Bayesian Methods in Finance

Name: Bayesian Methods in Finance
Price: 42.46 USD
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ISBN: 9780471920830

ISBN-10: 0471920835

ISBN-13: 9780471920830

Edition: 2008

Authors: Svetlozar T. Rachev, John S. J. Hsu, Biliana S. Bagasheva, Frank J. Fabozzi

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Description:

An accessible overview of the theory and practice of Bayesian methods in finance Bayesian Methods in Finance explains and illustrates the foundations of the Bayesian methodology in clear and accessible terms. It provides a unified examination of the use of the Bayesian theory and practice to analyze and evaluate asset management. With this book as their guide, readers will learn how to use Bayesian methods, and notably, the Markov Chain Monte Carlo toolbox, to incorporate the prior views of a fund manager into the asset allocation process, estimate and predict volatility, improve risk forecasts, calculate option prices, and combine the conclusions of different models. Bayesian Methods in…

Book details

List price: $95.00
Copyright year: 2008
Publisher: John Wiley & Sons, Incorporated
Publication date: 2/8/2008
Binding: Hardcover
Pages: 329
Size: 6.40" wide x 9.30" long x 1.20" tall
Weight: 1.188
Language: English

Svetlozar T. Rachev, PhD, Doctor of Science, is Chair-Professor at the University of Karlsruhe in the School of Economics and Business Engineering; Professor Emeritus at the University of California, Santa Barbara; and Chief-Scientist of FinAnalytica Inc. John S. J. Hsu, PhD, is Professor of Statistics and Applied Probability at the University of California, Santa Barbara. Biliana S. Bagasheva, PhD, has research interests in the areas of risk management, portfolio construction, Bayesian methods, and financial econometrics. Currently, she is a consultant in London. Frank J. Fabozzi, PhD, CFA, is Professor in the Practice of Finance and Becton Fellow at Yale University's School of Management…

Douglas J. Lucas is Executive Director and Head of CDO Research at UBS. He is also Chairman of The Bond Market Association's CDO Research Committee and ranked top three in CDO research in the Institutional Investor's fixed income analyst survey. Lucas has been involved in the CDO market for nearly two decades, having developed Moody's rating methodology for CDOs in 1989.LAURIE S. GOODMAN, PhD, is Managing Director and co-Head of Global Fixed Income Research at UBS. She manages U.S. Securitized Products and Treasury/Agency/Derivatives Research. Goodman has worked on Wall Street for over twenty years and is well regarded by the investor community, having won more #1 slots on the Institutional…



Preface


About the Author's



Introduction


A Few Notes on Notation


Overview



The Bayesian Paradigm


The Likelihood Function


The Poisson Distribution Likelihood Function


The Normal Distribution Likelihood Function


The Bayes' Theorem


Bayes' Theorem and Model Selection


Bayes' Theorem and Classification


Bayesian Inference for the Binomial Probability


Summary



Prior and Posterior Information, Predictive Inference


Prior Information


Informative Prior Elicitation


Noninformative Prior Distributions


Conjugate Prior Distributions


Empirical Bayesian Analysis


Posterior Inference


Posterior Point Estimates


Bayesian Intervals


Bayesian Hypothesis Comparison


Bayesian Predictive Inference


Illustration: Posterior Trade-off and the Normal Mean Parameter


Summary



Definitions of Some Univariate and Multivariate Statistical Distributions


The Univariate Normal Distribution


The Univariate Student's t-Distribution


The Inverted x[superscript 2] Distribution


The Multivariate Normal Distribution


The Multivariate Student's t-Distribution


The Wishart Distribution


The Inverted Wishart Distribution



Bayesian Linear Regression Model


The Univariate Linear Regression Model


Bayesian Estimation of the Univariate Regression Model


Illustration: The Univariate Linear Regression Model


The Multivariate Linear Regression Model


Diffuse Improper Prior


Summary



Bayesian Numerical Computation


Monte Carlo Integration


Algorithms for Posterior Simulation


Rejection Sampling


Importance Sampling


MCMC Methods


Linear Regression with Semiconjugate Prior


Approximation Methods: Logistic Regression


The Normal Approximation


The Laplace Approximation


Summary



Bayesian Framework For Portfolio Allocation


Classical Portfolio Selection


Portfolio Selection Problem Formulations


Mean-Variance Efficient Frontier


Illustration: Mean-Variance Optimal Portfolio with Portfolio Constraints


Bayesian Portfolio Selection



Mean and Covariance with Diffuse (Improper) Priors



Mean and Covariance with Proper Priors


The Efficient Frontier and the Optimal Portfolio


Illustration: Bayesian Portfolio Selection


Shrinkage Estimators


Unequal Histories of Returns


Dependence of the Short Series on the Long Series


Bayesian Setup


Predictive Moments


Summary



Prior Beliefs and Asset Pricing Models


Prior Beliefs and Asset Pricing Models


Preliminaries


Quantifying the Belief About Pricing Model Validity


Perturbed Model


Likelihood Function


Prior Distributions


Posterior Distributions


Predictive Distributions and Portfolio Selection


Prior Parameter Elicitation


Illustration: Incorporating Confidence about the Validity of an Asset Pricing Model


Model Uncertainty


Bayesian Model Averaging


Illustration: Combining Inference from the CAPM and the Fama and French Three-Factor Model


Summary



Numerical Simulation of the Predictive Distribution


Sampling from the Predictive Distribution



Likelihood Function of a Candidate Model



The Black-Litterman Portfolio Selection Framework


Preliminaries


Equilibrium Returns


Investor Views


Distributional Assumptions


Combining Market Equilibrium and Investor Views


The Choice of [tau] and [Omega]


The Optimal Portfolio Allocation


Illustration: Black-Litterman Optimal Allocation


Incorporating Trading Strategies into the Black-Litterman Model


Active Portfolio Management and the Black-Litterman Model


Views on Alpha and the Black-Litterman Model


Translating a Qualitative View into a Forecast for Alpha


Covariance Matrix Estimation


Summary



Market Efficiency and Return Predictability


Tests of Mean-Variance Efficiency


Inefficiency Measures in Testing the CAPM


Distributional Assumptions and Posterior Distributions


Efficiency under Investment Constraints


Illustration: The Inefficiency Measure, [Delta superscript R]


Testing the APT


Distributional Assumptions, Posterior and Predictive Distributions


Certainty Equivalent Returns


Return Predictability


Posterior and Predictive Inference


Solving the Portfolio Selection Problem


Illustration: Predictability and the Investment Horizon


Summary



Vector Autoregressive Setup



Volatility Models


Garch Models of Volatility


Stylized Facts about Returns


Modeling the Conditional Mean


Properties and Estimation of the GARCH(1,1) Process


Stochastic Volatility Models


Stylized Facts about Returns


Estimation of the Simple SV Model


Illustration: Forecasting Value-at-Risk


An Arch-Type Model or a Stochastic Volatility Model?


Where Do Bayesian Methods Fit?



Bayesian Estimation of ARCH-Type Volatility Models


Bayesian Estimation of the Simple GARCH(1,1) Model


Distributional Setup


Mixture of Normals Representation of the Student's t-Distribution


GARCH(1,1) Estimation Using the Metropolis-Hastings Algorithm


Illustration: Student's t GARCH(1,1) Model


Markov Regime-switching GARCH Models


Preliminaries


Prior Distributional Assumptions


Estimation of the MS GARCH(1,1) Model


Sampling Algorithm for the Parameters of the MS GARCH(1,1) Model


Illustration: Student's t MS GARCH(1,1) Model


Summary



Griddy Gibbs Sampler


Drawing from the Conditional Posterior Distribution of [nu]



Bayesian Estimation of Stochastic Volatility Models


Preliminaries of SV Model Estimation


Likelihood Function


The Single-Move MCMC Algorithm for SV Model Estimation


Prior and Posterior Distributions


Conditional Distribution of the Unobserved Volatility


Simulation of the Unobserved Volatility


Illustration


The Multimove MCMC Algorithm for SV Model Estimation


Prior and Posterior Distributions


Block Simulation of the Unobserved Volatility


Sampling Scheme


Illustration


Jump Extension of the Simple SV Model


Volatility Forecasting and Return Prediction


Summary



Kalman Filtering and Smoothing


The Kalman Filter Algorithm


The Smoothing Algorithm



Advanced Techniques for Bayesian Portfolio Selection


Distributional Return Assumptions Alternative to Normality


Mixtures of Normal Distributions


Asymmetric Student's t-Distributions


Stable Distributions


Extreme Value Distributions


Skew-Normal Distributions


The Joint Modeling of Returns


Portfolio Selection in the Setting of Nonnormality: Preliminaries


Maximization of Utility with Higher Moments


Coskewness


Utility with Higher Moments


Distributional Assumptions and Moments


Likelihood, Prior Assumptions, and Posterior Distributions


Predictive Moments and Portfolio Selection


Illustration: HLLM's Approach


Extending The Black-Litterman Approach: Copula Opinion Pooling


Market-Implied and Subjective Information


Views and View Distributions


Combining the Market and the Views: The Marginal Posterior View Distributions


Views Dependence Structure: The Joint Posterior View Distribution


Posterior Distribution of the Market Realizations


Portfolio Construction


Illustration: Meucci's Approach


Extending The Black-Litterman Approach:Stable Distribution


Equilibrium Returns Under Nonnormality


Summary



Some Risk Measures Employed in Portfolio Construction



CVaR Optimization



A Brief Overview of Copulas



Multifactor Equity Risk Models


Preliminaries


Statistical Factor Models


Macroeconomic Factor Models


Fundamental Factor Models


Risk Analysis Using a Multifactor Equity Model


Covariance Matrix Estimation


Risk Decomposition


Return Scenario Generation


Predicting the Factor and Stock-Specific Returns


Risk Analysis in a Scenario-Based Setting


Conditional Value-at-Risk Decomposition


Bayesian Methods for Multifactor Models


Cross-Sectional Regression Estimation


Posterior Simulations


Return Scenario Generation


Illustration


Summary


References


Index