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Fat-Tailed and Skewed Asset Return Distributions Implications for Risk Management, Portfolio Selection, and Option Pricing

by: Rachev, Svetlozar T.; Menn, Christian; Fabozzi, Frank J.

Fat-Tailed and Skewed Asset Return Distributions Implications for Risk Management, Portfolio Selection, and Option Pricing

by: Rachev, Svetlozar T.; Menn, Christian; Fabozzi, Frank J.

ISBN 13:
9780471718864
ISBN 10:
0471718866
Edition: 1st
Format: Hardcover
Copyright: 08/05/2005
Publisher: Wiley

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Summary

While mainstream financial theories and applications assume that asset returns are normally distributed, overwhelming empirical evidence shows otherwise. Yet many professionals don't appreciate the highly statistical models that take this empirical evidence into consideration. Fat-Tailed and Skewed Asset Return Distributions examines this dilemma and offers readers 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. Topics covered in this comprehensive book include an extensive discussion of probability distributions, estimating probability distributions, portfolio selection, alternative risk measures, and much more. 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.

Preface

About the Authors

xiii

CHAPTER 1 Introduction

(10)

Organization of the Book

(3)

References

(3)

PART ONE Probability and Statistics

(108)

CHAPTER 2 Discrete Probability Distributions

(10)

Basic Concepts

(1)

Discrete Probability Distributions Defined

(1)

Bernoulli Distribution

(1)

Binomial Distribution

(1)

Poisson Distribution

(5)

References

(2)

CHAPTER 3 Continuous Probability Distributions

(24)

Continuous Random Variables and Probability Distributions

(6)

The Normal Distribution

(3)

Other Popular Distributions

(14)

References

(1)

CHAPTER 4 Describing a Probability Distribution Function: Statistical Moments and Quantiles

(10)

Location

(1)

Dispersion

(1)

Asymmetry

(1)

Concentration in Tails

(1)

Statistical Moments

(1)

Quantiles

(3)

Sample Moments

(2)

Normal Distribution Revisited

(1)

References

(1)

CHAPTER 5 Joint Probability Distributions

(14)

Joint Probability Distributions Defined

(1)

Marginal Distributions

(1)

Dependence of Random Variables

(1)

Multivariate Normal Distribution

(7)

Elliptical Distributions

(3)

References

(1)

CHAPTER 6 Copulas

(10)

Drawbacks of Correlation

(1)

Overcoming the Drawbacks of Correlation: Copulas

(1)

Mathematical Definition of Copulas

(1)

References

(7)

CHAPTER 7 Stable Distributions

(12)

Properties of the Stable Distribution

(3)

Considerations in the Use of the Stable Distribution

(4)

Truncated Stable Distributions

(3)

References

(1)

CHAPTER 8 Estimation Methodologies

(26)

Fitting Probability Distributions by Maximum Likelihood Estimation

(3)

Confidence Bounds

(5)

Hypothesis Tests and P-Value

101

(4)

Relationship between Hypothesis Tests and Confidence Bounds

105

(4)

Fitting Stable Distributions

109

(2)

Comparing Probability Distributions: Testing for the Goodness of Fit

111

(6)

References

117

(2)

PART TWO Stochastic Processes

119

(42)

CHAPTER 9 Stochastic Processes in Discrete Time and Time Series Analysis

121

(22)

Stochastic Processes in Discrete Time

121

(9)

ARCH and GARCH Models

130

(3)

ARMA-GARCH Illustration

133

(7)

References

140

(3)

CHAPTER 10 Stochastic Processes in Continuous Time

143

(18)

The Poisson Process

144

(3)

Brownian Motion

147

(8)

Stochastic Differential Equations

155

(1)

Levy Processes

156

(2)

References

158

(3)

PART THREE Portfolio Selection

161

(52)

CHAPTER 11 Equity and Bond Return Distributions

163

(18)

Evidence from the U.S. Stock Market

163

(4)

Evidence from the U.S. Bond Market

167

(11)

References

178

(3)

CHAPTER 12 Risk Measures and Portfolio Selection

181

(18)

Desirable Features of Investment Risk Measures

181

(4)

Alternative Risk Measures for Portfolio Selection

185

(9)

References

194

(5)

CHAPTER 13 Risk Measures in Portfolio Optimization and Performance Measures

199

(14)

Efficient Frontiers and Return Distribution Assumption

200

(3)

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

203

(3)

Performance Measures

206

(4)

References

210

(3)

PART FOUR Risk Management

213

(80)

CHAPTER 14 Market Risk

215

(38)

Adoption of VaR for Measuring Market Risk

216

(2)

VaR and Bank Capital Requirements

218

(4)

Computation of VaR

222

(6)

Evaluation of VaR Methods: Strengths and Weaknesses

228

(2)

Stable Modeling of VaR

230

(9)

Alternative to VaR: Expected Tail Loss

239

(7)

References

246

(3)

Appendix: Coherent Risk Measures

249

(4)

CHAPTER 15 Credit Risk

253

(30)

Credit Risk

253

(1)

Credit Risk Framework for Banks: Basel I and Basel II

254

(2)

Overview of Credit Risk Modeling

256

(7)

Credit Risk Management Tools

263

(4)

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

267

(5)

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

272

(4)

Building An Econometric Model for the Intensity-Based Model

276

(2)

References

278

(5)

CHAPTER 16 Operational Risk

283

(10)

Operational Risk Defined

283

(3)

Capital Requirement for Operational Risk

286

(1)

Comparison of Market, Credit, and Operational Risk Distributions

287

(1)

Aggregated Stochastic Models for Operational Risk

288

(3)

References

291

(2)

PART FIVE Option Pricing

293

(60)

CHAPTER 17 Introduction to Option Pricing and the Binomial Model

295

(24)

Options Contracts

295

(2)

Basic Components of the Option Price

297

(1)

Boundary Conditions for the Price of an Option

298

(2)

Discrete-Time Option Pricing: Binomial Model

300

(12)

Convergence of the Binomial Model

312

(4)

References

316

(3)

CHAPTER 18 Black-Scholes Option Pricing Model

319

(18)

Motivation

319

(3)

Black-Scholes Formula

322

(1)

Computing a Call Option Price

323

(2)

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

325

(6)

Computing a Put Option Price

331

(1)

Assumptions Underlying the Black-Scholes Model and Basic Extensions

331

(3)

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

334

(2)

References

336

(1)

CHAPTER 19 Extension of the Black-Scholes Model and Alternative Approaches

337

(16)

The "Smile Effect"

337

(2)

Continuous-Time Models

339

(6)

Discrete-Time Models

345

(4)

References

349

(4)

INDEX

353

Amazon no longer offers textbook rentals. We do!

Fat-Tailed and Skewed Asset Return Distributions Implications for Risk Management, Portfolio Selection, and Option Pricing

Fat-Tailed and Skewed Asset Return Distributions Implications for Risk Management, Portfolio Selection, and Option Pricing

9780471718864

0471718866

Summary

Author Biography

Table of Contents

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