Fat-tailed and skewed asset return distributions : implications for risk management, portfolio selection, and option pricing / Sveltozar T. Rachev, Frank J. Fabozzi, Christian Menn.

Format:

Book

Author/Creator:

Rachev, S. T. (Svetlozar Todorov)

Contributor:

Fabozzi, Frank J.

Menn, Christian.

Series:

Frank J. Fabozzi series

The Frank J. Fabozzi series

Language:

English

Subjects (All):

Portfolio management.

Risk management.

Physical Description:

xiii, 369 pages : illustrations ; 24 cm.

Place of Publication:

Hoboken, N.J. : Wiley, 2005.

Summary:

Fat-Tailed and Skewed Asset Return Distributions While mainstream financial theories and applications assume that asset returns are normally distributed, the overwhelming empirical evidence shows otherwise. Yet many professionals fail to appreciate the highly statistical models that take this empirical evidence into consideration.

Svetlozar Rachev, Christian Menn, and Frank Fabozzi understand this dilemma, and in Fat-Tailed and Skewed Asset Return Distributions, they offer you 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.

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.

Contents:

Part 1 Probability and Statistics 11

Chapter 2 Discrete Probability Distributions 13

Discrete Probability Distributions Defined 14

Bernoulli Distribution 15

Binomial Distribution 15

Poisson Distribution 16

Chapter 3 Continuous Probability Distributions 23

Continuous Random Variables and Probability Distributions 23

The Normal Distribution 29

Other Popular Distributions 32

Chapter 4 Describing a Probability Distribution Function: Statistical Moments and Quantiles 47

Location 47

Dispersion 48

Asymmetry 48

Concentration in Tails 48

Statistical Moments 49

Quantiles 50

Sample Moments 53

Normal Distribution Revisited 55

Chapter 5 Joint Probability Distributions 57

Joint Probability Distributions Defined 57

Marginal Distributions 58

Dependence of Random Variables 59

Multivariate Normal Distribution 60

Elliptical Distributions 67

Chapter 6 Copulas 71

Drawbacks of Correlation 71

Overcoming the Drawbacks of Correlation: Copulas 72

Mathematical Definition of Copulas 73

Chapter 7 Stable Distributions 81

Properties of the Stable Distribution 82

Considerations in the Use of the Stable Distribution 85

Truncated Stable Distributions 89

Chapter 8 Estimation Methodologies 93

Fitting Probability Distributions by Maximum Likelihood Estimation 93

Confidence Bounds 96

Hypothesis Tests and P-Value 101

Relationship between Hypothesis Tests and Confidence Bounds 105

Fitting Stable Distributions 109

Comparing Probability Distributions: Testing for the Goodness of Fit 111

Part 2 Stochastic Processes 119

Chapter 9 Stochastic Processes in Discrete Time and Time Series Analysis 121

Stochastic Processes in Discrete Time 121

ARCH and GARCH Models 130

ARMA-GARCH Illustration 133

Chapter 10 Stochastic Processes in Continuous Time 143

The Poisson Process 144

Brownian Motion 147

Stochastic Differential Equations 155

Levy Processes 156

Part 3 Portfolio Selection 161

Chapter 11 Equity and Bond Return Distributions 163

Evidence from the U.S. Stock Market 163

Evidence from the U.S. Bond Market 167

Chapter 12 Risk Measures and Portfolio Selection 181

Desirable Features of Investment Risk Measures 181

Alternative Risk Measures for Portfolio Selection 185

Chapter 13 Risk Measures in Portfolio Optimization and Performance Measures 199

Efficient Frontiers and Return Distribution Assumption 200

Portfolio Optimization and Conditional Value-at-Risk versus Value-at-Risk 203

Performance Measures 206

Part 4 Risk Management 213

Chapter 14 Market Risk 215

Adoption of VaR for Measuring Market Risk 216

VaR and Bank Capital Requirements 218

Computation of VaR 222

Evaluation of VaR Methods: Strengths and Weaknesses 228

Stable Modeling of VaR 230

Alternative to VaR: Expected Tail Loss 239

Appendix Coherent Risk Measures 249

Chapter 15 Credit Risk 253

Credit Risk 253

Credit Risk Framework for Banks: Basel I and Basel II 254

Overview of Credit Risk Modeling 256

Credit Risk Management Tools 263

An Integrated Market and Credit Risk Management Framework Based on the Structural Approach 267

An Integrated Market and Credit Risk Management Framework Based on the Intensity-Based Model 272

Building An Econometric Model for the Intensity-Based Model 276

Chapter 16 Operational Risk 283

Operational Risk Defined 283

Capital Requirement for Operational Risk 286

Comparison of Market, Credit, and Operational Risk Distributions 287

Aggregated Stochastic Models for Operational Risk 288

Part 5 Option Pricing 293

Chapter 17 Introduction to Option Pricing and the Binomial Model 295

Options Contracts 295

Basic Components of the Option Price 297

Boundary Conditions for the Price of an Option 298

Discrete-Time Option Pricing: Binomial Model 300

Convergence of the Binomial Model 312

Chapter 18 Black-Scholes Option Pricing Model 319

Motivation 319

Black-Scholes Formula 322

Computing a Call Option Price 323

Sensitivity of Option Price to a Change in Factors: The Greeks 325

Computing a Put Option Price 331

Assumptions Underlying the Black-Scholes Model and Basic Extensions 331

Black-Scholes Model Applied to the Pricing of Options on Bonds: Importance of Assumptions 334

Chapter 19 Extension of the Black-Scholes Model and Alternative Approaches 337

The "Smile Effect" 337

Continuous-Time Models 339

Discrete-Time Models 345.

Notes:

Includes bibliographical references and index.

ISBN:

0471718866

OCLC:

67771565