Risk Finance and Asset Pricing: Value, Measurements, and Markets

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