Saddlepoint Approximations with Applications

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Author: Ronald W. Butler

Publisher: Cambridge University Press

ISBN: 1139466518

Category: Mathematics

Page: N.A

View: 2691

Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.

Statistical Methods for Financial Engineering

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Author: Bruno Remillard

Publisher: CRC Press

ISBN: 1439856958

Category: Business & Economics

Page: 496

View: 9780

While many financial engineering books are available, the statistical aspects behind the implementation of stochastic models used in the field are often overlooked or restricted to a few well-known cases. Statistical Methods for Financial Engineering guides current and future practitioners on implementing the most useful stochastic models used in financial engineering. After introducing properties of univariate and multivariate models for asset dynamics as well as estimation techniques, the book discusses limits of the Black-Scholes model, statistical tests to verify some of its assumptions, and the challenges of dynamic hedging in discrete time. It then covers the estimation of risk and performance measures, the foundations of spot interest rate modeling, Lévy processes and their financial applications, the properties and parameter estimation of GARCH models, and the importance of dependence models in hedge fund replication and other applications. It concludes with the topic of filtering and its financial applications. This self-contained book offers a basic presentation of stochastic models and addresses issues related to their implementation in the financial industry. Each chapter introduces powerful and practical statistical tools necessary to implement the models. The author not only shows how to estimate parameters efficiently, but he also demonstrates, whenever possible, how to test the validity of the proposed models. Throughout the text, examples using MATLAB® illustrate the application of the techniques to solve real-world financial problems. MATLAB and R programs are available on the author’s website.

Elements of Distribution Theory

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Author: Thomas A. Severini

Publisher: Cambridge University Press

ISBN: 1139446118

Category: Mathematics

Page: N.A

View: 5165

This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.

Saddlepoint Approximation Methods in Financial Engineering

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Author: Yue Kuen Kwok,Wendong Zheng

Publisher: Springer

ISBN: 3319741012

Category: Mathematics

Page: 128

View: 3658

This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables. The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quantitative analysts in financial institutions who strive for effective valuation of prices of exotic financial derivatives and risk positions of portfolios of risky instruments.

Statistical Models

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Author: A. C. Davison

Publisher: Cambridge University Press

ISBN: 9781139437417

Category: Mathematics

Page: N.A

View: 7990

Models and likelihood are the backbone of modern statistics. This 2003 book gives an integrated development of these topics that blends theory and practice, intended for advanced undergraduate and graduate students, researchers and practitioners. Its breadth is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics such as likelihood and linear and generalized linear models. Each chapter contains a wide range of problems and exercises. Practicals in the S language designed to build computing and data analysis skills, and a library of data sets to accompany the book, are available over the Web.

Asymptotic Chaos Expansions in Finance

Theory and Practice

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Author: David Nicolay

Publisher: Springer

ISBN: 1447165063

Category: Mathematics

Page: 491

View: 3634

Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (such as a stock price or FX rate), baskets (indexes, spreads) and term structure models (especially SV-HJM and SV-LMM). It also establishes fundamental links between the Wiener chaos of the instantaneous volatility and the small-time asymptotic structure of the stochastic implied volatility framework. It is addressed primarily to financial mathematics researchers and graduate students, interested in stochastic volatility, asymptotics or market models. Moreover, as it contains many self-contained approximation results, it will be useful to practitioners modelling the shape of the smile and its evolution.

Stochastic Processes

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Author: Richard F. Bass

Publisher: Cambridge University Press

ISBN: 113950147X

Category: Mathematics

Page: N.A

View: 4337

This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes and semigroup theory. Applications include the Black–Scholes formula for the pricing of derivatives in financial mathematics, the Kalman–Bucy filter used in the US space program and also theoretical applications to partial differential equations and analysis. Short, readable chapters aim for clarity rather than full generality. More than 350 exercises are included to help readers put their new-found knowledge to the test and to prepare them for tackling the research literature.

Bootstrap Methods and Their Application

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Author: A. C. Davison,D. V. Hinkley

Publisher: Cambridge University Press

ISBN: 9780521574716

Category: Computers

Page: 582

View: 3884

This book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; and methods for efficient computation, including improved Monte Carlo simulation. Each chapter includes both practical and theoretical exercises. Included with the book is a disk of purpose-written S-Plus programs for implementing the methods described in the text. Computer algorithms are clearly described, and computer code is included on a 3-inch, 1.4M disk for use with IBM computers and compatible machines. Users must have the S-Plus computer application. Author resource page: http://statwww.epfl.ch/davison/BMA/

Saddlepoint Approximations

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Author: Jens Ledet Jensen

Publisher: Oxford University Press

ISBN: 9780198522959

Category: Mathematics

Page: 332

View: 2380

Although introduced more than 60 years ago it is only during the last 15 years that there has been a systematic development of saddlepoint approximations. These approximations give a highly accurate expression for the tail of a distribution, not only in the centre of the distribution but alsofor very small tail probabilities. The price for this is a more cumbersome formula, the evaluation of which sometimes requires the use of a small personal computer. This book explains the ideas behind the saddlepoint approximations as well as giving a detailed mathematical description of thesubject. The emphasis is two- fold. One is on popularizing the formulae through many worked out and ready to use examples. The second is on giving a comprehensive mathematical background for further research in the field. Some of the major subjects treated are uniformity of the approximations, testsin exponential families, and compound sums with applications in insurance mathematics.

Metron

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Author: Corrado Gini

Publisher: N.A

ISBN: N.A

Category: Statistics

Page: N.A

View: 8666

Includes list of publications received.

Essentials of Statistical Inference

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Author: G. A. Young,R. L. Smith,R. L. (University of North Carolina Smith, Chapel Hill)

Publisher: Cambridge University Press

ISBN: 9780521839716

Category: Mathematics

Page: 225

View: 9293

Concise account of main approaches; first textbook to synthesize modern computation with basic theory.

Probability

Theory and Examples

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Author: Rick Durrett

Publisher: Cambridge University Press

ISBN: 113949113X

Category: Mathematics

Page: N.A

View: 6488

This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Breakthroughs in Statistics

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Author: Samuel Kotz,Norman Lloyd Johnson

Publisher: Springer Verlag

ISBN: 9780387949888

Category: Mathematics

Page: 559

View: 4572

Volume III includes more selections of articles that have initiated fundamental changes in statistical methodology. It contains articles published before 1980 that were overlooked in the previous two volumes plus articles from the 1980's - all of them chosen after consulting many of today's leading statisticians.

Nonparametric Estimation under Shape Constraints

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Author: Piet Groeneboom,Geurt Jongbloed,Jon A. Wellner

Publisher: Cambridge University Press

ISBN: 0521864011

Category: Business & Economics

Page: 428

View: 7899

This book introduces basic concepts of shape constrained inference and guides the reader to current developments in the subject.

Design of Comparative Experiments

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Author: R. A. Bailey

Publisher: Cambridge University Press

ISBN: 1139469916

Category: Mathematics

Page: N.A

View: 8636

This book should be on the shelf of every practising statistician who designs experiments. Good design considers units and treatments first, and then allocates treatments to units. It does not choose from a menu of named designs. This approach requires a notation for units that does not depend on the treatments applied. Most structure on the set of observational units, or on the set of treatments, can be defined by factors. This book develops a coherent framework for thinking about factors and their relationships, including the use of Hasse diagrams. These are used to elucidate structure, calculate degrees of freedom and allocate treatment subspaces to appropriate strata. Based on a one-term course the author has taught since 1989, the book is ideal for advanced undergraduate and beginning graduate courses. Examples, exercises and discussion questions are drawn from a wide range of real applications: from drug development, to agriculture, to manufacturing.

Exercises in Probability

A Guided Tour from Measure Theory to Random Processes, Via Conditioning

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Author: Loïc Chaumont,Marc Yor

Publisher: Cambridge University Press

ISBN: 1107606551

Category: Mathematics

Page: 279

View: 3896

Over 100 exercises with detailed solutions, insightful notes and references for further reading. Ideal for beginning researchers.