Statistical Consequences of Fat Tails

Statistical Consequences of Fat Tails

- Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions.This book, the first volume of the Technical Incerto, weaves a narrative around published journal ...

Author: Nassim Nicholas Taleb

Publisher:

ISBN: 1544508050

Category:

Page:

View: 396

The book investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible. Switching from thin tailed to fat tailed distributions requires more than "changing the color of the dress." Traditional asymptotics deal mainly with either n=1 or n=∞, and the real world is in between, under the "laws of the medium numbers"-which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence. A few examples: - The sample mean is rarely in line with the population mean, with effect on "naïve empiricism," but can be sometimes be estimated via parametric methods. - The "empirical distribution" is rarely empirical. - Parameter uncertainty has compounding effects on statistical metrics. - Dimension reduction (principal components) fails. - Inequality estimators (Gini or quantile contributions) are not additive and produce wrong results. - Many "biases" found in psychology become entirely rational under more sophisticated probability distributions. - Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.
Categories:

Control Performance Assessment Theoretical Analyses and Industrial Practice

Control Performance Assessment  Theoretical Analyses and Industrial Practice

J. 16(7), 1998–2003 (2016) Taleb, N.N.: Real-world Statistical Consequences of
Fat Tails: Papers and Commentary. STEM Academic Press, Technical Incerto
Collection (2018) Verboven, S., Hubert, M.: LIBRA: a Matlab library for robust ...

Author: Paweł D. Domański

Publisher: Springer Nature

ISBN: 9783030235932

Category: Technology & Engineering

Page: 367

View: 440

This book presents a comprehensive review of currently available Control Performance Assessment methods. It covers a broad range of classical and modern methods, with a main focus on assessment practice, and is intended to help practitioners learn and properly perform control assessment in the industrial reality. Further, it offers an educational guide for control engineers, who are currently in high demand in the industry. The book consists of three main parts. Firstly, a comprehensive review of available approaches is presented and discussed. The classical canon methods are extended with a discussion of nonlinear and complex alternative measures using non-Gaussian statistics, persistence and fractional calculations. Secondly, the methods’ applicability aspects are visualized with the aid of computer simulations, covering the most popular control philosophies used in the process industry. Lastly, a critical review of the methods discussed, on the basis of real-world industrial examples, rounds out the coverage.
Categories: Technology & Engineering

Unifying Themes in Complex Systems IX

Unifying Themes in Complex Systems IX

The Statistical Consequences of Fat Tails, vol. 1 (2018). www.
fooledbyrandomness.com Einmahl, J., Einmahl, J., de Haan, L.: Limits to Human
Life Span Through Extreme Value Theory. Center Discussion Paper Series No.
2017-051. CentER ...

Author: Alfredo J. Morales

Publisher: Springer

ISBN: 9783319966618

Category: Science

Page: 506

View: 477

Unifying Themes in Complex Systems is a well-established series of carefully edited conference proceedings that serve to document and archive the progress made regarding cross-fertilization in this field. The International Conference on Complex Systems (ICCS) creates a unique atmosphere for scientists from all fields, engineers, physicians, executives, and a host of other professionals, allowing them to explore common themes and applications of complex systems science. With this new volume, Unifying Themes in Complex Systems continues to establish common ground between the wide-ranging domains of complex systems science.
Categories: Science

Nonlinear Dynamics and Control

Nonlinear Dynamics and Control

Taleb, N.N.: Real-World Statistical Consequences of Fat Tails: Papers and
Commentary, Technical Incerto Collection. STEM Academic, Rockville (2018)
Impact of the Controller Algorithm on the Effect of Motor 156 P. D. Doma ́nski and
M.

Author: Walter Lacarbonara

Publisher: Springer Nature

ISBN: 9783030347475

Category: Science

Page: 349

View: 417

This second of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to Nonlinear Dynamics and Control. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation. Topics in Volume II include influence of nonlinearities on vibration control systems; passive, semi-active, active control of structures and systems; synchronization; robotics and human-machine interaction; network dynamics control (multi-agent systems, leader-follower dynamics, swarm dynamics, biological networks dynamics); and fractional-order control.
Categories: Science

The Mathematics of Financial Modeling and Investment Management

The Mathematics of Financial Modeling and Investment Management

Others consider a distribution fat-tailed if all its exponential moments are infinite,
E[e ] - °° for every s > 0. ... are the primary quantity to be modeled.2 Fat-tailedness
has a consequence of practical importance: the probability of extremal events (
i.e., the ... classes of fat-tailed distributions have been defined; each is
characterized by special statistical properties that are important in given
application domains.

Author: Sergio M. Focardi

Publisher: John Wiley & Sons

ISBN: 0471465992

Category: Business & Economics

Page: 800

View: 909

the mathematics of financial modeling & investment management The Mathematics of Financial Modeling & Investment Management covers a wide range of technical topics in mathematics and finance-enabling the investment management practitioner, researcher, or student to fully understand the process of financial decision-making and its economic foundations. This comprehensive resource will introduce you to key mathematical techniques-matrix algebra, calculus, ordinary differential equations, probability theory, stochastic calculus, time series analysis, optimization-as well as show you how these techniques are successfully implemented in the world of modern finance. Special emphasis is placed on the new mathematical tools that allow a deeper understanding of financial econometrics and financial economics. Recent advances in financial econometrics, such as tools for estimating and representing the tails of the distributions, the analysis of correlation phenomena, and dimensionality reduction through factor analysis and cointegration are discussed in depth. Using a wealth of real-world examples, Focardi and Fabozzi simultaneously show both the mathematical techniques and the areas in finance where these techniques are applied. They also cover a variety of useful financial applications, such as: * Arbitrage pricing * Interest rate modeling * Derivative pricing * Credit risk modeling * Equity and bond portfolio management * Risk management * And much more Filled with in-depth insight and expert advice, The Mathematics of Financial Modeling & Investment Management clearly ties together financial theory and mathematical techniques.
Categories: Business & Economics

Behavioral Finance for Private Banking

Behavioral Finance for Private Banking

A statistical consequence of prices being unpredictable is that returns are (log)‐
normally distributed—which is the content of the ... For example, they have fat
tails (i.e., too many very bad returns)—which Taleb (2007) called black swans.

Author: Kremena K. Bachmann

Publisher: John Wiley & Sons

ISBN: 9781119453710

Category: Business & Economics

Page: 256

View: 914

An essential framework for wealth management using behavioral finance Behavioral Finance for Private Banking provides a complete framework for wealth management tailored to the unique needs of each client. Merging behavioral finance with private banking, this framework helps you gain a greater understanding of your client’s wants, needs, and perspectives to streamline the decision making process. Beginning with the theoretical foundations of investment decision making and behavioral biases, the discussion delves into cultural differences in global business and asset allocation over the life cycle of the investment to help you construct a wealth management strategy catered to each individual’s needs. This new second edition has been updated to include coverage of fintech and neurofinance, an extension of behavioral finance that is beginning to gain traction in the private banking space. Working closely with clients entails deep interpersonal give and take. To be successful, private banking professionals must be as well-versed in behavioral psychology as they are in finance; this intersection is the heart of behavioral finance, and this book provides essential knowledge that can help you better serve your clients’ needs. Understand the internal dialogue at work when investment decisions are made Overcome the most common behavioral biases—and watch for your own Learn how fintech and neurofinance impact all aspects of private banking Set up a structured wealth management process that places the client’s needs front and center Private banking clients demand more than just financial expertise. They want an advisor who truly understands their needs, and can develop and execute the kind of strategy that will help them achieve their goals. Behavioral Finance for Private Banking provides a complete framework alongside insightful discussion to help you become the solution your clients seek.
Categories: Business & Economics

Future Perspectives in Risk Models and Finance

Future Perspectives in Risk Models and Finance

Tail. Probabilities. The literature in risk, insurance, and contracts has amply dealt
with the notion of information asymmetry (see ... Stiglitz 1988), but not with the
consequences of deeper information opacity (in spite of getting close, as in
Hölmstrom 1979), by which tail ... We define a fat tailed domain as follows: a
large share of the statistical properties come from the extremum; for a time series
involving n ...

Author: Alain Bensoussan

Publisher: Springer

ISBN: 9783319075242

Category: Business & Economics

Page: 315

View: 587

This book provides a perspective on a number of approaches to financial modelling and risk management. It examines both theoretical and practical issues. Theoretically, financial risks models are models of a real and a financial “uncertainty”, based on both common and private information and economic theories defining the rules that financial markets comply to. Financial models are thus challenged by their definitions and by a changing financial system fueled by globalization, technology growth, complexity, regulation and the many factors that contribute to rendering financial processes to be continuously questioned and re-assessed. The underlying mathematical foundations of financial risks models provide future guidelines for risk modeling. The book’s chapters provide selective insights and developments that can contribute to better understand the complexity of financial modelling and its ability to bridge financial theories and their practice. Future Perspectives in Risk Models and Finance begins with an extensive outline by Alain Bensoussan et al. of GLM estimation techniques combined with proofs of fundamental results. Applications to static and dynamic models provide a unified approach to the estimation of nonlinear risk models. A second section is concerned with the definition of risks and their management. In particular, Guegan and Hassani review a number of risk models definition emphasizing the importance of bi-modal distributions for financial regulation. An additional chapter provides a review of stress testing and their implications. Nassim Taleb and Sandis provide an anti-fragility approach based on “skin in the game”. To conclude, Raphael Douady discusses the noncyclical CAR (Capital Adequacy Rule) and their effects of aversion of systemic risks. A third section emphasizes analytic financial modelling approaches and techniques. Tapiero and Vallois provide an overview of mathematical systems and their use in financial modeling. These systems span the fundamental Arrow-Debreu framework underlying financial models of complete markets and subsequently, mathematical systems departing from this framework but yet generalizing their approach to dynamic financial models. Explicitly, models based on fractional calculus, on persistence (short memory) and on entropy-based non-extensiveness. Applications of these models are used to define a modeling approach to incomplete financial models and their potential use as a “measure of incompleteness”. Subsequently Bianchi and Pianese provide an extensive overview of multi-fractional models and their important applications to Asset price modeling. Finally, Tapiero and Jinquyi consider the binomial pricing model by discussing the effects of memory on the pricing of asset prices.
Categories: Business & Economics

Mathematical and Statistical Methods for Actuarial Sciences and Finance

Mathematical and Statistical Methods for Actuarial Sciences and Finance

... some anomalies regarding the Efficient Market Hypothesis and some scaling
behaviour, such as fat tails and clustered ... As a consequence, rationality
hypothesis is often replaced by the so-called “Bounded Rationality”; see [13] for
more ...

Author: Marco Corazza

Publisher: Springer Science & Business Media

ISBN: 8847014816

Category: Mathematics

Page: 314

View: 746

This book features selected papers from the international conference MAF 2008 that cover a wide variety of subjects in actuarial, insurance and financial fields, all treated in light of the successful cooperation between mathematics and statistics.
Categories: Mathematics

Agent Based Modeling

Agent Based Modeling

In their agent-based simulation of a stock market, however, Lux and Marchesi
find that the time series of returns exhibits both fat tails and volatility dependence.
31 Thus, they conclude that these statistical properties appear as emergent ...

Author: Norman Ehrentreich

Publisher: Springer Science & Business Media

ISBN: 9783540738794

Category: Business & Economics

Page: 232

View: 981

This book reconciles the existence of technical trading with the Efficient Market Hypothesis. By analyzing a well-known agent-based model, the Santa Fe Institute Artificial Stock Market (SFI-ASM), it finds that when selective forces are weak, financial evolution cannot guarantee that only the fittest trading rules will survive. Its main contribution lies in the application of standard results from population genetics which have widely been neglected in the agent-based community.
Categories: Business & Economics

Energy Risk Competitive Advantage

Energy  Risk   Competitive Advantage

Therefore highly unlikely events, sometimes resulting in extreme consequences,
are often poorly predicted using standard statistical methods. Figure 2–2
illustrates the normal distribution and these tail areas or zones as “fat tails.” Fig. 2
–2.

Author: Scott Randall

Publisher: PennWell Books

ISBN: 9781593701345

Category: Business & Economics

Page: 284

View: 514

"Both front-line information gatherers and executives assigned to oversight will find invaluable tools for data analysis, risk analysis, and systemic monitoring. In turn, these tools will allow leaders to put this information into action with confidence."--BOOK JACKET.
Categories: Business & Economics

JOURNSL OF BUSINESS AND ECONOMIC STATISTICS

JOURNSL OF BUSINESS AND ECONOMIC STATISTICS

Third, the finite-sample distortions appear to reflect problems with VT- This can
be seen by noting that there is almost no fat-tail or skewness problem in the row
corresponding to TRUE. This suggests that the distribution of the numerator in (9)
 ...

Author:

Publisher:

ISBN:

Category:

Page:

View: 425

Categories:

Tail Risk Killers How Math Indeterminacy and Hubris Distort Markets

Tail Risk Killers  How Math  Indeterminacy  and Hubris Distort Markets

While illustrating how to protect your assets from tail risk, he shows you how to: Implement the six axioms for risk management Prepare for the unintended consequences of central banks suppressing tail risk Identify and avoid the dark risks ...

Author: Jeffrey McGinn

Publisher: McGraw Hill Professional

ISBN: 9780071784917

Category: Business & Economics

Page: 384

View: 470

Reshape your investing strategy for an increasingly uncertain world “An engrossing, fast-paced, terrific read for anyone interested in the financial imbalances due to too much reliance on math and too little respect for indeterminacy.” —Tyler Durden, ZeroHedge.com The world does not unfold according to a fixed set of rules. It is a dynamical system whose evolution looks like a bell curve with fat “tails.” The same is true of financial markets. However, every day we rely on the certainty and precision of mathematical strategies that assume the contrary to control and grow wealth in markets. Tail Risk Killers shows you how the rigidity of model-based thinking has led to the fragility of today’s global financial marketplace, and it explains how to use adaptive trading strategies to mitigate risk in impending market conditions. Risk management veteran Jeff McGinn pokes holes in prevalent assumptions about how financial markets act that tend to underestimate the likelihood of occurrence of extreme events. Through clear, conversational writing, real-world anecdotes, and easy-tofollow formulas, he provides a glimpse into the way tomorrow’s successful traders are viewing financial markets—with an eye for probability distributions. While illustrating how to protect your assets from tail risk, he shows you how to: Implement the six axioms for risk management Prepare for the unintended consequences of central banks suppressing tail risk Identify and avoid the dark risks hidden in today’s derivative-laden financial system Anticipate the fate of credit default swaps that may not face extinction McGinn argues that the intervention of central banks has robbed global markets of their opportunities to adapt, but this highly relevant book shows you that it is not too late to adapt your portfolio to survive the extreme events that happen more often than popular financial models suggest. Tail Risk Killers helps you discover useful information and processes beyond the focus of industry standards, helps you connect the dots of evolving trading strategies and time your next trade for maximum profitability.
Categories: Business & Economics

Finance and Economics Discussion Series

Finance and Economics Discussion Series

... value at risk " ) , the difference between .02 and .01 can be large if the
distribution is assumed to have " fat tails . ... The models do not address the
statistical consequences of time aggregating asset returns needed to estimate
longer ...

Author:

Publisher:

ISBN: UCAL:C3676055

Category: Economics

Page:

View: 559

Categories: Economics

A Dictionary Geographical Statistical and Historical of the Various Countries Places and Principal Natural Objects in the World by J R M Culloch

A Dictionary Geographical  Statistical  and Historical of the Various Countries  Places  and Principal Natural Objects in the World by J  R  M Culloch

The breed of horses has de~ terioratcd, in consequence of the government
seizing for its use those that are most valuable. The cattle are ... Some of the
sheep are very fine, and all have the large fat tail which characterises the African
breeds.

Author:

Publisher:

ISBN: IBNF:CF005698346

Category:

Page: 502

View: 999

Categories:

Accounting for Value

Accounting for Value

Risk is in the tail, once called the “peso effect,” now popularized as “black-swan”
outcomes. It is here that we are really concerned about getting hit. Though
modern finance has long recognized that return distributions are fat-tailed, it has
had little to say about our risk in the ... Both methods are the modernist's
admirable attempts to quantify risk, one by assuming statistical parameters and
the other by ...

Author: Stephen Penman

Publisher: Columbia University Press

ISBN: 9780231521857

Category: Business & Economics

Page: 256

View: 301

Accounting for Value teaches investors and analysts how to handle accounting in evaluating equity investments. The book's novel approach shows that valuation and accounting are much the same: valuation is actually a matter of accounting for value. Laying aside many of the tools of modern finance the cost-of-capital, the CAPM, and discounted cash flow analysis Stephen Penman returns to the common-sense principles that have long guided fundamental investing: price is what you pay but value is what you get; the risk in investing is the risk of paying too much; anchor on what you know rather than speculation; and beware of paying too much for speculative growth. Penman puts these ideas in touch with the quantification supplied by accounting, producing practical tools for the intelligent investor. Accounting for value provides protection from paying too much for a stock and clues the investor in to the likely return from buying growth. Strikingly, the analysis finesses the need to calculate a "cost-of-capital," which often frustrates the application of modern valuation techniques. Accounting for value recasts "value" versus "growth" investing and explains such curiosities as why earnings-to-price and book-to-price ratios predict stock returns. By the end of the book, Penman has the intelligent investor thinking like an intelligent accountant, better equipped to handle the bubbles and crashes of our time. For accounting regulators, Penman also prescribes a formula for intelligent accounting reform, engaging with such controversial issues as fair value accounting.
Categories: Business & Economics

Growth Curve Modeling

Growth Curve Modeling

Fernandez , C. , Steel , M.F. On Bayesian Modeling of Fat Tails and Skewness .
Journal of ... Fowler, M.S. , Ruxton , G.D. Population Dynamic Consequences of
the Allee Effects . Journal of ... Fuller, W.A. Introduction to Statistical Time Series .

Author: Michael J. Panik

Publisher: John Wiley & Sons

ISBN: 9781118763940

Category: Mathematics

Page: 454

View: 215

Features recent trends and advances in the theory and techniques used to accurately measure and model growth Growth Curve Modeling: Theory and Applications features an accessible introduction to growth curve modeling and addresses how to monitor the change in variables over time since there is no “one size fits all” approach to growth measurement. A review of the requisite mathematics for growth modeling and the statistical techniques needed for estimating growth models are provided, and an overview of popular growth curves, such as linear, logarithmic, reciprocal, logistic, Gompertz, Weibull, negative exponential, and log-logistic, among others, is included. In addition, the book discusses key application areas including economic, plant, population, forest, and firm growth and is suitable as a resource for assessing recent growth modeling trends in the medical field. SAS® is utilized throughout to analyze and model growth curves, aiding readers in estimating specialized growth rates and curves. Including derivations of virtually all of the major growth curves and models, Growth Curve Modeling: Theory and Applications also features: • Statistical distribution analysis as it pertains to growth modeling • Trend estimations • Dynamic site equations obtained from growth models • Nonlinear regression • Yield-density curves • Nonlinear mixed effects models for repeated measurements data Growth Curve Modeling: Theory and Applications is an excellent resource for statisticians, public health analysts, biologists, botanists, economists, and demographers who require a modern review of statistical methods for modeling growth curves and analyzing longitudinal data. The book is also useful for upper-undergraduate and graduate courses on growth modeling.
Categories: Mathematics

Journal of the American Statistical Association

Journal of the American Statistical Association

The GLG model leads to heavier extreme tails than the Gaussian model as a
consequence of the In this article we have ... the GLG predictives clearly are more
concen - processes , particularly processes with fat - tailed finite - dimensiotrated
 ...

Author:

Publisher:

ISBN: UOM:49015003119501

Category: Statistics

Page:

View: 363

Categories: Statistics

Engineering Risk and Finance

Engineering Risk and Finance

... is then used to derive implied power laws and standardized probability
distributions that are both asymmetric and have fat tails. This approach provides
a parametric definition of the “missing”, namely the tail probabilities not
accounted for in selecting an ... assume responsibility for and pollution risks of
firms and consumers who consume and who do not assume their pollution
consequences. Both cases, call for an efficient regulation and statistical controls
which is the topic of Chap.

Author: Charles S. Tapiero

Publisher: Springer Science & Business Media

ISBN: 9781461462347

Category: Business & Economics

Page: 508

View: 506

Risk models are models of uncertainty, engineered for some purposes. They are “educated guesses and hypotheses” assessed and valued in terms of well-defined future states and their consequences. They are engineered to predict, to manage countable and accountable futures and to provide a frame of reference within which we may believe that “uncertainty is tamed”. Quantitative-statistical tools are used to reconcile our information, experience and other knowledge with hypotheses that both serve as the foundation of risk models and also value and price risk. Risk models are therefore common to most professions, each with its own methods and techniques based on their needs, experience and a wisdom accrued over long periods of time. This book provides a broad and interdisciplinary foundation to engineering risks and to their financial valuation and pricing. Risk models applied in industry and business, heath care, safety, the environment and regulation are used to highlight their variety while financial valuation techniques are used to assess their financial consequences. This book is technically accessible to all readers and students with a basic background in probability and statistics (with 3 chapters devoted to introduce their elements). Principles of risk measurement, valuation and financial pricing as well as the economics of uncertainty are outlined in 5 chapters with numerous examples and applications. New results, extending classical models such as the CCAPM are presented providing insights to assess the risks and their price in an interconnected, dependent and strategic economic environment. In an environment departing from the fundamental assumptions we make regarding financial markets, the book provides a strategic/game-like approach to assess the risk and the opportunities that such an environment implies. To control these risks, a strategic-control approach is developed that recognizes that many risks resulting by “what we do” as well as “what others do”. In particular we address the strategic and statistical control of compliance in large financial institutions confronted increasingly with a complex and far more extensive regulation.
Categories: Business & Economics

2003 CFA Level III Candidate Readings

2003 CFA Level III Candidate Readings

This is not the only way most desks measure Yet the hedging risk of inventory
remains their risks . ... These sorts It is common to ignore the fat tails , those
occaof risks may not be readily measurable in a value at risk sional events that ...
If these risks could be quantified , they distribution table at the back of the
statistics book .

Author: Association for Investment Management and Research

Publisher: Cfa Inst

ISBN: 0935015809

Category: Asset valuation

Page:

View: 572

Categories: Asset valuation

Environmental Modelling

Environmental Modelling

Any statistical distribution can be taken as representative of the values (e.g. see
Stedinger et al., 1993). ... Extreme events are rare with thin tailed (exponential)
distributions and occur with greater frequency with fat-tailed (power-law)
distributions. ... The behaviour of time series has many important consequences
in the environmental sciences, including risk analysis, prediction and forecasting,
and the ...

Author: John Wainwright

Publisher: John Wiley & Sons

ISBN: 9781118351482

Category: Technology & Engineering

Page: 496

View: 970

Simulation models are an established method used to investigate processes and solve practical problems in a wide variety of disciplines. Central to the concept of this second edition is the idea that environmental systems are complex, open systems. The authors present the diversity of approaches to dealing with environmental complexity and then encourage readers to make comparisons between these approaches and between different disciplines. Environmental Modelling: Finding Simplicity in Complexity 2nd edition is divided into four main sections: An overview of methods and approaches to modelling. State of the art for modelling environmental processes Tools used and models for management Current and future developments. The second edition evolves from the first by providing additional emphasis and material for those students wishing to specialize in environmental modelling. This edition: Focuses on simplifying complex environmental systems. Reviews current software, tools and techniques for modelling. Gives practical examples from a wide variety of disciplines, e.g. climatology, ecology, hydrology, geomorphology and engineering. Has an associated website containing colour images, links to WWW resources and chapter support pages, including data sets relating to case studies, exercises and model animations. This book is suitable for final year undergraduates and postgraduates in environmental modelling, environmental science, civil engineering and biology who will already be familiar with the subject and are moving on to specialize in the field. It is also designed to appeal to professionals interested in the environmental sciences, including environmental consultants, government employees, civil engineers, geographers, ecologists, meteorologists, and geochemists.
Categories: Technology & Engineering