Financial economics:
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| Format: | Buch |
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Cambridge, Massachusetts ; London, England
<<The>> MIT Press
[2022]
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvii, 1128 Seiten Diagramme |
| ISBN: | 9780262046848 |
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| 245 | 1 | 0 | |a Financial economics |c Antonio Mele |
| 264 | 1 | |a Cambridge, Massachusetts ; London, England |b <<The>> MIT Press |c [2022] | |
| 264 | 4 | |c © 2022 | |
| 300 | |a xvii, 1128 Seiten |b Diagramme | ||
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| adam_text | Contents Introduction 1 I Foundations 1 The Classic Capital Asset Pricing Model 17 1.1 Introduction 17 1.2 Portfolio Selection 19 1.2.1 Wealth Constraints 19 1.2.2 Portfolio Choice: The “Capital Market Line” 20 1.2.3 Without the Safe Asset: The “Efficient Portfolio Frontier” 20 1.2.4 Risk-Return Trade-Offs in the Two-Asset Case 21 1.2.5 Risk Parity and the Global Minimum Variance Portfolio 23 1.2.6 The Market Portfolio 24 1.3 The Capital Asset Pricing Model 27 1.3.1 Restrictions on Securities Expected Returns 27 1.3.2 The Low-Beta Anomaly 29 1.3.3 Zero-Beta CAPM 30 1.3.4 An Excursion into Risk Premiums and Certainty Equivalents 31 1.3.5 Back to CAPM: Equilibrium with Expected Utility 35 1.3.6 The Black-Litterman Model 38 1.3.7 Knightian Uncertainty and Global Minimum Variance Portfolio 40 1.4 The Arbitrage Pricing Theory 42 1.4.1 Exact APT 42 1.4.2 Risk Neutral Tilts or the Fundamental Theorem of Asset Pricing 44 1.4.3 Uncertainty and Asset Evaluation 47 1.4.4 The APT with Idiosyncratic Risk and a Large Number of Assets 47 1.5 Empirical Evidence 48 1.5.1 Fama-MacBeth Two-Step Regressions 49 1.5.2 Macroeconomic Forces 49 1.5.3 The Fama and French Model 49 1.5.4 “Smart Beta,” or Factor Investing 52 1.5.5 “Lucky Factors” 53 15
vi Contents l .A Portfolio Choice 54 l.B Market Portfolio and the Security Market Line l.C Risk and Risk Aversion 60 l.D Money Demand and Liquidity Traps 64 l .E Parameter Uncertainty 66 References 67 2 3 58 Arbitrage, Equilibrium, and Pricing 69 2.1 Introduction 69 2.2 The Static General Equilibrium in a Nutshell 71 2.2.1 Walras’s Law 72 2.2.2 Competitive Equilibrium 72 2.2.3 Optimality 73 2.3 The Role of Financial Securities in Markets with Uncertainty 77 2.3.1 Commodity Markets 77 2.3.2 Financial Securities and Rational Expectations 77 2.3.3 Laws of Large Numbers, Risk Aversion, and the Slicing of Risks 2.3.4 Arrow-Debreu Securities 81 2.4 Arbitrage and Replication: Examples 84 2.4.1 Rain and Sunshine 84 2.4.2 Replication and Pricing: The Role of Complete Markets 86 2.5 No-Arbitrage: Theory 87 2.5.1 Lands of Cockaigne 87 2.5.2 Enforced Asset Prices 89 2.6 Equivalent Martingales and Equilibrium 90 2.6.1 Equilibrium with Financial Markets: Definition 90 2.6.2 Rational Expectations 91 2.6.3 Pricing Kernels 92 2.6.4 Equilibrium, Risk Sharing, and Incomplete Markets 94 2.7 Consumption CAPM 100 2.7.1 Risk Neutral Pricing and Macroeconomic Risks 101 2.7.2 CCAPM versus CAPM 102 2 .A Proof of Selected Results 102 References 104 Infinite Horizon Economies 107 3.1 Introduction 107 3.2 Consumption-Based Asset Evaluation 108 3.2.1 Recursive Plans: Introduction 108 3.2.2 Asset Pricing: The Marginálist Argument 110 3.2.3 Elasticity of Intertemporal Substitution 110 3.2.4 Lucas’s Model 111 3.3 Production: Foundational Issues 115 3.3.1 Decentralized Economy 115 3.3.2 The Social Planner
Solution 117 79
Contents vii 3.3.3 Dynamics 118 3.3.4 Stochastic Economies 120 3.4 Production-Based Asset Pricing 124 3.4.1 Firms 125 3.4.2 Consumers 129 3.4.3 Equilibrium 130 3.5 Production, Money, and Asset Prices in Overlapping Generations Models 130 3.5.1 Introduction: Endowment Economies 131 3.5.2 Monetary Economies 134 3.5.3 Capital Accumulation and Bubbles 137 3.6 Dynamic Efficiency 140 3.6.1 Production Economies 140 3.6.2 Money 142 3.A Finite Difference Equations and Determinacy 142 3.B Neoclassical Growth in Continuous Time 146 3.C Optimization of Continuous Time Systems 151 References 154 4 Continuous Time Models 157 4.1 Introduction 157 4.2 An Introduction to No-Arbitrage and Equilibrium 159 4.2.1 Time 159 4.2.2 The Origins: Black-Scholes 159 4.2.3 Asset Prices As Feynman-Kac Representations 165 4.2.4 The Girsanov Theorem 167 4.2.5 The APT in Continuous Time 170 4.2.6 Example: No-Arbitrage in the Lucas Tree 173 4.3 Martingales and Arbitrage I: Viability 179 4.3.1 Trees 179 4.3.2 Martingale Restrictions 180 4.3.3 Market Completeness 181 4.4 Martingales and Arbitrage II: Optimization 183 4.4.1 Complete Markets and Single Budget Constraints 183 4.4.2 Optimization 184 4.4.3 Marginal Utility of Income 185 4.4.4 Example: Log Utility 186 4.4.5 Equilibrium 186 4.5 Martingales and Arbitrage III: Distorsions and Numéraires 187 4.5.1 Leading Example: Consumption-Based Probabilities 188 4.5.2 Numéraire Pricing 190 4.6 Equilibrium with State Variables and a Representative Agent 193 4.6.1 Constant Investment Opportunity Sets 194 4.6.2 Stochastic Opportunity Sets 194 4.6.3 Arrow-Debreu
Densities and Restrictions on Expected Returns 4.6.4 Interest Rates 203 199
viii Contents 4.7 Portfolio Constraints 205 4.7.1 Admissible Portfolio Choices 206 4.7.2 Artificial Markets 207 4.8 Inaction: The Economies of American Options 209 4.8.1 Early Exercise Premiums: An Introductory Example 209 4.8.2 Risk Aversion 211 4.8.3 Real Options Theory 212 4.8.4 Perpetual Puts 213 4.8.5 Perpetual Calls 215 4.8.6 Further Topics on Real Options and Controlled Brownian Motions 217 4.9 Jumps 220 4.9.1 Poisson Jumps 220 4.9.2 A Rare Event Interpretation 221 4.9.3 Properties and Related Distributions 222 4.9.4 Cox Processes 223 4.9.5 Asset Prices As Jump-Diffusion Processes 223 4.9.6 An Option Pricing Formula 225 4.A Introduction to Stochastic Calculus for Finance 226 4.B Self-Financed Strategies 244 4.C Proof of Selected Results 246 4.D The Green’s Function 250 4.E Portfolio Constraints 252 4.F Jumps 254 References 257 5 Information, Security Design, and Financial Contracting 261 5.1 Introduction 261 5.2 Conceptual Challenges to Frictionless Markets: Information Problems 262 5.2.1 The Economics of Information 262 5.2.2 Information Problems in Financial Markets 263 5.3 Three Information Problems 265 5.3.1 Adverse Selection and Trading 265 5.3.2 Moral Hazard and Securitization 266 5.3.3 Signaling: Callable Bonds, Equity, and Short-Term Debt 273 5.3.4 Other Classical Problems: Short-Term Debt and Equity Sales 279 5.4 The Classics: Capital Structure and Modigliani-Miller Propositions 284 5.4.1 Irrelevance of Capital Structure 284 5.4.2 Dynamic Versions of Irrelevance 286 5.5 Debt and Moral Hazard 287 5.5.1 Symmetric Information Again: Full Insurance 287 5.5.2
Moral Hazard 288 5.6 Debt with Costly State Verification 291 5.6.1 Symmetric Information 291 5.6.2 Asymmetric Information 291 5.6.3 Investments and Agency Costs 293
Contents Liquidity Management and Dynamic Security Design 294 5.7.1 Liquidity Constraints and Optimal Dividend Policy 294 5.7.2 A Model of Continuous Time Contracting 299 5 .A Proofs for Section 5.3 305 5 .В Debt and Moral Hazard 307 5 .C Dynamic Problems 308 References 310 5.7 6 Taking Models to Data 313 6.1 Introduction 313 6.2 Data Generating Processes 314 6.2.1 Models: Specification and Identification 314 6.2.2 Restrictions on the DGP 314 6.2.3 Parameter Estimation 315 6.2.4 Basic Properties of Density Functions 316 6.2.5 The Cramer-Rao Lower Bound 316 6.3 Maximum Likelihood Estimation 317 6.3.1 Definition 317 6.3.2 Factorizations 317 6.3.3 Asymptotic Properties 317 6.4 M-Estimators 319 6.5 Pseudo- or Quasi-Maximum Likelihood 321 6.6 Generalized Method of Moments 321 6.6.1 Theory 322 6.6.2 Early Asset Pricing Tests 324 6.7 Simulation-Based Estimators 325 6.7.1 Three Simulation-Based Estimators 326 6.7.2 Asymptotic Normality 328 6.7.3 A Fourth Estimator: Simulated Maximum Likelihood 331 6.7.4 Progress 333 6.7.5 In Practice? Latent Factors and Identification 333 6 .A Primers 334 6 .В Maximum Likelihood 337 6 .C Maximum Likelihood Estimator for Dependent Processes References 340 II Empirical Lessons and Market Inefficiencies 343 7 Neoclassical Kernels and Puzzles 345 7.1 Introduction 345 7.2 The Equity Premium Puzzle 346 7.2.1 A Single-Factor Model 346 7.2.2 Equity Premium and Interest Rate Puzzles 7.3 The Hansen-Jagannathan Cup 352 349 338 ix
Contents Multifactor Extensions: The Aggregate Equity Market 355 7.4.1 Exponential Affine Pricing Kernels 355 7.4.2 With Log-Normal Returns 357 7 .5 Relations to the Classic Capital Asset Pricing Model 359 7.5.1 Market Portfolios and Pricing Kernel Bounds 359 7.5.2 A Semantic Digression on Market Portfolios 359 7.5.3 The Maximum Correlation Portfolio 360 7.5.4 Duality 362 7 .6 The Conditional Capital Asset Pricing Model 363 7 .A Proof of Selected Results 365 References 369 ΊΑ 8 Aggregate Fluctuations in Equity Markets 371 8.1 Introduction 371 8.2 Empirical Evidence: A Bird’s Eye View 372 8.2.1 Equity Markets and the Business Cycle 373 8.2.2 Predictability 377 8.2.3 Risk-Return Trade-offs 379 8.3 Volatility: A Business Cycle Perspective 380 8.3.1 Volatility Cycles 381 8.3.2 Understanding the Empirical Evidence 383 8.3.3 What to Do with Stock Market Volatility? 386 8.3.4 What Did We Learn? 392 8.4 Rational Market Fluctuations 392 8.4.1 The Dynamics of Asset Returns 392 8.4.2 Markov Pricing Kernels, Asset Returns, and Volatility 394 8.5 Time-Varying Risk Premiums 396 8.5.1 External Habit 397 8.5.2 Countercyclical Statistics 398 8.5.3 Some Additional Literature 402 8.5.4 The Term Structure of Interest Rates 402 8.6 Large Price Swings As a Learning-Induced Phenomenon 404 8.6.1 Information 404 8.6.2 An Introductory Model of Learning 405 8.6.3 Convexity Again and Two Models of Learning 409 8.7 Retained Earnings and Market-to-Book Ratios 413 8.7.1 Plowbacks and Growth Opportunities 416 8.7.2 Random Dividends Distribution 414 8.A Estimation, Calibration, and Simulation Methods 416
8.В A Multifactor Security Model 420 8.C Arrow-Debreu Partial Differential Equations 420 8.D Volatility, Options, and Convexity 421 8.E Linearity-Generating Processes 431 8.F Habit 433
Contents 8 .G Learning 435 8 .H Market-to-Book Ratios References 437 9 437 Macrofinance 441 9.1 Introduction 441 9.2 Nonexpected Utility 444 9.2.1 Recursive Formulations 444 9.2.2 Preferences for Early Resolution of Uncertainty and Long-Run Risks 446 9.2.3 Testable Restrictions 448 9.2.4 Risk Premiums and Interest Rates 449 9.2.5 The Campbell-Shiller Approximation 451 9.2.6 Risks for the Long Run 451 9.3 Heterogeneous Agents and “Catching up with the Joneses” 453 9.4 Idiosyncratic Risk and Incomplete Markets 456 9.4.1 A Static Model of Idiosyncratic Risk 456 9.4.2 Idiosyncratic Shocks Unrelated to Aggregate Risk 458 9.4.3 Self-Insurance and Persistence of Idiosyncratic Shocks 459 9.4.4 Countercyclical Income Inequality 459 9.4.5 A Model with Restricted Market Participation 461 9.5 Disagreement and Learning 464 9.5.1 Learning with Multiple Signals 465 9.5.2 Overconfidence and Bubbles 465 9.5.3 General Equilibrium Without Frictions 470 9.6 Coping with Knightian Uncertainty 479 9.6.1 Prelude 479 9.6.2 Uncertainty Aversion and the Ellsberg Paradox 480 9.6.3 Portfolio Selection and Market Participation 483 9.6.4 A Model of Multiple Likelihoods 487 9.7 Government Spending and Asset Prices 492 9.7.1 Assumptions 492 9.7.2 Government Debt 492 9.7.3 Ricardian Equivalence 493 9.7.4 Government Size and Asset Prices 494 9.8 Leverage and Volatility 495 9.8.1 Primitives 496 9.8.2 Equity Volatility and Leverage 497 9.8.3 Bankruptcy 498 9.9 Multiple Trees and the Cross-Section of Asset Returns 499 9.9.1 A Model of the Cross-Section of Expected Returns 499 9.9.2 Exogenous Aggregate Output
and Habit Formation 504 9.9.3 Discussion: Predictability 506 9.9.4 Stochastic Strings 506 xi
xii Contents 9.10 Prices, Quantities, and the Separation Hypothesis 508 9.10.1 Production Puzzles 509 9.10.2 Risk-Sensitive Models 510 9.10.3 Irrelevance 512 9.10.4 Preferences for Robustness and Detection Error Probabilities 9.11 Procyclicality and the Financial Accelerator Doctrine 515 9,11.1 Procyclicality 515 9.11.2 Introduction: Credit Rationing 517 9.11.3 Credit Cycles I: Propagation 518 9.11.4 Credit Cycles II: Amplification 524 9.11.5 Financial Intermediation and Business Cycles: Additional Mechanisms 529 9.11.6 The State of Current Research 537 9 .A Nonexpected Utility 538 9. В Economies with Heterogeneous Agents 546 9 .C Knightian Uncertainty 553 9 .D Credit Rationing 554 References 55 8 10 Information and Other Market Frictions 563 10.1 Introduction 563 10.2 Prelude: Imperfect Information in Macroeconomics 565 10.3 Informational Efficiency: A Road Map 568 10.4 Walrasian Equilibria as Informationally Inefficient Outcomes 569 10.5 Rational Expectations Equilibrium 571 10.6 Noisy Rational Expectations Equilibrium 574 10.6.1 Asymmetric Information: Information Transmission 575 10.6.2 Differential Information: Information Aggregation 582 10.6.3 Higher Order Beliefs and Beauty Contests 585 10.7 Dealers Markets: Introduction 587 10.7.1 Markets with Symmetric Information 588 10.7.2 With Asymmetric Information: Bid-Ask Spreads 589 10.7.3 Inventory Risk and Bid-Ask Spreads 592 10.7.4 Empirical Measures of Liquidity 594 10.8 Markets with Strategic Players 595 10.8.1 Kyle’s Baseline Model 596 10.8.2 Markets with Multiple Traders and Dealers 598 10.8.3 Dynamic Markets 604
10.8.4 Gravitational Pull Problems 609 10.8.5 Mandatory Disclosure 611 10.9 Limits of Arbitrage and Further Frictions 614 10.9.1 A Simple Model of Risky Arbitrage 615 10.9.2 Funding and Early Liquidation Constraints 617 10.9.3 Market Segmentation and Bond Supply Shocks 622 10.9.4 Liquidity and Runs 625 513
Contents 10.10 Over-the-Counter Markets 630 10.10.1 Background 630 10.10.2 Search 631 10.10.3 A Model with Symmetric Information 631 10.A The Projection Theorem 635 10.В Proof of Selected Results 636 10.C Market Segmentation 641 10.D Search 642 10.E Introduction to Pricing Behavior in Macroeconomics 643 References 647 ІП 11 Asset Pricing and Reality 651 Options and Volatility 653 11.1 Introduction 653 11.2 Forwards and Futures 655 11.2.1 Forwards: Definition and Pricing in Frictionless Markets 656 11.2.2 Forwards As a Means to Borrow Money, and Pricing Again 657 11.2.3 Marking to Market 657 11.2.4 Futures 657 11.2.5 Backwardation and Contango 659 11.3 Optionality and No-Arbitrage Bounds 663 11.3.1 Model-Free Properties 664 11.3.2 Limiting Behavior and Arbitrage Bounds 666 11.3.3 Wasting Assets and Convexity 667 11.3.4 Hedging 667 11.3.5 A Case Study: Accumulators and Decumulators 669 11.4 Classical Evaluation and Properties 670 11.4.1 A Pricing Formula 670 11.4.2 Black-Scholes 671 11.4.3 Future Options and Black’s Formula 674 11.4.4 Surprising Cancellations and “Preference-Free” Formulae 675 11.4.5 Properties of Options in Diffusive Models 675 11.5 Stochastic Volatility 678 11.5.1 Statistical Models of Changing Volatility 678 11.5.2 Implied Volatility, Smiles, and Skews 680 11.5.3 Option Pricing under Stochastic Volatility 686 11.6 Trading Volatility with Options 696 11.6.1 Option Portfolios and a Taxonomy 696 11.6.2 Delta-Neutral Portfolios 698 11.6.3 Delta-Hedged Strategies and Variance Risk Premiums 702 11.6.4 Perfect Hedging: Price Independence 707 11.7 Local Volatility
708 11.7.1 Issues 709 11.7.2 Implied Binomial Trees 710 xiii
xiv Contents 11.7.3 The Perfect Fit in Continuous Time 713 11.7.4 Relations with Implied Volatility 715 11.8 The Price of (Equity) Volatility 717 11.8.1 One Introductory Example: Range-Based Volatility 11.8.2 “Fear Gauge” Contracts 719 11.8.3 Hedging Variance Swaps 723 11.8.4 Forward Volatility Trading 724 11.8.5 Marking to Market 725 11.8.6 Stochastic Interest Rates 726 11.8.7 A Digression on Skewness 726 11.9 VIX Derivatives 728 11.9.1 Model-Free Future Pricing 728 11.9.2 A Simple VIX Future Pricing Model 730 11.9.3 Options and the Volatility of Volatility 732 11.9.4 Replicating Variance Futures 733 11.10 Endogenous Risk and Market Dysfunctionalities 735 11.10.1 Cyclical Hedging 737 11.10.2 Market Crashes 738 11. A The Original Formulation of Black-Scholes 746 1 1.В Black 1976 746 11 .C Stochastic Volatility 747 ll .D Local Volatility 750 11 .E Spanning and Variance Contracts 752 References 755 12 717 Engineering of Fixed Income Securities 759 12.1 Introduction 759 12.1.1 No-Arbitrage Models 760 12.1.2 Relative Pricing in Fixed Income Markets 760 12.1.3 Many Evaluation Paradigms 761 12.1.4 Plan of the Chapter 762 12.2 Markets and Interest Rate Conventions 762 12.2.1 Markets for Interest Rates 762 12.2.2 Mathematical Definitions of Interest Rates 765 12.2.3 Yields to Maturity on Coupon-Bearing Bonds 767 12.2.4 Accruals, Invoice, and Clean Prices on Coupon-Bearing Bonds 12.3 Duration, Convexity Hedging, and Trading 770 12.3.1 Duration 770 12.3.2 Convexity 772 12.3.3 Asset-Liability Management 772 12.4 Foundational Issues in Interest Rate Modeling 781 12.4.1 Tree
Representation of the Short-Term Rate 782 12.4.2 Tree Pricing 787 12.4.3 Introduction to Calibration 788 12.4.4 Calibrating Probabilities Through Derivative Data 800 12.4.5 Extensions to Trinomial Trees 807 768
Contents 12.5 The Ho-Lee Model 807 12.5.1 The Tree 808 12.5.2 Price Movements and the Martingale Restriction 809 12.5.3 The Recombining Condition and Interest Rate Volatility 810 12.5.4 Model Solution 811 12.5.5 Model Calibration 813 12.5.6 An Example 813 12.5.7 Continuous Time Approximations with an Application to Barbell Trading 816 12.6 Beyond Но-Lee: Calibration Through Arrow-Debreu Securities 821 12.6.1 Extracting Arrow-Debreu Securities from the Yield Curve 822 12.6.2 Implementation with Two Model Examples 825 12.6.3 Numerical Examples 827 12.7 Callables, Puttables, and Convertibles with Trees 835 12.7.1 Foundational Issues 835 12.7.2 Callable Bonds 838 12.7.3 Convertible Bonds 842 12.8 Probabilities of Fed Funds Target Changes 845 12.A Bootstrapping and No-Arbitrage Restrictions 847 12.В Bond Sharpe Ratios 852 12.C Но-Lee Representations 853 References 855 13 Interest Rates 857 13.1 Introduction 857 13.2 Bond Prices and Interest Rates 859 13.2.1 A First Representation of Bond Prices 859 13.2.2 Forward Rates 861 13.2.3 A Second Representation of Bond Prices 862 13.3 Stylized Facts 862 13.3.1 The Expectation Hypothesis 862 13.3.2 Bond Returns Predictability 864 13.3.3 The Yield Curve and the Business Cycle 865 13.3.4 Additional Stylized Facts about the US Yield Curve 868 13.3.5 Common Factors Affecting the Yield Curve 868 13.4 Models of the Short-Term Rate: Introduction 872 13.4.1 Models versus Representations 873 13.4.2 The Bond Pricing Equation 874 13.4.3 Stochastic Duration 878 13.4.4 Some Famous Models 879 13.4.5 Interest Rate Volatility and the Business Cycle 887
13.4.6 Jumps, Volatility, and Default 890 13.5 Multifactor Models of the Short-Term Rate 896 13.5.1 Stochastic Volatility 896 13.5.2 Three-Factor Models 901 XV
xvi Contents 13.5.3 Affine and Quadratic Term Structure Models 902 13.5.4 Unspanned Stochastic Volatility 904 13.5.5 Topics Regarding Estimation and Trading Strategies 905 13.6 No-Arbitrage Models: Early Formulations 908 13.6.1 Fitting the Yield-Curve, Perfectly 908 13.6.2 Ho and Lee 909 13.6.3 Hull and White 910 13.7 The Heath-Jarrow-Morton Framework 911 13.7.1 The Framework 911 13.7.2 The Model 913 13.7.3 The Dynamics of the Short-Term Rate 913 13.7.4 Embedding 914 13.7.5 Stochastic String Shocks Models 915 13.8 Interest Rate Derivatives 918 13.8.1 Persistence and Volatility in Fixed Income Markets 918 13.8.2 Hypothetical Continuous Payoffs 921 13.8.3 Forward Martingale Probabilities 922 13.8.4 European Options on Bonds 923 13.8.5 Callable Bonds and Convexity Risks 926 13.8.6 Options on Fixed Coupon Bonds 932 13.8.7 Interest Rate Swaps 934 13.8.8 Caps and Floors 938 13.8.9 Swaptions 939 13.9 Market Models 940 13.9.1 Models and Market Practice 940 13.9.2 No-Arbitrage Restrictions 941 13.9.3 Applications to Derivatives Evaluation 943 13.9.4 Multiple Curves 947 13.10 Volatility Surfaces 950 13.10.1 Implied Volatilities 950 13.10.2 Local Volatilities and SABR Models 951 13.A Bond Prices and Arbitrage Restrictions 954 13.В Forward Probabilities 955 13.C Factors and Components 957 13.D Jumps 958 13.E Exponential-Affine Models 961 13.F Expectation Theory and Embedding 963 13.G Strings 965 13.H Changes of Numéraire 965 13.1 Convexity Risks in Gaussian Markets 966 References 967 14 Risky Debt and Credit Derivatives 973 14.1 Introduction 973 14.1.1 A Brief History of Credit Risk
and Financial Innovation 14.1.2 Plan of the Chapter 976 973
Contents xvii 14.2 Conceptual Approaches to the Evaluation of Defaultable Securities 977 14.2.1 Firm Value, or Structural, Approach 977 14.2.2 The Structural Approach in Theory: Strategic Defaulting 989 14.2.3 In Practice: The Pricing of Convertible Bonds 994 14.2.4 Sovereign Risk 997 14.2.5 Reduced Form Approaches: Rare Events or Intensity Models 1001 14.2.6 Ratings 1006 14.3 Credit Derivatives and Structured Products Based Thereon 1011 14.3.1 Options and Spreads 1011 14.3.2 Credit Default Swaps 1012 14.3.3 Evaluation with Random Intensity Rates 1018 14.3.4 The Pricing of Credit Products 1025 14.3.5 Collateralized Debt Obligations 1031 14.4 Managing Loan Losses 1045 14.4.1 Regulatory Framework 1045 14.4.2 Foundations of Risk Management 1048 14.4.3 Measures of Systemic Risk 1053 14.4.4 Credit Risk, Correlation, and Loss Probabilities 1055 14.5 The Global Financial Crisis of the Late 2000s 1059 14.5.1 Credit Bubbles, Procyclicality, and “Quantitative Easing” 1059 14.5.2 The 2007 Subprime Crisis 1062 14.5.3 Procyclicality 1067 14.5.4 Credit Crunches and Quantitative Easing 1074 14.5.5 Where Did Quantitative Easing go? 1077 14.A Strategic Defaulting 1081 14.В Proof of Selected Results 1082 14.C Transition Probability Matrices and Pricing 1083 14.D Stochastic Default Intensity and Bond Spreads 1084 14.E Bond and Credit Default Swap spreads 1085 14.F Conditional Probabilities of Survival 1086 14.G CDS Index Swaps and Swaptions 1086 14.H Copulae 1089 14.1 Pricing CDOs with Imperfect Correlation 1091 References 1092 Index 1095
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Contents Introduction 1 I Foundations 1 The Classic Capital Asset Pricing Model 17 1.1 Introduction 17 1.2 Portfolio Selection 19 1.2.1 Wealth Constraints 19 1.2.2 Portfolio Choice: The “Capital Market Line” 20 1.2.3 Without the Safe Asset: The “Efficient Portfolio Frontier” 20 1.2.4 Risk-Return Trade-Offs in the Two-Asset Case 21 1.2.5 Risk Parity and the Global Minimum Variance Portfolio 23 1.2.6 The Market Portfolio 24 1.3 The Capital Asset Pricing Model 27 1.3.1 Restrictions on Securities Expected Returns 27 1.3.2 The Low-Beta Anomaly 29 1.3.3 Zero-Beta CAPM 30 1.3.4 An Excursion into Risk Premiums and Certainty Equivalents 31 1.3.5 Back to CAPM: Equilibrium with Expected Utility 35 1.3.6 The Black-Litterman Model 38 1.3.7 Knightian Uncertainty and Global Minimum Variance Portfolio 40 1.4 The Arbitrage Pricing Theory 42 1.4.1 Exact APT 42 1.4.2 Risk Neutral Tilts or the Fundamental Theorem of Asset Pricing 44 1.4.3 Uncertainty and Asset Evaluation 47 1.4.4 The APT with Idiosyncratic Risk and a Large Number of Assets 47 1.5 Empirical Evidence 48 1.5.1 Fama-MacBeth Two-Step Regressions 49 1.5.2 Macroeconomic Forces 49 1.5.3 The Fama and French Model 49 1.5.4 “Smart Beta,” or Factor Investing 52 1.5.5 “Lucky Factors” 53 15
vi Contents l .A Portfolio Choice 54 l.B Market Portfolio and the Security Market Line l.C Risk and Risk Aversion 60 l.D Money Demand and Liquidity Traps 64 l .E Parameter Uncertainty 66 References 67 2 3 58 Arbitrage, Equilibrium, and Pricing 69 2.1 Introduction 69 2.2 The Static General Equilibrium in a Nutshell 71 2.2.1 Walras’s Law 72 2.2.2 Competitive Equilibrium 72 2.2.3 Optimality 73 2.3 The Role of Financial Securities in Markets with Uncertainty 77 2.3.1 Commodity Markets 77 2.3.2 Financial Securities and Rational Expectations 77 2.3.3 Laws of Large Numbers, Risk Aversion, and the Slicing of Risks 2.3.4 Arrow-Debreu Securities 81 2.4 Arbitrage and Replication: Examples 84 2.4.1 Rain and Sunshine 84 2.4.2 Replication and Pricing: The Role of Complete Markets 86 2.5 No-Arbitrage: Theory 87 2.5.1 Lands of Cockaigne 87 2.5.2 Enforced Asset Prices 89 2.6 Equivalent Martingales and Equilibrium 90 2.6.1 Equilibrium with Financial Markets: Definition 90 2.6.2 Rational Expectations 91 2.6.3 Pricing Kernels 92 2.6.4 Equilibrium, Risk Sharing, and Incomplete Markets 94 2.7 Consumption CAPM 100 2.7.1 Risk Neutral Pricing and Macroeconomic Risks 101 2.7.2 CCAPM versus CAPM 102 2 .A Proof of Selected Results 102 References 104 Infinite Horizon Economies 107 3.1 Introduction 107 3.2 Consumption-Based Asset Evaluation 108 3.2.1 Recursive Plans: Introduction 108 3.2.2 Asset Pricing: The Marginálist Argument 110 3.2.3 Elasticity of Intertemporal Substitution 110 3.2.4 Lucas’s Model 111 3.3 Production: Foundational Issues 115 3.3.1 Decentralized Economy 115 3.3.2 The Social Planner
Solution 117 79
Contents vii 3.3.3 Dynamics 118 3.3.4 Stochastic Economies 120 3.4 Production-Based Asset Pricing 124 3.4.1 Firms 125 3.4.2 Consumers 129 3.4.3 Equilibrium 130 3.5 Production, Money, and Asset Prices in Overlapping Generations Models 130 3.5.1 Introduction: Endowment Economies 131 3.5.2 Monetary Economies 134 3.5.3 Capital Accumulation and Bubbles 137 3.6 Dynamic Efficiency 140 3.6.1 Production Economies 140 3.6.2 Money 142 3.A Finite Difference Equations and Determinacy 142 3.B Neoclassical Growth in Continuous Time 146 3.C Optimization of Continuous Time Systems 151 References 154 4 Continuous Time Models 157 4.1 Introduction 157 4.2 An Introduction to No-Arbitrage and Equilibrium 159 4.2.1 Time 159 4.2.2 The Origins: Black-Scholes 159 4.2.3 Asset Prices As Feynman-Kac Representations 165 4.2.4 The Girsanov Theorem 167 4.2.5 The APT in Continuous Time 170 4.2.6 Example: No-Arbitrage in the Lucas Tree 173 4.3 Martingales and Arbitrage I: Viability 179 4.3.1 Trees 179 4.3.2 Martingale Restrictions 180 4.3.3 Market Completeness 181 4.4 Martingales and Arbitrage II: Optimization 183 4.4.1 Complete Markets and Single Budget Constraints 183 4.4.2 Optimization 184 4.4.3 Marginal Utility of Income 185 4.4.4 Example: Log Utility 186 4.4.5 Equilibrium 186 4.5 Martingales and Arbitrage III: Distorsions and Numéraires 187 4.5.1 Leading Example: Consumption-Based Probabilities 188 4.5.2 Numéraire Pricing 190 4.6 Equilibrium with State Variables and a Representative Agent 193 4.6.1 Constant Investment Opportunity Sets 194 4.6.2 Stochastic Opportunity Sets 194 4.6.3 Arrow-Debreu
Densities and Restrictions on Expected Returns 4.6.4 Interest Rates 203 199
viii Contents 4.7 Portfolio Constraints 205 4.7.1 Admissible Portfolio Choices 206 4.7.2 Artificial Markets 207 4.8 Inaction: The Economies of American Options 209 4.8.1 Early Exercise Premiums: An Introductory Example 209 4.8.2 Risk Aversion 211 4.8.3 Real Options Theory 212 4.8.4 Perpetual Puts 213 4.8.5 Perpetual Calls 215 4.8.6 Further Topics on Real Options and Controlled Brownian Motions 217 4.9 Jumps 220 4.9.1 Poisson Jumps 220 4.9.2 A Rare Event Interpretation 221 4.9.3 Properties and Related Distributions 222 4.9.4 Cox Processes 223 4.9.5 Asset Prices As Jump-Diffusion Processes 223 4.9.6 An Option Pricing Formula 225 4.A Introduction to Stochastic Calculus for Finance 226 4.B Self-Financed Strategies 244 4.C Proof of Selected Results 246 4.D The Green’s Function 250 4.E Portfolio Constraints 252 4.F Jumps 254 References 257 5 Information, Security Design, and Financial Contracting 261 5.1 Introduction 261 5.2 Conceptual Challenges to Frictionless Markets: Information Problems 262 5.2.1 The Economics of Information 262 5.2.2 Information Problems in Financial Markets 263 5.3 Three Information Problems 265 5.3.1 Adverse Selection and Trading 265 5.3.2 Moral Hazard and Securitization 266 5.3.3 Signaling: Callable Bonds, Equity, and Short-Term Debt 273 5.3.4 Other Classical Problems: Short-Term Debt and Equity Sales 279 5.4 The Classics: Capital Structure and Modigliani-Miller Propositions 284 5.4.1 Irrelevance of Capital Structure 284 5.4.2 Dynamic Versions of Irrelevance 286 5.5 Debt and Moral Hazard 287 5.5.1 Symmetric Information Again: Full Insurance 287 5.5.2
Moral Hazard 288 5.6 Debt with Costly State Verification 291 5.6.1 Symmetric Information 291 5.6.2 Asymmetric Information 291 5.6.3 Investments and Agency Costs 293
Contents Liquidity Management and Dynamic Security Design 294 5.7.1 Liquidity Constraints and Optimal Dividend Policy 294 5.7.2 A Model of Continuous Time Contracting 299 5 .A Proofs for Section 5.3 305 5 .В Debt and Moral Hazard 307 5 .C Dynamic Problems 308 References 310 5.7 6 Taking Models to Data 313 6.1 Introduction 313 6.2 Data Generating Processes 314 6.2.1 Models: Specification and Identification 314 6.2.2 Restrictions on the DGP 314 6.2.3 Parameter Estimation 315 6.2.4 Basic Properties of Density Functions 316 6.2.5 The Cramer-Rao Lower Bound 316 6.3 Maximum Likelihood Estimation 317 6.3.1 Definition 317 6.3.2 Factorizations 317 6.3.3 Asymptotic Properties 317 6.4 M-Estimators 319 6.5 Pseudo- or Quasi-Maximum Likelihood 321 6.6 Generalized Method of Moments 321 6.6.1 Theory 322 6.6.2 Early Asset Pricing Tests 324 6.7 Simulation-Based Estimators 325 6.7.1 Three Simulation-Based Estimators 326 6.7.2 Asymptotic Normality 328 6.7.3 A Fourth Estimator: Simulated Maximum Likelihood 331 6.7.4 Progress 333 6.7.5 In Practice? Latent Factors and Identification 333 6 .A Primers 334 6 .В Maximum Likelihood 337 6 .C Maximum Likelihood Estimator for Dependent Processes References 340 II Empirical Lessons and Market Inefficiencies 343 7 Neoclassical Kernels and Puzzles 345 7.1 Introduction 345 7.2 The Equity Premium Puzzle 346 7.2.1 A Single-Factor Model 346 7.2.2 Equity Premium and Interest Rate Puzzles 7.3 The Hansen-Jagannathan Cup 352 349 338 ix
Contents Multifactor Extensions: The Aggregate Equity Market 355 7.4.1 Exponential Affine Pricing Kernels 355 7.4.2 With Log-Normal Returns 357 7 .5 Relations to the Classic Capital Asset Pricing Model 359 7.5.1 Market Portfolios and Pricing Kernel Bounds 359 7.5.2 A Semantic Digression on Market Portfolios 359 7.5.3 The Maximum Correlation Portfolio 360 7.5.4 Duality 362 7 .6 The Conditional Capital Asset Pricing Model 363 7 .A Proof of Selected Results 365 References 369 ΊΑ 8 Aggregate Fluctuations in Equity Markets 371 8.1 Introduction 371 8.2 Empirical Evidence: A Bird’s Eye View 372 8.2.1 Equity Markets and the Business Cycle 373 8.2.2 Predictability 377 8.2.3 Risk-Return Trade-offs 379 8.3 Volatility: A Business Cycle Perspective 380 8.3.1 Volatility Cycles 381 8.3.2 Understanding the Empirical Evidence 383 8.3.3 What to Do with Stock Market Volatility? 386 8.3.4 What Did We Learn? 392 8.4 Rational Market Fluctuations 392 8.4.1 The Dynamics of Asset Returns 392 8.4.2 Markov Pricing Kernels, Asset Returns, and Volatility 394 8.5 Time-Varying Risk Premiums 396 8.5.1 External Habit 397 8.5.2 Countercyclical Statistics 398 8.5.3 Some Additional Literature 402 8.5.4 The Term Structure of Interest Rates 402 8.6 Large Price Swings As a Learning-Induced Phenomenon 404 8.6.1 Information 404 8.6.2 An Introductory Model of Learning 405 8.6.3 Convexity Again and Two Models of Learning 409 8.7 Retained Earnings and Market-to-Book Ratios 413 8.7.1 Plowbacks and Growth Opportunities 416 8.7.2 Random Dividends Distribution 414 8.A Estimation, Calibration, and Simulation Methods 416
8.В A Multifactor Security Model 420 8.C Arrow-Debreu Partial Differential Equations 420 8.D Volatility, Options, and Convexity 421 8.E Linearity-Generating Processes 431 8.F Habit 433
Contents 8 .G Learning 435 8 .H Market-to-Book Ratios References 437 9 437 Macrofinance 441 9.1 Introduction 441 9.2 Nonexpected Utility 444 9.2.1 Recursive Formulations 444 9.2.2 Preferences for Early Resolution of Uncertainty and Long-Run Risks 446 9.2.3 Testable Restrictions 448 9.2.4 Risk Premiums and Interest Rates 449 9.2.5 The Campbell-Shiller Approximation 451 9.2.6 Risks for the Long Run 451 9.3 Heterogeneous Agents and “Catching up with the Joneses” 453 9.4 Idiosyncratic Risk and Incomplete Markets 456 9.4.1 A Static Model of Idiosyncratic Risk 456 9.4.2 Idiosyncratic Shocks Unrelated to Aggregate Risk 458 9.4.3 Self-Insurance and Persistence of Idiosyncratic Shocks 459 9.4.4 Countercyclical Income Inequality 459 9.4.5 A Model with Restricted Market Participation 461 9.5 Disagreement and Learning 464 9.5.1 Learning with Multiple Signals 465 9.5.2 Overconfidence and Bubbles 465 9.5.3 General Equilibrium Without Frictions 470 9.6 Coping with Knightian Uncertainty 479 9.6.1 Prelude 479 9.6.2 Uncertainty Aversion and the Ellsberg Paradox 480 9.6.3 Portfolio Selection and Market Participation 483 9.6.4 A Model of Multiple Likelihoods 487 9.7 Government Spending and Asset Prices 492 9.7.1 Assumptions 492 9.7.2 Government Debt 492 9.7.3 Ricardian Equivalence 493 9.7.4 Government Size and Asset Prices 494 9.8 Leverage and Volatility 495 9.8.1 Primitives 496 9.8.2 Equity Volatility and Leverage 497 9.8.3 Bankruptcy 498 9.9 Multiple Trees and the Cross-Section of Asset Returns 499 9.9.1 A Model of the Cross-Section of Expected Returns 499 9.9.2 Exogenous Aggregate Output
and Habit Formation 504 9.9.3 Discussion: Predictability 506 9.9.4 Stochastic Strings 506 xi
xii Contents 9.10 Prices, Quantities, and the Separation Hypothesis 508 9.10.1 Production Puzzles 509 9.10.2 Risk-Sensitive Models 510 9.10.3 Irrelevance 512 9.10.4 Preferences for Robustness and Detection Error Probabilities 9.11 Procyclicality and the Financial Accelerator Doctrine 515 9,11.1 Procyclicality 515 9.11.2 Introduction: Credit Rationing 517 9.11.3 Credit Cycles I: Propagation 518 9.11.4 Credit Cycles II: Amplification 524 9.11.5 Financial Intermediation and Business Cycles: Additional Mechanisms 529 9.11.6 The State of Current Research 537 9 .A Nonexpected Utility 538 9. В Economies with Heterogeneous Agents 546 9 .C Knightian Uncertainty 553 9 .D Credit Rationing 554 References 55 8 10 Information and Other Market Frictions 563 10.1 Introduction 563 10.2 Prelude: Imperfect Information in Macroeconomics 565 10.3 Informational Efficiency: A Road Map 568 10.4 Walrasian Equilibria as Informationally Inefficient Outcomes 569 10.5 Rational Expectations Equilibrium 571 10.6 Noisy Rational Expectations Equilibrium 574 10.6.1 Asymmetric Information: Information Transmission 575 10.6.2 Differential Information: Information Aggregation 582 10.6.3 Higher Order Beliefs and Beauty Contests 585 10.7 Dealers Markets: Introduction 587 10.7.1 Markets with Symmetric Information 588 10.7.2 With Asymmetric Information: Bid-Ask Spreads 589 10.7.3 Inventory Risk and Bid-Ask Spreads 592 10.7.4 Empirical Measures of Liquidity 594 10.8 Markets with Strategic Players 595 10.8.1 Kyle’s Baseline Model 596 10.8.2 Markets with Multiple Traders and Dealers 598 10.8.3 Dynamic Markets 604
10.8.4 Gravitational Pull Problems 609 10.8.5 Mandatory Disclosure 611 10.9 Limits of Arbitrage and Further Frictions 614 10.9.1 A Simple Model of Risky Arbitrage 615 10.9.2 Funding and Early Liquidation Constraints 617 10.9.3 Market Segmentation and Bond Supply Shocks 622 10.9.4 Liquidity and Runs 625 513
Contents 10.10 Over-the-Counter Markets 630 10.10.1 Background 630 10.10.2 Search 631 10.10.3 A Model with Symmetric Information 631 10.A The Projection Theorem 635 10.В Proof of Selected Results 636 10.C Market Segmentation 641 10.D Search 642 10.E Introduction to Pricing Behavior in Macroeconomics 643 References 647 ІП 11 Asset Pricing and Reality 651 Options and Volatility 653 11.1 Introduction 653 11.2 Forwards and Futures 655 11.2.1 Forwards: Definition and Pricing in Frictionless Markets 656 11.2.2 Forwards As a Means to Borrow Money, and Pricing Again 657 11.2.3 Marking to Market 657 11.2.4 Futures 657 11.2.5 Backwardation and Contango 659 11.3 Optionality and No-Arbitrage Bounds 663 11.3.1 Model-Free Properties 664 11.3.2 Limiting Behavior and Arbitrage Bounds 666 11.3.3 Wasting Assets and Convexity 667 11.3.4 Hedging 667 11.3.5 A Case Study: Accumulators and Decumulators 669 11.4 Classical Evaluation and Properties 670 11.4.1 A Pricing Formula 670 11.4.2 Black-Scholes 671 11.4.3 Future Options and Black’s Formula 674 11.4.4 Surprising Cancellations and “Preference-Free” Formulae 675 11.4.5 Properties of Options in Diffusive Models 675 11.5 Stochastic Volatility 678 11.5.1 Statistical Models of Changing Volatility 678 11.5.2 Implied Volatility, Smiles, and Skews 680 11.5.3 Option Pricing under Stochastic Volatility 686 11.6 Trading Volatility with Options 696 11.6.1 Option Portfolios and a Taxonomy 696 11.6.2 Delta-Neutral Portfolios 698 11.6.3 Delta-Hedged Strategies and Variance Risk Premiums 702 11.6.4 Perfect Hedging: Price Independence 707 11.7 Local Volatility
708 11.7.1 Issues 709 11.7.2 Implied Binomial Trees 710 xiii
xiv Contents 11.7.3 The Perfect Fit in Continuous Time 713 11.7.4 Relations with Implied Volatility 715 11.8 The Price of (Equity) Volatility 717 11.8.1 One Introductory Example: Range-Based Volatility 11.8.2 “Fear Gauge” Contracts 719 11.8.3 Hedging Variance Swaps 723 11.8.4 Forward Volatility Trading 724 11.8.5 Marking to Market 725 11.8.6 Stochastic Interest Rates 726 11.8.7 A Digression on Skewness 726 11.9 VIX Derivatives 728 11.9.1 Model-Free Future Pricing 728 11.9.2 A Simple VIX Future Pricing Model 730 11.9.3 Options and the Volatility of Volatility 732 11.9.4 Replicating Variance Futures 733 11.10 Endogenous Risk and Market Dysfunctionalities 735 11.10.1 Cyclical Hedging 737 11.10.2 Market Crashes 738 11. A The Original Formulation of Black-Scholes 746 1 1.В Black 1976 746 11 .C Stochastic Volatility 747 ll .D Local Volatility 750 11 .E Spanning and Variance Contracts 752 References 755 12 717 Engineering of Fixed Income Securities 759 12.1 Introduction 759 12.1.1 No-Arbitrage Models 760 12.1.2 Relative Pricing in Fixed Income Markets 760 12.1.3 Many Evaluation Paradigms 761 12.1.4 Plan of the Chapter 762 12.2 Markets and Interest Rate Conventions 762 12.2.1 Markets for Interest Rates 762 12.2.2 Mathematical Definitions of Interest Rates 765 12.2.3 Yields to Maturity on Coupon-Bearing Bonds 767 12.2.4 Accruals, Invoice, and Clean Prices on Coupon-Bearing Bonds 12.3 Duration, Convexity Hedging, and Trading 770 12.3.1 Duration 770 12.3.2 Convexity 772 12.3.3 Asset-Liability Management 772 12.4 Foundational Issues in Interest Rate Modeling 781 12.4.1 Tree
Representation of the Short-Term Rate 782 12.4.2 Tree Pricing 787 12.4.3 Introduction to Calibration 788 12.4.4 Calibrating Probabilities Through Derivative Data 800 12.4.5 Extensions to Trinomial Trees 807 768
Contents 12.5 The Ho-Lee Model 807 12.5.1 The Tree 808 12.5.2 Price Movements and the Martingale Restriction 809 12.5.3 The Recombining Condition and Interest Rate Volatility 810 12.5.4 Model Solution 811 12.5.5 Model Calibration 813 12.5.6 An Example 813 12.5.7 Continuous Time Approximations with an Application to Barbell Trading 816 12.6 Beyond Но-Lee: Calibration Through Arrow-Debreu Securities 821 12.6.1 Extracting Arrow-Debreu Securities from the Yield Curve 822 12.6.2 Implementation with Two Model Examples 825 12.6.3 Numerical Examples 827 12.7 Callables, Puttables, and Convertibles with Trees 835 12.7.1 Foundational Issues 835 12.7.2 Callable Bonds 838 12.7.3 Convertible Bonds 842 12.8 Probabilities of Fed Funds Target Changes 845 12.A Bootstrapping and No-Arbitrage Restrictions 847 12.В Bond Sharpe Ratios 852 12.C Но-Lee Representations 853 References 855 13 Interest Rates 857 13.1 Introduction 857 13.2 Bond Prices and Interest Rates 859 13.2.1 A First Representation of Bond Prices 859 13.2.2 Forward Rates 861 13.2.3 A Second Representation of Bond Prices 862 13.3 Stylized Facts 862 13.3.1 The Expectation Hypothesis 862 13.3.2 Bond Returns Predictability 864 13.3.3 The Yield Curve and the Business Cycle 865 13.3.4 Additional Stylized Facts about the US Yield Curve 868 13.3.5 Common Factors Affecting the Yield Curve 868 13.4 Models of the Short-Term Rate: Introduction 872 13.4.1 Models versus Representations 873 13.4.2 The Bond Pricing Equation 874 13.4.3 Stochastic Duration 878 13.4.4 Some Famous Models 879 13.4.5 Interest Rate Volatility and the Business Cycle 887
13.4.6 Jumps, Volatility, and Default 890 13.5 Multifactor Models of the Short-Term Rate 896 13.5.1 Stochastic Volatility 896 13.5.2 Three-Factor Models 901 XV
xvi Contents 13.5.3 Affine and Quadratic Term Structure Models 902 13.5.4 Unspanned Stochastic Volatility 904 13.5.5 Topics Regarding Estimation and Trading Strategies 905 13.6 No-Arbitrage Models: Early Formulations 908 13.6.1 Fitting the Yield-Curve, Perfectly 908 13.6.2 Ho and Lee 909 13.6.3 Hull and White 910 13.7 The Heath-Jarrow-Morton Framework 911 13.7.1 The Framework 911 13.7.2 The Model 913 13.7.3 The Dynamics of the Short-Term Rate 913 13.7.4 Embedding 914 13.7.5 Stochastic String Shocks Models 915 13.8 Interest Rate Derivatives 918 13.8.1 Persistence and Volatility in Fixed Income Markets 918 13.8.2 Hypothetical Continuous Payoffs 921 13.8.3 Forward Martingale Probabilities 922 13.8.4 European Options on Bonds 923 13.8.5 Callable Bonds and Convexity Risks 926 13.8.6 Options on Fixed Coupon Bonds 932 13.8.7 Interest Rate Swaps 934 13.8.8 Caps and Floors 938 13.8.9 Swaptions 939 13.9 Market Models 940 13.9.1 Models and Market Practice 940 13.9.2 No-Arbitrage Restrictions 941 13.9.3 Applications to Derivatives Evaluation 943 13.9.4 Multiple Curves 947 13.10 Volatility Surfaces 950 13.10.1 Implied Volatilities 950 13.10.2 Local Volatilities and SABR Models 951 13.A Bond Prices and Arbitrage Restrictions 954 13.В Forward Probabilities 955 13.C Factors and Components 957 13.D Jumps 958 13.E Exponential-Affine Models 961 13.F Expectation Theory and Embedding 963 13.G Strings 965 13.H Changes of Numéraire 965 13.1 Convexity Risks in Gaussian Markets 966 References 967 14 Risky Debt and Credit Derivatives 973 14.1 Introduction 973 14.1.1 A Brief History of Credit Risk
and Financial Innovation 14.1.2 Plan of the Chapter 976 973
Contents xvii 14.2 Conceptual Approaches to the Evaluation of Defaultable Securities 977 14.2.1 Firm Value, or Structural, Approach 977 14.2.2 The Structural Approach in Theory: Strategic Defaulting 989 14.2.3 In Practice: The Pricing of Convertible Bonds 994 14.2.4 Sovereign Risk 997 14.2.5 Reduced Form Approaches: Rare Events or Intensity Models 1001 14.2.6 Ratings 1006 14.3 Credit Derivatives and Structured Products Based Thereon 1011 14.3.1 Options and Spreads 1011 14.3.2 Credit Default Swaps 1012 14.3.3 Evaluation with Random Intensity Rates 1018 14.3.4 The Pricing of Credit Products 1025 14.3.5 Collateralized Debt Obligations 1031 14.4 Managing Loan Losses 1045 14.4.1 Regulatory Framework 1045 14.4.2 Foundations of Risk Management 1048 14.4.3 Measures of Systemic Risk 1053 14.4.4 Credit Risk, Correlation, and Loss Probabilities 1055 14.5 The Global Financial Crisis of the Late 2000s 1059 14.5.1 Credit Bubbles, Procyclicality, and “Quantitative Easing” 1059 14.5.2 The 2007 Subprime Crisis 1062 14.5.3 Procyclicality 1067 14.5.4 Credit Crunches and Quantitative Easing 1074 14.5.5 Where Did Quantitative Easing go? 1077 14.A Strategic Defaulting 1081 14.В Proof of Selected Results 1082 14.C Transition Probability Matrices and Pricing 1083 14.D Stochastic Default Intensity and Bond Spreads 1084 14.E Bond and Credit Default Swap spreads 1085 14.F Conditional Probabilities of Survival 1086 14.G CDS Index Swaps and Swaptions 1086 14.H Copulae 1089 14.1 Pricing CDOs with Imperfect Correlation 1091 References 1092 Index 1095 |
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| spelling | Mele, Antonio Verfasser (DE-588)171331478 aut Financial economics Antonio Mele Cambridge, Massachusetts ; London, England <<The>> MIT Press [2022] © 2022 xvii, 1128 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Kapitalmarkttheorie (DE-588)4137411-3 gnd rswk-swf Kapitalmarkttheorie (DE-588)4137411-3 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033336142&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title_exact_search_txtP | Financial economics |
| title_full | Financial economics Antonio Mele |
| title_fullStr | Financial economics Antonio Mele |
| title_full_unstemmed | Financial economics Antonio Mele |
| title_short | Financial economics |
| title_sort | financial economics |
| topic | Kapitalmarkttheorie (DE-588)4137411-3 gnd |
| topic_facet | Kapitalmarkttheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033336142&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT meleantonio financialeconomics |