Risk Finance and Asset Pricing

CHARLES S. TAPIERO is the Topfer Distinguished Professor of Financial Engineering and Technology Management at the New York University Polytechnic Institute. He is also Chair and founder of the Department of Finance and Risk Engineering, as well as cofounder and co–Editor in Chief of Risk and Decision Analysis. An active researcher and consultant, Professor Tapiero has published over 350 papers and thirteen books on a broad range of issues spanning risk analysis, actuarial and financial risk engineering, and management, including Risk and Financial Management: Mathematical and Computational Methods, also by Wiley.

• Introduction xv Who This Book Is For xviHow This Book Is Structured xviiWhat's on the Companion Web Site xixCHAPTER 1 Risk, Finance, Corporate Management, and Society 1Overview 1Risks Everywhere—A Consequence of Uncertainty 1Risk and Finance: Basic Concepts 4Finance and Risks 6Financial Instruments 7Securities or Stocks 7Example: An IBM Day-Trades Record 7Bonds 9Portfolios 10Example: Constructing a Portfolio 11Derivatives and Options 12Real and Financial Assets 15Financial Markets 16Option Contracts 16Problem 1.1: Options and Their Prices 17Options and Specific Needs 18Example: Options and The Price of Equity 19Example: Management Stock Options 19Options and Trading in Specialized Markets 20Trading the CO2 Index 20Trading on Commodities (Metal, Gold, Silver, Corn, Oil) 20Trading the Weather and Insurance 21Securitization, Mortgage-Backed Securities, and Credit Derivatives 21Real-Life Crises and Finance 22The ARS Crisis 22The Banking–Money System Crisis 23The 2008 Meltdown and Financial Theory 24Finance and Ethics 27Crime and Punishment 29Summary 30CHAPTER 2 Applied Finance 35Overview 35Finance and Practice 35Risk Finance and Insurance 35Infrastructure Finance 36Finance, the Environment, and Exchange-Traded Funds Indexes 37Finance and Your Pension 38Contract Pricing and Franchises 39Catastrophic Risks, Insurance and Finance 40The Price of Safety 41The Price of Inventories 42Pricing Reliability and Warranties 42The Price of Quality Claims 43Financial Risk Pricing: A Historical Perspective 44Essentials of Financial Risk Management 47Comprehensive Financial Risk Management 49Technology and Complexity 49Retailing and Finance 51Finance, Cyber Risks, and Terrorism 52IT and Madoff 52Virtual Markets 52Virtual Products 52Virtual Markets Participants 53Virtual Economic Universes 53Market Making and Pricing Practice 53Market Makers, Market Liquidity, and Bid-Ask Spreads 55Alternative Market Structures 56Summary 57CHAPTER 3 Risk Measurement and Volatility 63Overview 63Risk, Volatility, and Measurement 63Moments and Measures of Volatility 66Expectations, Volatility, Skewness, Kurtosis, and the Range 67Example: IBM Returns Statistics 69Example: Moments and the CAPM 70Problem 3.1: Calculating the Beta of a Security 72Modeling Rates of Return 72Models of Rate of Returns 73Statistical Estimations 77Least Squares Estimation 77Maximum Likelihood 79ARCH and GARCH Estimators 80Example: The AR(1)-ARCH(1) Model 81Example: A GARCH (1,1) Model 83High-Low Estimators of Volatility 83Extreme Measures, Volume, and Intraday Prices 84Statistical Orders, Volume, and Prices 85Problem 3.2: The Probability of the Range 87Intraday Prices and Extreme Distributions 87Data Transformation 88Example: Taylor Series 89Value at Risk and Risk Exposure 90VaR and Its Application 92Example: VaR and Shortfall 94Example: VaR, Normal ROR, and Portfolio Design 95The Estimation of Gains and Losses 97Summary 99CHAPTER 4 Risk Finance Modeling and Dependence 109Overview 109Introduction 109Dependence and Probability Models 111Statistical Dependence 111Dependence and Quantitative Statistical Probability Models 113Many Sources of Normal Risk: Aggregation and Risk Factors Reduction 114Example: Risk Factors Aggregation 115Example: Principal Component Analysis (PCA) 116Example: A Bivariate Data Matrix and PCA 117Example: A Market Index and PCA 119Dependence and Copulas 120Example: The Gumbel Copula, the Highs and the Lows 123Example: Copulas and Conditional Dependence 124Example: Copulas and the Conditional Distribution 125Financial Modeling and Intertemporal Models 126Time, Memory, and Causal Dependence 127Quantitative Time and Change 129Persistence and Short-term Memory 130The R/S Index 133Summary 135CHAPTER 5 Risk, Value, and Financial Prices 141Overview 141Value and Price 141Utility, Risk, and Money 143Utility’s Normative Principles: A Historical Perspective 144Prelude to Utility and Expected Utility 145Lotteries and Utility Functions 147Example: The Utility of a Lottery 148Quadratic Utility and Portfolio Pricing 149Utility and an Insurance Exchange 150Example: The Power Utility Function 151Example: Valuation and the Pricing of Cash Flows 152Example: Risk and the Financial Meltdown 153Utility Rational Foundations 155The Risk Premium 155Utility and Its Behavioral Derivatives 156Examples: Specific Utility Functions 159The Price and the Utility of Consumption 161Example: Kernel Pricing and the Exponential Utility Function 164Example: The Pricing Kernel and the CAPM 165Example: Kernel Pricing and the HARA Utility Function 166The Price and Demand for Insurance 167Summary 170CHAPTER 6 Applied Utility Finance 177Overview 177Risk and the Utility of Time 177Expected Utility and the Time Utility Price of Money 177Risk, Safety, and Reliability 178Asset Allocation and Investments 180Example: A Two-Securities Problem 182Example: A Two-Stocks Portfolio 184Problem 6.1: The Efficiency Frontier 185Problem 6.2: A Two-Securities Portfolio 187Conditional Kernel Pricing and the Price of Infrastructure Investments 188Conditional Kernel Pricing and the Pricing of Inventories 191Agency and Utility 193Example: A Linear Risk-Sharing Rule 194Information Asymmetry: Moral Hazard and Adverse Selection 195Adverse Selection 196The Moral Hazard Problem 197Signaling and Screening 199Summary 200CHAPTER 7 Derivative Finance and Complete Markets 205Overview 205The Arrow-Debreu Fundamental Approach to Asset Pricing 206Example: Generalization to n States 210Example: Binomial Option Pricing 212Problem 7.1: The Implied Risk-Neutral Probability 213Example: The Price of a Call Option 213Example: A Generalization to Multiple Periods 215Problem 7.2: Options and Their Prices 218Put-Call Parity 218Problem 7.3: Proving the Put-Call Parity 219Example: Put-Call Parity and Dividend Payments 219Problem 7.4: Options Put-Call Parity 220The Price Deflator and the Pricing Martingale 220Pricing and Complete Markets 222Risk-Neutral Pricing and Market Completeness 224Options Galore 226Packaged and Binary Options 227Example: Look-Back Options 227Example: Asian Options 227Example: Exchange Options 228Example: Chooser Options 228Example: Barrier and Other Options 228Example: Passport Options 229Options and Their Real Uses 229Fixed-Income Problems 231Example: Pricing a Forward 231Example: Pricing a Fixed-Rate Bond 232Pricing a Term Structure of Interest Rates 232Example: The Term Structure of Interest Rates 234Problem 7.5: Annuities and Obligations 235Options Trading, Speculation, and Risk Management 235Option Trading Strategies 237Problem 7.6: Portfolio Strategies 240Summary 245Appendix A: Martingales 246Essentials of Martingales 246The Change of Measures and Martingales 248Example: Change of Measure in a Binomial Model 249Example: A Two-Stage Random Walk and the Radon Nikodym Derivative 251Appendix B: Formal Notations, Key Terms, and Definitions 253CHAPTER 8 Options Applied 259Overview 259Option Applications 259Risk-Free Portfolios and Immunization 260Selling Short 261Future Prices 262Problem 8.1: Pricing a Multiperiod Forward 264Pricing and New Insurance Business 264Example: Options Implied Insurance Pricing 266Option Pricing in a Trinomial Random Walk 267Pricing and Spread Options 269Self-Financing Strategy 270Random Volatility and Options Pricing 271Real Assets and Real Options 273The Option to Acquire the License for a New Technology 275The Black-Scholes Vanilla Option 276The Binomial Process as a Discrete Time Approximation 277The Black-Scholes Model Option Price and Portfolio Replication 278Risk-Neutral Pricing and the Pricing Martingale 281The Greeks and Their Applications 284Summary 287CHAPTER 9 Credit Scoring and the Price of Credit Risk 291Overview 291Credit and Money 291Credit and Credit Risk 294Pricing Credit Risk: Principles 296Credit Scoring and Granting 299What Is an Individual Credit Score? 299Bonds Rating or Scoring Business Enterprises 300Scoring/Rating Financial Enterprises and Financial Products 301Credit Scoring: Real Approaches 304The Statistical Estimation of Default 305Example: A Separatrix 310Example: The Separatrix and Bayesian Probabilities 311Probability Default Models 312Example: A Bivariate Dependent Default Distribution 314Example: A Portfolio of Default Loans 315Example: A Portfolio of Dependent Default Loans 316Problem 9.1: The Joint Bernoulli Default Distribution 317Credit Granting 317Example: Credit Granting and Creditor’s Risks 319Example: A Bayesian Default Model 322Example: A Financial Approach 323Example: An Approximate Solution 326Problem 9.2: The Rate of Return of Loans 327The Reduced Form (Financial) Model 327Example: Calculating the Spread of a Default Bond 328Example: The Loan Model Again 329Example: Pricing Default Bonds 330Example: Pricing Default Bonds and the Hazard Rate 331Examples 332Example: The Bank Interest Rate on a House Loan 333Example: Buy Insurance to Protect the Portfolio from Loan Defaults 333Problem 9.3: Use the Portfolio as an Underlying and Buy or Sell Derivatives on This Underlying 334Problem 9.4: Lending Rates of Return 334Credit Risk and Collateral Pricing 334Example: Hedge Funds Rates of Return 337Example: Equity-Linked Life Insurance 338Example: Default and the Price of Homes 339Example: A Bank’s Profit from a Loan 341Risk Management and Leverage 342Summary 344CHAPTER 10 Multi-Name and Structured Credit Risk Portfolios 353Overview 353Introduction 353Credit Default Swaps 357Example: Total Return Swaps 359Pricing Credit Default Swaps—The Implied Market Approach 359Example: The CDS Price Spread 360Example: An OTC (Swap) Contract under Risk-Neutral Pricing and Collateral Prices 362Example: Pricing a Project Launch 364Credit Derivatives: A Historical Perspective 368Credit Derivatives: Historical Modeling 369Credit Derivatives and Product Innovation 372CDO Example: Collateralized Mortgage Obligations (CMOs) 376Example: The CDO and SPV 377Modeling Credit Derivatives 379CDO: Quantitative Models 380Example: A CDO with Numbers 380Example: A CDO of Zero Coupon Bonds 382Example: A CDO of Default Coupon-Paying bonds 385Example: A CDO of Rated Bonds 387Examples: Default Models for Bonds 391CDO Models and Price Applications 395Example: The KMV Loss Model 396CDOs of Baskets of Various Assets 397Credit Risk versus Insurance 398Summary 399CHAPTER 11 Engineered Implied Volatility and Implied Risk-Neutral Distributions 407Overview 407Introduction 407The Implied Volatility 409Example: The Implied Volatility in a Lognormal Process 410The Dupire Model 411The Implied Risk-Neutral Distribution 412Example: An Implied Binomial Distribution 413Example: Calculating the Implied Risk-Neutral Probability 414Implied Distributions: Parametric Models 417Example: The Generalized Beta of the Second Kind 418The A-parametric Approach and the Black-Scholes Model 420Example: The Shimko Technique 421The Implied Risk Neutral Distribution and Entropy 423Examples and Applications 426Risk Attitude, Implied Risk-Neutral Distribution and Entropy 431Summary 432Appendix: The Implied Volatility—The Dupire Model 433Acknowledgments 439About the Author 441Index 443