Over the past two decades, financial firms, companies, and governments have shifted greater attention to financial manipulations in which they capitalized on leverage and short–term returns. These actually resulted in an explosive and global growth in financial activity. A financial Pandora′s box had been opened, and countries and blue chip corporations believing in perpetual growth and once thought too big to fail, found themselves strangled with a debt they were not able to bear.

The recent market melt–down and credit liquidity crisis created full realization that complex financial products when misunderstood and misused can have devastating effects. *Risk Finance and Asset Pricing: Value, Measurements, and Markets *is a comprehensive introduction to financial engineering that presents the foundations of asset pricing and risk management, while stressing real–world applications.

Written for both beginning and practicing financial engineers, author Charles Tapiero the Topfer Distinguished Professor of Financial Engineering and Technology Management at the NYU Polytechnic Institute provides:

- A non–quantitative introduction to the business of finance, risk, and their many applications
- An overview of the statistical approaches for measuring risk
- An introduction to the concept of utility and financial risk management
- An outline of the Arrow–Debreu framework in discrete states and time for assets and derivatives (options) pricing
- An outline of credit risk, scoring, and complex structured financial products such as credit derivatives, their models, their demystification, pricing, and finally, a cursory view of technical approaches to implied pricing

Each chapter includes a summary of the techniques described, and concludes with a series of problems so readers can test what they′ve learned.

Financial engineering, despite its challenges and opportunities, when misunderstood, has the potential to wreak havoc on world economies and individual portfolios. *Risk Finance and Asset Pricing* presents a new direction in financial engineering education that combines reality and theory so that risk finance might again work as intended.

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

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