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Representation Of Probability Distributions With Implied Volatility And Biological Rationale
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Book Synopsis Representation of Probability Distributions With Implied Volatility and Biological Rationale by : Felix Polyakov
Download or read book Representation of Probability Distributions With Implied Volatility and Biological Rationale written by Felix Polyakov and published by . This book was released on 2018 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic and financial theories and practice essentially deal with uncertain future. Humans encounter uncertainty in different kinds of activity, from sensory-motor control to dynamics in financial markets, what has been subject of extensive studies. Representation of uncertainty with normal or lognormal distribution is a common feature of many of those studies. For example, proposed Bayessian integration of Gaussian multisensory input in the brain or log-normal distribution of future asset price in renowned Black-Scholes-Merton (BSM) model for pricing contingent claims.Standard deviation of log(future asset price) scaled by square root of time in the BSM model is called implied volatility. Actually, log(future asset price) is not normally distributed and traders account for that to avoid losses. Nevertheless the BSM formula derived under the assumption of constant volatility remains a major uniform framework for pricing options in financial markets. I propose that one of the reasons for such a high popularity of the BSM formula could be its ability to translate uncertainty measured with implied volatility into price in a way that is compatible with human intuition for measuring uncertainty.The present study deals with mathematical relationship between uncertainty and the BSM implied volatility. Examples for a number of common probability distributions are presented. Overall, this work proposes that representation of various probability distributions in terms of the BSM implied volatility profile may be meaningful in both biological and financial worlds. Necessary background from financial mathematics is provided in the text.
Book Synopsis Implied Probability Distributions by : Mark Rubinstein
Download or read book Implied Probability Distributions written by Mark Rubinstein and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An earlier article, quot;Implied Binomial Trees,quot; introduced a theoretical model for implying the stochastic process of an underlying asset price from the prices of associated options. This sequel provides details concerning application of the model to the full record of Samp;P 500 index options transactions from April 2, 1986 through December 31, 1993. Most prominently, it introduces a revised optimization technique for estimating expiration-date risk-neutral probability distributions which is probably theoretically superior and definitely orders of magnitude faster than the approaches outlined in the antecedent paper. This method maximizes the smoothness of the distribution while at the same time insuring that multimodalities are not unrealistically strong. With the exception of the lower left-hand tail of the distribution, alternative optimization specifications typically produce approximately the same implied distributions. Considerable care is taken to specify such parameters as interest rates, dividends, and synchronous index levels, as well as to filter for general arbitrage violations resulting implied probability distributions exhibit changes in skewness as time-to-expiration approaches which are consistent and to use time aggregation to correct for unrealistic persistent jaggedness of implied volatility smiles. The with theoretical predictions. While time patterns of skewness and kurtosis exhibit a discontinuity across the divide of the 1987 market crash, they remain remarkably stable on either side of the divide. Moreover, since the crash, the risk-neutral probability of a four standard deviation decline in the Samp;P index (-46% over a year) is 100 times more likely than would appear to be the case under the assumption of lognormality.
Book Synopsis Characterizations of Probability Distributions. by : Janos Galambos
Download or read book Characterizations of Probability Distributions. written by Janos Galambos and published by Lecture Notes in Mathematics. This book was released on 1978-09 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preliminaries and basic results; Characterizations based on truncated distributions; Characterizations by properties of order statistics; Characterization of the poisson process; Characterizations of multivariate exponential distributions.
Book Synopsis The Fundamentals of Heavy Tails by : Jayakrishnan Nair
Download or read book The Fundamentals of Heavy Tails written by Jayakrishnan Nair and published by Cambridge University Press. This book was released on 2022-06-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.
Book Synopsis Revisiting Risk-Weighted Assets by : Vanessa Le Leslé
Download or read book Revisiting Risk-Weighted Assets written by Vanessa Le Leslé and published by International Monetary Fund. This book was released on 2012-03-01 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we provide an overview of the concerns surrounding the variations in the calculation of risk-weighted assets (RWAs) across banks and jurisdictions and how this might undermine the Basel III capital adequacy framework. We discuss the key drivers behind the differences in these calculations, drawing upon a sample of systemically important banks from Europe, North America, and Asia Pacific. We then discuss a range of policy options that could be explored to fix the actual and perceived problems with RWAs, and improve the use of risk-sensitive capital ratios.
Book Synopsis The Volatility Surface by : Jim Gatheral
Download or read book The Volatility Surface written by Jim Gatheral and published by . This book was released on 2006 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Dynamic Hedging by : Nassim Nicholas Taleb
Download or read book Dynamic Hedging written by Nassim Nicholas Taleb and published by John Wiley & Sons. This book was released on 1997-01-14 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Destined to become a market classic, Dynamic Hedging is the only practical reference in exotic options hedgingand arbitrage for professional traders and money managers Watch the professionals. From central banks to brokerages to multinationals, institutional investors are flocking to a new generation of exotic and complex options contracts and derivatives. But the promise of ever larger profits also creates the potential for catastrophic trading losses. Now more than ever, the key to trading derivatives lies in implementing preventive risk management techniques that plan for and avoid these appalling downturns. Unlike other books that offer risk management for corporate treasurers, Dynamic Hedging targets the real-world needs of professional traders and money managers. Written by a leading options trader and derivatives risk advisor to global banks and exchanges, this book provides a practical, real-world methodology for monitoring and managing all the risks associated with portfolio management. Nassim Nicholas Taleb is the founder of Empirica Capital LLC, a hedge fund operator, and a fellow at the Courant Institute of Mathematical Sciences of New York University. He has held a variety of senior derivative trading positions in New York and London and worked as an independent floor trader in Chicago. Dr. Taleb was inducted in February 2001 in the Derivatives Strategy Hall of Fame. He received an MBA from the Wharton School and a Ph.D. from University Paris-Dauphine.
Book Synopsis Mathematical Modeling and Methods of Option Pricing by : Lishang Jiang
Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.
Book Synopsis Probability Theory and Stochastic Processes with Applications (Second Edition) by : Oliver Knill
Download or read book Probability Theory and Stochastic Processes with Applications (Second Edition) written by Oliver Knill and published by World Scientific Publishing Company. This book was released on 2017-01-31 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.
Book Synopsis Why Are There So Many Banking Crises? by : Jean-Charles Rochet
Download or read book Why Are There So Many Banking Crises? written by Jean-Charles Rochet and published by Princeton University Press. This book was released on 2008-01-23 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost every country in the world has sophisticated systems to prevent banking crises. Yet such crises--and the massive financial and social damage they can cause--remain common throughout the world. Does deposit insurance encourage depositors and bankers to take excessive risks? Are banking regulations poorly designed? Or are banking regulators incompetent? Jean-Charles Rochet, one of the world's leading authorities on banking regulation, argues that the answer in each case is "no." In Why Are There So Many Banking Crises?, he makes the case that, although many banking crises are precipitated by financial deregulation and globalization, political interference often causes--and almost always exacerbates--banking crises. If, for example, political authorities are allowed to pressure banking regulators into bailing out banks that should be allowed to fail, then regulation will lack credibility and market discipline won't work. Only by insuring the independence of banking regulators, Rochet says, can market forces work and banking crises be prevented and minimized. In this important collection of essays, Rochet examines the causes of banking crises around the world in recent decades, focusing on the lender of last resort; prudential regulation and the management of risk; and solvency regulations. His proposals for reforms that could limit the frequency and severity of banking crises should interest a wide range of academic economists and those working for central and private banks and financial services authorities.
Book Synopsis Introduction to Econophysics by : Rosario N. Mantegna
Download or read book Introduction to Econophysics written by Rosario N. Mantegna and published by Cambridge University Press. This book was released on 1999-11-13 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.
Book Synopsis The Future of Everything by : David Orell
Download or read book The Future of Everything written by David Orell and published by Basic Books. This book was released on 2008-02-26 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hurricane Katrina, the internet stock bubble, disease outbreaks -- are these predictable, preventable events, or are we merely the playthings of chaos? A compelling, irreverent, elegantly written history of our future that addresses the most important issues of our time, Apollo's Arrow examines such questions as: How well can we predict the future? Can past discoveries help us understand tomorrow's weather patterns, or tell us what our financial future will look like? Will scientists ever be able to forecast catastrophes, or will we always be at the mercy of Mother Nature, waiting for the next storm, epidemic, or economic crash to thunder through our lives? David Orrell looks back to show us how past scientists (and some charlatans) predicted the future, and where we are on the path to truly understanding what comes next. He asks how today's scientists can claim to predict future climate events when even three-day forecasts prove a serious challenge. Can we predict and control epidemics? Can we accurately foresee our financial future? Or will we only find out about tomorrow when tomorrow arrives?
Book Synopsis Decision Making Under Uncertainty by : Mykel J. Kochenderfer
Download or read book Decision Making Under Uncertainty written by Mykel J. Kochenderfer and published by MIT Press. This book was released on 2015-07-24 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to decision making under uncertainty from a computational perspective, covering both theory and applications ranging from speech recognition to airborne collision avoidance. Many important problems involve decision making under uncertainty—that is, choosing actions based on often imperfect observations, with unknown outcomes. Designers of automated decision support systems must take into account the various sources of uncertainty while balancing the multiple objectives of the system. This book provides an introduction to the challenges of decision making under uncertainty from a computational perspective. It presents both the theory behind decision making models and algorithms and a collection of example applications that range from speech recognition to aircraft collision avoidance. Focusing on two methods for designing decision agents, planning and reinforcement learning, the book covers probabilistic models, introducing Bayesian networks as a graphical model that captures probabilistic relationships between variables; utility theory as a framework for understanding optimal decision making under uncertainty; Markov decision processes as a method for modeling sequential problems; model uncertainty; state uncertainty; and cooperative decision making involving multiple interacting agents. A series of applications shows how the theoretical concepts can be applied to systems for attribute-based person search, speech applications, collision avoidance, and unmanned aircraft persistent surveillance. Decision Making Under Uncertainty unifies research from different communities using consistent notation, and is accessible to students and researchers across engineering disciplines who have some prior exposure to probability theory and calculus. It can be used as a text for advanced undergraduate and graduate students in fields including computer science, aerospace and electrical engineering, and management science. It will also be a valuable professional reference for researchers in a variety of disciplines.
Book Synopsis Regression and Other Stories by : Andrew Gelman
Download or read book Regression and Other Stories written by Andrew Gelman and published by Cambridge University Press. This book was released on 2020-07-23 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical approach to using regression and computation to solve real-world problems of estimation, prediction, and causal inference.
Download or read book Active Inference written by Thomas Parr and published by MIT Press. This book was released on 2022-03-29 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive treatment of active inference, an integrative perspective on brain, cognition, and behavior used across multiple disciplines. Active inference is a way of understanding sentient behavior—a theory that characterizes perception, planning, and action in terms of probabilistic inference. Developed by theoretical neuroscientist Karl Friston over years of groundbreaking research, active inference provides an integrated perspective on brain, cognition, and behavior that is increasingly used across multiple disciplines including neuroscience, psychology, and philosophy. Active inference puts the action into perception. This book offers the first comprehensive treatment of active inference, covering theory, applications, and cognitive domains. Active inference is a “first principles” approach to understanding behavior and the brain, framed in terms of a single imperative to minimize free energy. The book emphasizes the implications of the free energy principle for understanding how the brain works. It first introduces active inference both conceptually and formally, contextualizing it within current theories of cognition. It then provides specific examples of computational models that use active inference to explain such cognitive phenomena as perception, attention, memory, and planning.
Book Synopsis OpenIntro Statistics by : David Diez
Download or read book OpenIntro Statistics written by David Diez and published by . This book was released on 2015-07-02 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. We feature real data whenever possible, and files for the entire textbook are freely available at openintro.org. Visit our website, openintro.org. We provide free videos, statistical software labs, lecture slides, course management tools, and many other helpful resources.
Book Synopsis Empirical Asset Pricing by : Wayne Ferson
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.
