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"This book, Measuring Market Risk with Value at Risk by Vipul Bansal and Pietro Penza, has three advantages over earlier works on the subject. First, it takes a decidedly global approach-an essential ingredient for any comprehensive work on market risk. Second, it ties the scientifically grounded, yet intuitively appealing, VaR measure to earlier, more idiosyncratic measures of market risk that are used in specific market environs (e.g., duration in fixed income). Finally, it encompasses all of the accepted approaches to calculating a VaR measure and presents them in a clearly explained fashion with supporting illustrations and completely worked-out examples." -from the Foreword by John F. Marshall, PhD, Principal, Marshall, Tucker & Associates, LLC "Measuring Market Risk with Value at Risk offers a much-needed intellectual bridge, a translation from the esoteric realm of mathematical finance to the domain of financial managers who seek guidance in applying developments from this important field of research as well as that of MBA-level graduate instruction. I believe the authors have done a commendable job of providing a carefully crafted, highly readable, and most useful work, and intend to recommend it to all those involved in business risk management applications." -Anthony F. Herbst, PhD, Professor of Finance and C.R. and D.S. Carter Chair, The University of Texas, El Paso and Founding editor of The Journal of Financial Engineering (1991-1998) "Finally there's a book that strikes a balance between rigor and application in the area of risk management in the banking industry. This innovative book is a MUST for both novices and professionals alike." -Robert P. Yuyuenyongwatana, PhD, Associate Professor of Finance, Cameron University "Measuring Market Risk with Value at Risk is one of the most complete discussions of this emerging topic in finance that I have seen. The authors develop a logical and rigorous framework for using VaR models, providing both historical references and analytical applications." -Kevin Wynne, PhD, Associate Professor of Finance, Lubin School of Business, Pace University

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CONTENTS
CHAPTER 1 : GLOBAL BANKING INDUSTRY = 1
 Defining a Bank = 2
 The Fall of Retail Banking = 4
 Private Banking = 5
 Global Investment Banking = 6
 Recent Trends in the Global Banking Industry = 7
 Consolidation = 8
 Horizontal Consolidation = 9
 Contamination - The Rise of Global Players = 11
 Strategic Refocusing = 12
 Risk Management and Strategy = 13
 Notes = 15
CHAPTER 2 : RISK MANAGEMENT APPROACHES IN BANKING ACTIVITY = 19
 Types of Risk in Banking Activity = 20
 The Risk Management Process = 23
 Financial Risk Management : Main Characteristics = 25
 The Traditional Approach to Managing Financial Risk : Asset and Liability Management = 26
 From A & LM to Value at Risk - Measuring Financial Risk in an Integrated Framework = 32
 Notes = 35
CHAPTER 3 : FINANCIAL RISK MANAGEMENT AND REGULATIONS = 37
 The Standardized Approach = 38
 The 1995 BIS Market Risk Proposal : The 1996 Amendment = 43
 Internal Models Approach : Generalities = 44
 Internal Models : Qualitative Requirements = 45
 Internal Model : Quantitative and Modeling Requirements = 46
 New Capital Requirements : Combining Credit Risk and Market Risk = 48
 Backtesting of Internal Models = 49
 Stress Testing of Internal Models = 50
 The Pros and Cons of the Standardized Approach and the Internal Models = 51
 Appendix : Regulations and Credit Risk Management = 52
 Shortcomings of the Basle Approach = 55
 Recent Development of Regulatory Bodies on Credit Risk = 57
 Recent Development in Credit Risk Management : Internal Credit Risk Models = 58
 Notes = 60
CHAPTER 4 : A SIMPLE INTRODUCTION TO VALUE AT RISK = 61
 What Is Value at Risk? = 62
 A Formal Definition of VaR = 65
 A Nonparametric Approach = 65
 A Parametric Approach = 67
 Marking-to-Market and VaR with Delta Factors = 70
 Marking-to-Market an IRS = 72
 From Single-Asset Risk to Portfolio Risk = 77
 VaR in Practice : The Case of Chase Manhattan Bank = 81
 Conclusion = 83
 Appendix : Simulating a Stock Index Time Series = 84
 Notes = 84
CHAPTER 5 : MEASURING PRICES AND RETURNS = 87
 Performance Measurement = 87
 Single-Period Returns = 88
 Multiperiodal Returns = 90
 Percentage Returns and Limited Liability = 92
 Properties of Log Returns = 95
 Measuring Returns for a Portfolio of Assets = 102
CHAPTER 6 : STATISTICS FOR PRICES AND RETURNS = 105
 Stochastic Processes and Return Modeling = 105
 Stationary Processes = 107
 Gaussian Processes = 108
 Discrete Stochastic Processes for Measuring Returns = 110
 The White Noise Process = 112
 Autoregressive Processes = 113
 Moving Average Processes = 114
 General ARMA Processes = 115
 The Random Walk = 116
 Continuous Stochastic Processes = 118
 Appendix : Alternative Models for Stock Prices = 123
 Effects on VaR = 126
 Notes = 127
CHAPTER 7 : ESTIMATING AND FORECASTING VOLATILITY = 129
 The Concept of Volatility and Correlation = 129
 Moving-Average Methods for Estimating Volatility = 131
 Autoregressive Conditional Heteroskedasticity Models = 135
 Implied-Volatility Models = 140
 Forecasting the Variance-Covariance Matrix for VaR Calculations = 146
 Conditional Heteroskedasticity in Actual Time Series = 148
 Notes = 149
CHAPTER 8 : THE DISTRIBUTION OF RETURNS = 151
 Unconditional Distribution = 151
 Unconditional Normal Distribution = 153
 Leptokurtic Distribution and Returns = 155
 Mixed Distribution = 156
 Notes = 157
CHAPTER 9 : FRACTAL DISTRIBUTIONS AND APPLICATIONS TO VaR = 159
 Stable Distributions and Their Properties = 159
 Formal Properties of Fractal Distributions = 162
 Effects on the Calculation of VaR = 164
 The Noah Effect = 166
 The Joseph Effect = 168
 Modern Portfolio Theory and Fractal Distributions = 169
 Conclusion = 171
 Appendix : Estimation and Forecasting When Returns Are Not Normally Distributed = 172
 Notes = 180
CHAPTER 10 : FIXED-INCOME MAPPING = 181
 Bond Pricing Using Yield to Maturity = 181
 The Yield Curve = 185
 The Duration Approach = 188
 Convexity = 192
 The Cash-Flow Approach = 196
 Estimating the Yield／Spot-Rate Curve through Econometric Techniques = 200
 Mapping of Cash Flows = 201
 Accounting for "Pull to Par" and "Roll Down" = 204
 Notes = 206
CHAPTER 11 : EQUITY PRICING = 209
 The Standard Approach to Equity Pricing : The Capital Asset Pricing Model = 209
 Using the CAPM for VaR = 210
 Problems in Estimating the CAPM = 211
 An Alternative Approach : The Arbitrage Pricing Theory = 214
 Calculating VaR for CAPM and APT = 215
 Notes = 217
CHAPTER 12 : DERIVATIVE PRICING = 219
 Forwards = 219
 Risk of Forward Contracts = 221
 VaR for Forward Contracts = 223
 VaR for Swaps = 224
 Plain-Vanilla Option Pricing = 224
 Decomposing an Option into Risk Factors = 226
 Using the Greeks : Delta = 227
 Using the Greeks : Gamma = 231
 Delta and Gamma in the Context of VaR = 232
 The Other Greeks : Lambda, Rho, and Theta = 232
 A Comprehensive Example = 233
 Alternative Option Pricing Formulas = 235
 Exotic Options = 236
 Correlation Options = 241
 Calculating VaR for Nonlinear Instruments : A Simplified Approach = 243
 Notes = 245
CHAPTER 13 : CALCULATING VaR : AN OVERVIEW = 247
 Issues for Calculating Value at Risk = 247
 Portfolio Sensitivity Assumptions = 248
 Distributional Assumptions = 251
 Summary of Issues Regarding VaR Calculations = 252
 Notes = 253
CHAPTER 14 : PARAMETRIC NORMAL MODELS = 255
 Portfolio-Normal Method = 255
 Asset-Normal(RiskMetrics) Approach = 257
 The Delta-Normal Method = 258
 Delta-Gamma Methodology = 261
 Confidence Interval for Parametric VaR = 265
 Conclusion = 266,
 Notes = 266
CHAPTER 15 : HISTORICAL SIMULATION MODELS = 267
 Simulation versus Parametric Approach : An Overview = 267
 Defining the Approach = 269
 Assumptions of Historical Simulation Models = 269
 Advantages and Disadvantages of Historical Simulation = 270
CHAPTER 16 : MONTE CARLO SIMULATION MODELS = 273
 Simulating a Single Price = 274
 Simulating Alternative Approaches = 275
 Creating a Random Series of Innovations = 277
 Simulation with Multiple Variables = 278
 The Use of Non-Normal Distributions in Monte Carlo Simulations = 280
 Calculating VaR = 281
 Modeling the Term Structure of Interest Rates = 282
 Conclusion = 284
 Notes = 284
CHAPTER 17 : FINAL REMARKS : LIMITS OF VaR = 285
 Limits of VaR = 285
 Limits of VaR Methodologies = 287
 Note = 292
INDEX = 293