Praise for Risk Finance and Asset Pricing: Value, Measurements, and Markets
"An impressive text on financial engineering that stands out as a logical and well-written description of many of the important models in quantitative finance, providing numerous relevant examples and instructive problems that help to drill home these conceptual underpinnings. The combination is especially useful for the pedagogic delivery of materials in financial engineering courses andpractitioner applications of real-world issues. I highly recommend it to enhance student andpractitioner understanding of financial markets."
—Edward I. Altman, Max L. Heine Professor of Finance and Director of Credit and Debt Markets Research Program at the NYU Salomon Center, Stern School of Business
"Recession frequently leads both students and the general public to realize that they have given far from sufficient attention to the role and nature of risk in the arena of investment. All too often, they have been lured to their financial destruction by mysterious types of assets whose nature they did not understand. Students in the fields of finance and investment, in particular, are surely ready for guidance in the field. Here is a book that provides it very effectively. Comprehensive, rigorous, and clearly written, it will be considered indispensible by instructors, students, and thoughtful investors."
—William Baumol, Professor of Economics and Director, C.V. Starr Center for Applied Economics, NYU
"Charles Tapiero has raised masterfully both the essential problems and questions that we are confronting in a post financial crisis world and reveals the many approaches and techniques that can be used to provide answers for better financial risk management."
—Professor Alain Bensoussan, Distinguished Research Professor of Operations Management, Director of the International Center for Decision and Risk Analysis, University of Texas
"Charles Tapiero is a world-renowned scholar who has made numerous contributions in the field of risk management. His book is a timely and much needed integration of the latest developments in theory and practice. Replete with real-world examples, it is a must-read for practitioners, researchers, and students interested in the field of financial engineering and risk management."
—Lorne N. Switzer, Professor of Finance and Associate Director, Institute for Governance in Private and Public Organizations, John Molson School of Business, Concordia University
"Charles Tapiero is one of the best collaborators I ever had. He ferrets out hidden risks and reduces complexity to being tractable. He writes in a clear style without taxing the reader."
—Nassim Nicholas Taleb, Author of The Black Swan, Distinguished Professor of Risk Engineering, NYU-Polytechnic Institute
Introduction xv
Who This Book Is For xvi
How This Book Is Structured xvii
What's on the Companion Web Site xix
CHAPTER 1 Risk, Finance, Corporate Management, and Society 1
Overview 1
Risks Everywhere—A Consequence of Uncertainty 1
Risk and Finance: Basic Concepts 4
Finance and Risks 6
Financial Instruments 7
Securities or Stocks 7
Example: An IBM Day-Trades Record 7
Bonds 9
Portfolios 10
Example: Constructing a Portfolio 11
Derivatives and Options 12
Real and Financial Assets 15
Financial Markets 16
Option Contracts 16
Problem 1.1: Options and Their Prices 17
Options and Specific Needs 18
Example: Options and The Price of Equity 19
Example: Management Stock Options 19
Options and Trading in Specialized Markets 20
Trading the CO2 Index 20
Trading on Commodities (Metal, Gold, Silver, Corn, Oil) 20
Trading the Weather and Insurance 21
Securitization, Mortgage-Backed Securities, and Credit Derivatives 21
Real-Life Crises and Finance 22
The ARS Crisis 22
The Banking–Money System Crisis 23
The 2008 Meltdown and Financial Theory 24
Finance and Ethics 27
Crime and Punishment 29
Summary 30
CHAPTER 2 Applied Finance 35
Overview 35
Finance and Practice 35
Risk Finance and Insurance 35
Infrastructure Finance 36
Finance, the Environment, and Exchange-Traded Funds Indexes 37
Finance and Your Pension 38
Contract Pricing and Franchises 39
Catastrophic Risks, Insurance and Finance 40
The Price of Safety 41
The Price of Inventories 42
Pricing Reliability and Warranties 42
The Price of Quality Claims 43
Financial Risk Pricing: A Historical Perspective 44
Essentials of Financial Risk Management 47
Comprehensive Financial Risk Management 49
Technology and Complexity 49
Retailing and Finance 51
Finance, Cyber Risks, and Terrorism 52
IT and Madoff 52
Virtual Markets 52
Virtual Products 52
Virtual Markets Participants 53
Virtual Economic Universes 53
Market Making and Pricing Practice 53
Market Makers, Market Liquidity, and Bid-Ask Spreads 55
Alternative Market Structures 56
Summary 57
CHAPTER 3 Risk Measurement and Volatility 63
Overview 63
Risk, Volatility, and Measurement 63
Moments and Measures of Volatility 66
Expectations, Volatility, Skewness, Kurtosis, and the Range 67
Example: IBM Returns Statistics 69
Example: Moments and the CAPM 70
Problem 3.1: Calculating the Beta of a Security 72
Modeling Rates of Return 72
Models of Rate of Returns 73
Statistical Estimations 77
Least Squares Estimation 77
Maximum Likelihood 79
ARCH and GARCH Estimators 80
Example: The AR(1)-ARCH(1) Model 81
Example: A GARCH (1,1) Model 83
High-Low Estimators of Volatility 83
Extreme Measures, Volume, and Intraday Prices 84
Statistical Orders, Volume, and Prices 85
Problem 3.2: The Probability of the Range 87
Intraday Prices and Extreme Distributions 87
Data Transformation 88
Example: Taylor Series 89
Value at Risk and Risk Exposure 90
VaR and Its Application 92
Example: VaR and Shortfall 94
Example: VaR, Normal ROR, and Portfolio Design 95
The Estimation of Gains and Losses 97
Summary 99
CHAPTER 4 Risk Finance Modeling and Dependence 109
Overview 109
Introduction 109
Dependence and Probability Models 111
Statistical Dependence 111
Dependence and Quantitative Statistical Probability Models 113
Many Sources of Normal Risk: Aggregation and Risk Factors Reduction 114
Example: Risk Factors Aggregation 115
Example: Principal Component Analysis (PCA) 116
Example: A Bivariate Data Matrix and PCA 117
Example: A Market Index and PCA 119
Dependence and Copulas 120
Example: The Gumbel Copula, the Highs and the Lows 123
Example: Copulas and Conditional Dependence 124
Example: Copulas and the Conditional Distribution 125
Financial Modeling and Intertemporal Models 126
Time, Memory, and Causal Dependence 127
Quantitative Time and Change 129
Persistence and Short-term Memory 130
The R/S Index 133
Summary 135
CHAPTER 5 Risk, Value, and Financial Prices 141
Overview 141
Value and Price 141
Utility, Risk, and Money 143
Utility’s Normative Principles: A Historical Perspective 144
Prelude to Utility and Expected Utility 145
Lotteries and Utility Functions 147
Example: The Utility of a Lottery 148
Quadratic Utility and Portfolio Pricing 149
Utility and an Insurance Exchange 150
Example: The Power Utility Function 151
Example: Valuation and the Pricing of Cash Flows 152
Example: Risk and the Financial Meltdown 153
Utility Rational Foundations 155
The Risk Premium 155
Utility and Its Behavioral Derivatives 156
Examples: Specific Utility Functions 159
The Price and the Utility of Consumption 161
Example: Kernel Pricing and the Exponential Utility Function 164
Example: The Pricing Kernel and the CAPM 165
Example: Kernel Pricing and the HARA Utility Function 166
The Price and Demand for Insurance 167
Summary 170
CHAPTER 6 Applied Utility Finance 177
Overview 177
Risk and the Utility of Time 177
Expected Utility and the Time Utility Price of Money 177
Risk, Safety, and Reliability 178
Asset Allocation and Investments 180
Example: A Two-Securities Problem 182
Example: A Two-Stocks Portfolio 184
Problem 6.1: The Efficiency Frontier 185
Problem 6.2: A Two-Securities Portfolio 187
Conditional Kernel Pricing and the Price of Infrastructure Investments 188
Conditional Kernel Pricing and the Pricing of Inventories 191
Agency and Utility 193
Example: A Linear Risk-Sharing Rule 194
Information Asymmetry: Moral Hazard and Adverse Selection 195
Adverse Selection 196
The Moral Hazard Problem 197
Signaling and Screening 199
Summary 200
CHAPTER 7 Derivative Finance and Complete Markets 205
Overview 205
The Arrow-Debreu Fundamental Approach to Asset Pricing 206
Example: Generalization to n States 210
Example: Binomial Option Pricing 212
Problem 7.1: The Implied Risk-Neutral Probability 213
Example: The Price of a Call Option 213
Example: A Generalization to Multiple Periods 215
Problem 7.2: Options and Their Prices 218
Put-Call Parity 218
Problem 7.3: Proving the Put-Call Parity 219
Example: Put-Call Parity and Dividend Payments 219
Problem 7.4: Options Put-Call Parity 220
The Price Deflator and the Pricing Martingale 220
Pricing and Complete Markets 222
Risk-Neutral Pricing and Market Completeness 224
Options Galore 226
Packaged and Binary Options 227
Example: Look-Back Options 227
Example: Asian Options 227
Example: Exchange Options 228
Example: Chooser Options 228
Example: Barrier and Other Options 228
Example: Passport Options 229
Options and Their Real Uses 229
Fixed-Income Problems 231
Example: Pricing a Forward 231
Example: Pricing a Fixed-Rate Bond 232
Pricing a Term Structure of Interest Rates 232
Example: The Term Structure of Interest Rates 234
Problem 7.5: Annuities and Obligations 235
Options Trading, Speculation, and Risk Management 235
Option Trading Strategies 237
Problem 7.6: Portfolio Strategies 240
Summary 245
Appendix A: Martingales 246
Essentials of Martingales 246
The Change of Measures and Martingales 248
Example: Change of Measure in a Binomial Model 249
Example: A Two-Stage Random Walk and the Radon Nikodym Derivative 251
Appendix B: Formal Notations, Key Terms, and Definitions 253
CHAPTER 8 Options Applied 259
Overview 259
Option Applications 259
Risk-Free Portfolios and Immunization 260
Selling Short 261
Future Prices 262
Problem 8.1: Pricing a Multiperiod Forward 264
Pricing and New Insurance Business 264
Example: Options Implied Insurance Pricing 266
Option Pricing in a Trinomial Random Walk 267
Pricing and Spread Options 269
Self-Financing Strategy 270
Random Volatility and Options Pricing 271
Real Assets and Real Options 273
The Option to Acquire the License for a New Technology 275
The Black-Scholes Vanilla Option 276
The Binomial Process as a Discrete Time Approximation 277
The Black-Scholes Model Option Price and Portfolio Replication 278
Risk-Neutral Pricing and the Pricing Martingale 281
The Greeks and Their Applications 284
Summary 287
CHAPTER 9 Credit Scoring and the Price of Credit Risk 291
Overview 291
Credit and Money 291
Credit and Credit Risk 294
Pricing Credit Risk: Principles 296
Credit Scoring and Granting 299
What Is an Individual Credit Score? 299
Bonds Rating or Scoring Business Enterprises 300
Scoring/Rating Financial Enterprises and Financial Products 301
Credit Scoring: Real Approaches 304
The Statistical Estimation of Default 305
Example: A Separatrix 310
Example: The Separatrix and Bayesian Probabilities 311
Probability Default Models 312
Example: A Bivariate Dependent Default Distribution 314
Example: A Portfolio of Default Loans 315
Example: A Portfolio of Dependent Default Loans 316
Problem 9.1: The Joint Bernoulli Default Distribution 317
Credit Granting 317
Example: Credit Granting and Creditor’s Risks 319
Example: A Bayesian Default Model 322
Example: A Financial Approach 323
Example: An Approximate Solution 326
Problem 9.2: The Rate of Return of Loans 327
The Reduced Form (Financial) Model 327
Example: Calculating the Spread of a Default Bond 328
Example: The Loan Model Again 329
Example: Pricing Default Bonds 330
Example: Pricing Default Bonds and the Hazard Rate 331
Examples 332
Example: The Bank Interest Rate on a House Loan 333
Example: Buy Insurance to Protect the Portfolio from Loan Defaults 333
Problem 9.3: Use the Portfolio as an Underlying and Buy or Sell Derivatives on This Underlying 334
Problem 9.4: Lending Rates of Return 334
Credit Risk and Collateral Pricing 334
Example: Hedge Funds Rates of Return 337
Example: Equity-Linked Life Insurance 338
Example: Default and the Price of Homes 339
Example: A Bank’s Profit from a Loan 341
Risk Management and Leverage 342
Summary 344
CHAPTER 10 Multi-Name and Structured Credit Risk Portfolios 353
Overview 353
Introduction 353
Credit Default Swaps 357
Example: Total Return Swaps 359
Pricing Credit Default Swaps—The Implied Market Approach 359
Example: The CDS Price Spread 360
Example: An OTC (Swap) Contract under Risk-Neutral Pricing and Collateral Prices 362
Example: Pricing a Project Launch 364
Credit Derivatives: A Historical Perspective 368
Credit Derivatives: Historical Modeling 369
Credit Derivatives and Product Innovation 372
CDO Example: Collateralized Mortgage Obligations (CMOs) 376
Example: The CDO and SPV 377
Modeling Credit Derivatives 379
CDO: Quantitative Models 380
Example: A CDO with Numbers 380
Example: A CDO of Zero Coupon Bonds 382
Example: A CDO of Default Coupon-Paying bonds 385
Example: A CDO of Rated Bonds 387
Examples: Default Models for Bonds 391
CDO Models and Price Applications 395
Example: The KMV Loss Model 396
CDOs of Baskets of Various Assets 397
Credit Risk versus Insurance 398
Summary 399
CHAPTER 11 Engineered Implied Volatility and Implied Risk-Neutral Distributions 407
Overview 407
Introduction 407
The Implied Volatility 409
Example: The Implied Volatility in a Lognormal Process 410
The Dupire Model 411
The Implied Risk-Neutral Distribution 412
Example: An Implied Binomial Distribution 413
Example: Calculating the Implied Risk-Neutral Probability 414
Implied Distributions: Parametric Models 417
Example: The Generalized Beta of the Second Kind 418
The A-parametric Approach and the Black-Scholes Model 420
Example: The Shimko Technique 421
The Implied Risk Neutral Distribution and Entropy 423
Examples and Applications 426
Risk Attitude, Implied Risk-Neutral Distribution and Entropy 431
Summary 432
Appendix: The Implied Volatility—The Dupire Model 433
Acknowledgments 439
About the Author 441
Index 443
Overview
Praise for Risk Finance and Asset Pricing: Value, Measurements, and Markets
"An impressive text on financial engineering that stands out as a logical and well-written description of many of the important models in quantitative finance, providing numerous relevant examples and instructive problems that help to drill home these conceptual underpinnings. The combination is especially useful for the pedagogic delivery of materials in financial engineering courses andpractitioner applications of real-world issues. I ...