing assets at central banks. The individual chapters are written by central bankers, academics, and representatives from International Financial Institutions, each representing a particular aspect of the asset management practice. Practical and powerful insights from a hall of fame of investors, central bankers and scholars, are packed into this one volume. If you could have only one book on central bank asset management, this would be it. —Peter R. Fisher, Clinical Professor, Tuck School of Business at Dartmouth Jacob Bjorheim draws on his long experience in sovereign asset management to pull together a rich collection of insights from a broad range of expertise. Asset management at central banks has evolved and expanded considerably over the past decade. This book is a timely source of information and guidance. —Guy Debelle, Deputy Governor, Reserve Bank of Australia Central bank balance sheets have grown at a tremendous pace over the last decade and a half. Drawing on contributions from scholars and experienced central bankers from around the world, this timely and insightful book sheds light on how central banks are, and should be, managing their growing balance sheets. —Kjell G. Nyborg, Chaired Professor of Finance, University of Zurich, Author of Collateral Frameworks: The Open Secret of Central Banks Central banks and monetary authorities are charged with, and being held accountable for, managing portfolios of foreign currency assets of unprecedented size. The essays in this admirable book, written by some of the worlds most highly experienced officials, cover the full range of why and how this is currently being done and how new developments are affecting old practices. Interesting conceptually and immensely useful practically. —William White, Senior Fellow at the C.D. Howe Institute, former Head of the Monetary and Economic Department with the Bank for International Settlements (BIS) and chairman of the Economic and Development Review Committee at the OECD An excellent and timely review of modern international reserve management, which ought to be read by everyone working with, or simply interested in, international asset management and finance as well as monetary and economic policy. The spectrum of authors is broad and their combined insight is very valuable. —Tom A. Fearnley, Investment Director, Norwegian Ministry of Finance With “Asset Management at Central Banks and Monetary Authorities”, Jacob Bjorheim has achieved an editorial tour de force. The book assembles the insightful views of the leading experts in the field, both from an academic and practitioners’ perspective. It bridges the gap between the macroeconomics of central banks and the financial management of their reserves. A must read to understand how central banks are special in the group of institutional investors. —Eric Bouyé, Head of Asset Allocation and Quantitative Strategies, Treasury Department, The World Bank The balance sheet is a large and important toolbox for any central bank and specifically the foreign exchange reserves constitute one the more powerful of these tools. This book provides excellent insight in the various perspectives of managing reserves at a central bank. —Heidi Elmér, Director of Markets Department, Severiges Riksbank The world of international reserves has changed since the global financial crisis. In this volume, Jacob Bjorheim has assembled a stellar cast of experts to explain how and what that means for reserves management. With chapter authors like Andrew Ang, Jennifer Johnson-Calari, Robert McCauley, Ravi Menon, Simon Potter and Philip Turner, it is a book that every reserve manager must read. —Eli Remolona, Professor of Finance and Director of Central Banking, Asia School of Business in collaboration with MIT Sloan Jacob Bjorheim has succeeded in bringing together a first-class team of experts, and organising their contributions in an articulated journey from the central banks’ policy mandate to their asset management practices. An indispensable post-crisis update of the subject and a a required reading for anyone professionally involved with central bank’s asset management, or simply curious about a topic benefitting otherwise from limited research. —Louis de Montpellier, Former Global Head, Official Institutions Group, SSGA, and former Deputy Head, Banking Department, Bank for International Settlements (BIS), Basel At last, a book that shares with a wider audience, deep insight in a unique, challenging and ethical approach of asset management developed and implemented in the secretive world of central banks. If you wonder how to manage funds that stand ready for use at short notice in times of stress then this book is for you. Two features make it such a valuable read and a must-have reference: First, the very comprehensive list of themes covered from a rich diversity of angles. Second, the very impressive list of prominent institutions and authors that have contributed and shared their analysis and practical approaches of the issues presented. What is better than to get the information directly from first-hand practitioners, experts and managers themselves in their own words? —Jean-Pierre Matt, Former Head of Financial Analysis at the Bank for International Settlements (BIS) and founder of Quanteis This book holds the promise to become the go-to guide for anyone wishing to learn more about the management of official foreign exchange reserves. Central bankers in particular, but also those providing services to central banks, will find benefit from the broad scope in subject matter and varied perspectives being presented. I am yet to see a compendium on official reserve management with similar reach in subject matter. —Leon Myburgh, Former Head Financial Markets Department, South African Reserve Bank (SARB), Pretoria This is an immensely timely book at a time when central bank operations, and their balance sheets, remain “larger for longer”. Following the Financial Crisis 10 years ago, and with the Covid-19 Recession about to break, central bank balance sheets are at the forefront of the authorities’ response to economic issues as never before. Yet the management of their now large-scale assets remains a little known and little studied area. The authors of this book combine extensive technical and practical experience, and their observations will fill an important gap in the literature at a critical time. —Freyr Hermannsson, Former Head of Treasury, Central Bank of Iceland, Reykjavík

Book Handbook Of Heavy tailed Distributions In Asset Management And Risk Management

Download or read book Handbook Of Heavy tailed Distributions In Asset Management And Risk Management written by Michele Leonardo Bianchi and published by World Scientific. This book was released on 2019-03-08 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.