Cheng-Few Lee, Alice C. Lee, John Lee - Handbook of Quantitative Finance and Risk Management / Настольная книга количественных финансов и риск-менеджмента [2010, PDF, ENG]

Handbook of Quantitative Finance and Risk Management 3
Preface 5
About the Editors 6
Contents 8
List of Contributors 32
Chapter 1 Theoretical Framework of Finance 38
1.1 Introduction 38
1.2 Discounted Cash-Flow Valuation Theory 38
1.2.1 Bond Valuation 39
1.2.2 Common-Stock Valuation 40
1.3 M and M Valuation Theory 41
1.3.1 Review and Extension of M and M Proposition I 43
1.3.2 Millers Proposition on Debt and Taxes 44
1.4 Markowitz Portfolio Theory 45
1.5 Capital Asset Pricing Model 45
1.6 Arbitrage Pricing Theory 47
1.6.1 Rosss Arbitrage Model Specification 47
1.7 Option Valuation 49
1.8 Futures Valuation and Hedging 50
1.8.1 Futures Markets: Overview 51
1.8.2 The Valuation of Futures Contracts 52
1.8.3 Hedging Concepts and Strategies 54
1.9 Conclusion 57
References 57
Chapter 2 Investment, Dividend, Financing, and Production Policies: Theory and Implications 58
2.1 Introduction 58
2.2 Investment and Dividend Interactions: The Internal Versus External Financing Decision 58
2.3 Interactions Between Dividend and Financing Policies 60
2.4 Interactions Between Financing and Investment Decisions 63
2.4.1 Risk-Free Debt Case 63
2.5 Implications of Financing and Investment Interactions for Capital Budgeting 65
2.5.1 Arditti and Levy Method 66
2.5.2 Myers Adjusted-Present-Value Method 67
2.6 Implications of Different Policies on the Beta Coefficient 69
2.7 Conclusion 71
Notes 71
References 71
Appendix 2A Stochastic Dominance and its Applications to Capital-Structure Analysis with Default Risk 73
Chapter 3 Research Methods in Quantitative Finance and Risk Management 76
3.1 Introduction 76
3.2 Statistics 76
3.3 Econometrics 78
3.4 Mathematics 81
3.5 Other Disciplines 83
3.6 Conclusion 84
References 85
Chapter 4 Foundation of Portfolio Theory 86
4.1 Introduction 86
4.2 Risk Classification and Measurement 86
4.2.1 Call Risk 88
4.2.2 Convertible Risk 88
4.2.3 Default Risk 88
4.2.4 Interest-Rate Risk 89
4.2.5 Management Risk 89
4.2.6 Marketability (Liquidity) Risk 89
4.2.7 Political Risk 89
4.2.8 Purchasing-Power Risk 90
4.2.9 Systematic and Unsystematic Risk 90
4.3 Portfolio Analysis and Application 90
4.3.1 Expected Return on a Portfolio 90
4.3.2 Variance and Standard Deviation of a Portfolio 91
4.3.3 The Two-Asset Case 91
4.4 The Efficient Portfolio and Risk Diversification 93
4.4.1 The Efficient Portfolio 93
4.4.2 Corporate Application of Diversification 94
4.4.3 The Dominance Principle 94
4.4.4 Three Performance Measures 95
4.5 Determination of Commercial Lending Rate 97
4.6 The Market Rate of Return and Market Risk Premium 99
4.7 Conclusion 101
References 101
Chapter 5 Risk-Aversion, Capital Asset Allocation, and Markowitz Portfolio-Selection Model 102
5.1 Introduction 102
5.2 Measurement of Return and Risk 102
5.2.1 Return 102
5.2.2 Risk 103
5.3 Utility Theory, Utility Functions, and Indifference Curves 104
5.3.1 Utility Functions 104
5.3.2 Risk Aversion and Utility Values 107
5.3.3 Capital Allocation Across Risky and Risk-Free Portfolios 108
5.3.4 Indifference Curves 108
5.4 Efficient Portfolios 110
5.4.1 Portfolio Combinations 111
5.4.2 Short Selling 112
5.4.3 Three-Security Empirical Solution 116
5.4.4 Portfolio Determination with Speci c Adjustment for Short Selling 122
5.4.5 Portfolio Determination Without Short Selling 124
5.5 Conclusion 124
References 124
Chapter 6 Capital Asset Pricing Model and Beta Forecasting 126
6.1 Introduction 126
6.2 A Graphical Approach to the Derivation of the Capital Asset Pricing Model 126
6.2.1 The Lending, Borrowing, and Market Portfolios 126
6.2.2 The Capital Market Line 127
6.2.3 The Security Market Line: The Capital Asset Pricing Model 128
6.3 Mathematical Approach to the Derivation of the Capital Asset Pricing Model 129
6.4 The Market Model and Risk Decomposition 130
6.4.1 The Market Model 130
6.4.2 Risk Decomposition 130
6.4.3 Why Beta Is Important for Security Analysis 131
6.4.4 Determination of Systematic Risk 132
6.5 Growth Rates, Accounting Betas, and Variance in EBIT 133
6.5.1 Growth Rates 133
6.5.2 Accounting Beta 134
6.5.3 Variance in EBIT 134
6.5.4 Capital-Labor Ratio 134
6.5.5 Fixed Costs and Variable Costs 134
6.5.6 Beta Forecasting 135
6.5.7 Market-Based versus Accounting-Based Beta Forecasting 135
6.6 Some Applications and Implications of the Capital Asset Pricing Model 137
6.7 Conclusion 138
References 138
Appendix 6A Empirical Evidence for the Risk-Return Relationship 139
Appendix 6B Anomalies in the Semi-strong Efficient-Market Hypothesis 142
Chapter 7 Index Models for Portfolio Selection 143
7.1 Introduction 143
7.2 The Single-Index Model 143
7.2.1 Deriving the Single-Index Model 144
7.2.2 Portfolio Analysis and the Single-Index Model 147
7.2.3 The Market Model and Beta 149
7.3 Multiple Indexes and the Multiple-Index Model 150
7.4 Conclusion 153
References 154
Appendix 7A A Linear-Programming Approach to Portfolio-Analysis Models 154
Appendix 7B Expected Return, Variance, and Covariance for a Multi-index Model 155
Chapter 8 Performance-Measure Approaches for Selecting Optimum Portfolios 157
8.1 Introduction 157
8.2 Sharpe Performance-Measure Approach with Short Sales Allowed 157
8.3 Treynor-Measure Approach with Short Sales Allowed 160
8.4 Treynor-Measure Approach with Short Sales Not Allowed 162
8.5 Impact of Short Sales on Optimal-Weight Determination 164
8.6 Economic Rationale of the Treynor Performance-Measure Method 164
8.7 Conclusion 165
References 165
Appendix 8A Derivation of Equation (8.6) 165
Appendix 8B Derivation of Equation (8.10) 166
Appendix 8C Derivation of Equation (8.15) 167
Chapter 9 The Creation and Control of Speculative Bubbles in a Laboratory Setting 168
9.1 Introduction 168
9.2 Bubbles in the Asset Markets 170
9.3 Experimental Design 171
9.3.1 General Market Design 171
9.3.2 Dividend Design 172
9.3.3 Investment Horizon 173
9.3.4 Risk Aversion 175
9.3.5 Validation Procedures 175
9.4 Results and Analysis 176
9.4.1 Control Experiments 176
9.4.2 The Formation of Bubbles 179
9.4.3 The Control of Bubbles 180
9.4.4 The Impact of Risk Aversion 181
9.4.5 The Formation of Negative Bubbles 182
9.4.6 Statistical Analysis 184
9.4.7 Further Tests 189
9.5 Conclusions 192
References 194
Chapter 10 Portfolio Optimization Models and MeanVariance Spanning Tests 196
10.1 Introduction of Markowitz Portfolio-Selection Model 196
10.2 Measurement of Return and Risk 197
10.2.1 Return 197
10.2.2 Risk 197
10.3 Efficient Portfolio 197
10.3.1 Two-Risky-Assets Portfolio 198
10.3.2 The Concept of Markowitz Efficient Frontier 198
10.3.3 Short Selling 199
10.3.4 Calculating the Minimum Variance Portfolio 200
10.3.5 Calculating the Weights of Optimal Risky Portfolio 201
10.3.6 Finding the Efficient Frontier of Risky Assets 201
10.3.7 Finding the Optimal Risky Portfolio 201
10.4 MeanVariance Spanning Test 203
10.4.1 MeanVariance Spanning and Intersection Tests 203
10.4.2 Step-Down Tests for MeanVariance Spanning 205
10.4.3 MeanVariance Spanning Tests Under Non-normality and Heteroskedasticity 205
10.5 Alternative Computer Program to Calculate Efficient Frontier 206
10.5.1 Application: Microsoft Excel 206
10.5.2 Application: MATLAB 209
10.6 Conclusion 213
References 215
Chapter 11 Combining Fundamental Measures for Stock Selection 216
11.1 Introduction 216
11.2 Bayesian Triangulation 218
11.3 Triangulation in Forensic Valuation 220
11.4 Bayesian Triangulation in Asset Pricing Settings 221
11.4.1 Black and Litterman: Combining Private Views with CAPM 222
11.4.2 Incorporating Bayesian Priors in Regression Estimates of Model Parameters 222
11.4.3 Bayesian Model Averaging 223
11.4.4 Bayesian Guidance for Improving Forecasting 223
11.5 The Data Snooping Trap 225
11.6 Using Guidance from Theory to Mitigate Data Snooping 226
11.7 Avoiding Data-Snooping Pitfalls in Financial Statement Analysis 228
11.8 Conclusion 230
References 231
Appendix 11A Proof of Theorem 11.1 232
Chapter 12 On Estimation Risk and Power Utility Portfolio Selection 234
12.1 Introduction 234
12.2 Literature Review 234
12.3 The Multiperiod Investment Model 236
12.4 The Data 237
12.5 Alternative Ways of Estimating the Joint Return Distribution 237
12.6 Alternate Ways of Evaluating Investment Performance 239
12.7 The Results 241
12.8 Conclusion 247
12.9 Addendum 248
References 249
Chapter 13 International Portfolio Management: Theory and Method 251
13.1 Introduction 251
13.2 Overview of International Portfolio Management 252
13.3 Literature Review 256
13.4 Forming the Optimal Global Portfolio 256
13.5 The Benefits of International Diversification Around the World 257
13.6 The Optimal Portfolio Components 259
13.7 Conclusion 262
References 263
Chapter 14 The Le Chatelier Principle in the Markowitz Quadratic Programming Investment Model: A Case of World Equity Fund Market 265
14.1 Introduction 265
14.2 Data and Methodology 266
14.3 The Le Chtelier Principle in the Markowitz Investment Model 266
14.4 An Application of the Le Chtelier PrincipleintheWorldEquityMarket 267
14.5 Conclusion 275
References 275
Chapter 15 Risk-Averse Portfolio Optimization via Stochastic Dominance Constraints 276
15.1 Introduction 276
15.2 The Portfolio Problem 277
15.3 Stochastic Dominance 278
15.3.1 Direct Forms 278
15.3.2 Inverse Forms 279
15.3.3 Relations to Value at Risk and Conditional Value at Risk 280
15.4 The Dominance-Constrained Portfolio Problem 281
15.4.1 Direct Formulation 281
15.4.2 Inverse Formulation 282
15.5 Optimality and Duality 283
15.5.1 Primal Form 283
15.5.2 Inverse Form 284
15.6 Numerical Illustration 285
15.7 Conclusions 286
References 286
Chapter 16 Portfolio Analysis 288
16.1 Introduction 288
16.2 Inputs for Portfolio Analysis 288
16.3 The Security Analysts Job 288
16.4 Four Assumptions Underlying Portfolio Analysis 289
16.5 Different Approaches to Diversification 289
16.6 A Portfolios Expected Return Formula 290
16.7 The Quadratic Risk Formula for a Portfolio 290
16.8 The Covariance Between Returns from Two Assets 291
16.9 Portfolio Analysis of a Two-Asset Portfolio 291
16.9.1 Perfectly Positively Correlated Returns, Fig. 16.3a 292
16.9.2 Uncorrelated Assets, Fig. 16.3b 292
16.9.3 Perfectly Negatively Correlated Returns, Fig. 16.3c 292
16.9.4 Portfolio Analysis Using Markowitz Diversification, Fig. 16.3d 293
16.10 Mathematical Portfolio Analysis 294
16.11 Calculus Minimization of Risk: A Three-Security Portfolio 294
16.12 Conclusion 295
References 295
Chapter 17 Portfolio Theory, CAPM and Performance Measures 296
17.1 Portfolio Theory and CAPM: Foundations and Current Application 296
17.1.1 Introduction 296
17.1.2 The Mean-variance Model 297
17.1.3 The Efficient Frontier 297
17.1.4 Efficient Frontier with a Risk-free Asset 298
17.1.5 Efficient Frontier with Inequality Restrictions 299
17.1.6 Application to the Market 299
17.1.7 The Capital Asset Pricing Model 299
17.1.8 The Market Model 300
17.1.9 Relation Between the Market Model and CAPM 301
17.1.10 The Pricing Model 301
17.1.11 Contrasts and Controversy Regarding the CAPM 301
17.2 Performance Measures Related to Portfolio Theory and the CAPM: Classic Indices, Derivative Indices, and New Approaches 303
17.2.1 Introduction 303
17.2.2 Classic Performance Measures 303
17.2.3 M2 and M2 for Beta 304
17.2.4 Information Ratio and Tracking Error 304
17.2.5 PIRR Index 305
17.2.6 PIRR Index for Beta 305
17.3 Empirical Analysis: Performance Rankings and Performance Persistence 306
17.3.1 Performance Rankings 306
17.3.2 Performance Persistence 307
17.4 Summary and Conclusions 309
References 309
Chapter 18 Intertemporal Equilibrium Models, Portfolio Theory and the Capital Asset Pricing Model 311
18.1 Introduction 311
18.2 Intertemporal Equilibrium Models 311
18.3 Relationship to Observed Security Returns 312
18.4 Intertemporal Equilibrium and the Capital Asset Pricing Model 313
18.5 Hansen Jagannathan Bounds 313
18.6 Are Stochastic Discount Factors Positive? 314
18.7 Conclusion 314
References 315
Chapter 19 Persistence, Predictability, and Portfolio Planning 316
19.1 Introduction 316
19.2 Detecting and Exploiting Predictability 317
19.2.1 Implications of a Model of Stock Price Behavior 317
19.2.2 Detecting Predictive Power in Finite Samples 319
19.3 Stock Price Variation and Variation in the Expected Returns 323
19.4 Economic Signi cance of Predictability 325
19.5 Forecasts of Equity Returns 330
19.5.1 Models and Estimation Procedure 331
19.5.2 Estimates 332
19.5.3 Return Prediction 337
19.5.4 Historical Simulations 337
19.6 Conclusion 341
References 341
Appendix 19A The Optimal Strategy 342
Appendix 19B The Unconditional Strategy 343
Appendix 19C The Myopic Strategy 344
Appendix 19D The Optimal Buy-and-Hold Strategy 345
Chapter 20 Portfolio Insurance Strategies: Review of Theory and Empirical Studies 346
20.1 Introduction 346
20.2 Theory of Alternative Portfolio Insurance Strategies 346
20.2.1 Portfolio Insurance with Synthetic Put (Option-Based Portfolio Insurance) 347
20.2.2 Constant Proportion Portfolio Insurance 348
20.2.3 Portfolio Insurance with Downside Risk Control (Risk-Based Portfolio Insurance) 350
20.3 Empirical Comparison of Alternative Portfolio Insurance Strategies 351
20.3.1 Zhu and Kavee (1988) 351
20.3.2 Perold and Sharpe (1988) 354
20.3.3 Rendleman and OBrien (1990) 354
20.3.4 Loria et al. (1991) 354
20.3.5 Do and Faff (2004) 355
20.3.6 Cesari and Cremonini (2003) 355
20.3.7 Herold et al. (2005) 356
20.3.8 Hamidi et al. (2007) 356
20.3.9 Ho et al. (2008) 356
20.4 Recent Market Developments 356
20.4.1 Type of Risky Asset 356
20.4.2 Market Size 357
20.4.3 Market Participants 357
20.4.4 Modi ed CPPI Mechanisms 357
20.4.5 Structured Products 358
20.5 Implications for Financial Market Stability 358
20.5.1 Ampli cation of Market Price Movements 358
20.5.2 Gap Risk 358
20.6 Conclusion 359
References 359
Chapter 21 Security Market Microstructure: The Analysis of a Non-Frictionless Market 360
21.1 Introduction 360
21.2 Microstructures Challenge 361
21.3 The Perfectly Liquid Environment of CAPM 362
21.3.1 The Expected Utility of End of Period Wealth 363
21.3.2 The Reservation Demand Curve 363
21.3.3 The Ordinary Demand Curve 364
21.3.4 The Risk Premium and the Market Price of Risk 364
21.3.5 The Investors Optimal Point on the Capital Market Line 364
21.3.6 The ith Risky Assets Point on the Security Market Line 365
21.4 What Microstructure Analysis Has to Offer: Personal Re ections 366
21.4.1 The Early Focus 366
21.4.2 The Current Focus 367
21.4.3 Future Directions 369
21.5 From Theory to Application 371
21.5.1 Technological Developments 371
21.5.2 Regulatory Initiatives 371
21.6 Deutsche Brse: The Emergence of a Modern, Electronic Market 372
21.6.1 The German Equities Market in the Mid-1990s 372
21.6.2 Designing a New Trading System 372
21.7 Conclusion: The Roadmap and the Road 374
References 374
Appendix 21A Risk Aversion and Risk Premium Measures 376
Appendix 21B Designing Xetra 377
Chapter 22 Options Strategies and Their Applications 380
22.1 Introduction 380
22.2 The Option Market and Related Definitions 380
22.2.1 What Is an Option? 380
22.2.2 Types of Options and Their Characteristics 381
22.2.3 Relationships Between the Option Price and the Underlying Asset Price 381
22.2.4 Types of Underlying Assets 384
22.2.5 Institutional Characteristics 384
22.3 Put-Call Parity 385
22.3.1 European Options 385
22.3.2 American Options 386
Futures Options 387
22.3.3 Market Application 388
22.4 Risk-Return Characteristics of Options 388
22.4.1 Long Call 388
22.4.2 Short Call 389
22.4.3 Long Put 391
22.4.4 Short Put 391
22.4.5 Long Straddle 392
22.4.6 Short Straddle 393
22.4.7 Long Vertical (Bull) Spread 394
22.4.8 Short Vertical (Bear) Spread 395
22.4.9 Calendar (Time) Spreads 396
22.5 Examples of Alternative Option Strategies 397
22.5.1 Protective Put 397
22.5.2 Covered Call 397
22.5.3 Collar 399
22.6 Conclusion 400
References 400
Chapter 23 Option Pricing Theory and Firm Valuation 401
23.1 Introduction 401
23.2 Basic Concepts of Options 401
23.2.1 Option Price Information 403
23.3 Factors Affecting Option Value 404
23.3.1 Determining the Value of a Call Option Before the Expiration Date 404
23.4 Determining the Value of Options 408
23.4.1 Expected Value Estimation 408
23.4.2 The Black-Scholes Option Pricing Model 409
23.4.3 Taxation of Options 411
23.4.4 American Options 411
23.5 Option Pricing Theory and Capital Structure 411
23.5.1 Proportion of Debt in Capital Structure 413
23.5.2 Riskiness of Business Operations 413
23.6 Warrants 414
23.7 Conclusion 415
References 416
Chapter 24 Applications of the Binomial Distribution to Evaluate Call Options 417
24.1 Introduction 417
24.2 What Is an Option? 417
24.3 The Simple Binomial Option Pricing Model 417
24.4 The Generalized Binomial Option Pricing Model 419
24.5 Conclusion 421
References 421
Chapter 25 Multinomial Option Pricing Model 423
25.1 Introduction 423
25.2 Multinomial Option Pricing Model 423
25.2.1 Derivation of the Option Pricing Model 423
25.2.2 The Black and Scholes Model as a Limiting Case 424
25.3 A Lattice Framework for Option Pricing 426
25.3.1 Modi cation of the Two-State Approach for a Single State Variable 426
25.3.2 A Lattice Model for Valuation of Options on Two Underlying Assets 427
25.4 Conclusion 430
References 430
Appendix 25A 430
Chapter 26 Two Alternative Binomial Option Pricing Model Approaches to Derive Black-Scholes Option Pricing Model 433
26.1 Introduction 433
26.2 The Two-State Option Pricing Model of Rendleman and Bartter 433
26.2.1 The Discrete Time Model 433
26.2.2 The Continuous Time Model 435
26.3 The Binomial Option Pricing Model of Cox, Ross, and Rubinstein 439
26.3.1 The Binomial Option Pricing Formula of CRR 439
26.3.2 Limiting Case 439
26.4 Comparison of the Two Approaches 441
26.5 Conclusion 442
References 442
Appendix 26A The Binomial Theorem 443
Lindberg-Levy Central Limit Theorem 443
Chapter 27 Normal, Lognormal Distribution and Option Pricing Model 444
27.1 Introduction 444
27.2 The Normal Distribution 444
27.3 The Lognormal Distribution 445
27.4 The Lognormal Distribution and Its Relationship to the Normal Distribution 445
27.5 Multivariate Normal and Lognormal Distributions 446
27.6 The Normal Distribution as an Application to the Binomial and Poisson Distributions 448
27.7 Applications of the Lognormal Distribution in Option Pricing3 449
27.8 Conclusion 451
References 451
Chapter 28 Bivariate Option Pricing Models 452
28.1 Introduction 452
28.2 The Bivariate Normal Density Function 452
28.3 American Call Option and the Bivariate Normal CDF 453
28.4 Valuating American Options 454
28.5 Non-Dividend-Paying Stocks 456
28.6 Dividend-Paying Stocks 456
28.7 Conclusion 461
References 461
Chapter 29 Displaced Log Normal and Lognormal American Option Pricing: AComparison 462
29.1 Introduction 462
29.2 The American Option Pricing Model Under the Lognormal Process 462
29.3 The Geske-Roll-Whaley Model 463
29.4 Conclusion 465
References 465
Appendix 29A 466
Chapter 30 Its Calculus and the Derivation of the BlackScholes Option-Pricing Model 470
30.1 Introduction 470
30.2 The IT Process and Financial Modeling 470
30.3 ITS Lemma 474
30.4 Stochastic Differential-Equation Approach to Stock-price Behavior 475
30.5 The Pricing of an Option 477
30.6 A Reexamination of Option Pricing 478
30.7 Extending the Risk-Neutral Argument: The Martingale Approach 481
30.8 Remarks on Option Pricing 486
30.9 Conclusion 488
References 488
Appendix 30A An Alternative Method To Derive the BlackScholes Option-Pricing Model 489
Chapter 31 Constant Elasticity of Variance Option Pricing Model: Integration and Detailed Derivation 494
31.1 Introduction 494
31.2 The CEV Diffusion and Its Transition Probability Density Function 494
31.3 Review of Noncentral Chi-Square Distribution 496
31.4 The Noncentral Chi-square Approach to Option Pricing Model 497
31.4.1 Detailed Derivations of C 1 and C 2 497
31.4.2 Some Computational Considerations 500
31.5 Conclusion 501
References 501
Appendix 31A Proof of Fellers Lemma 501
Chapter 32 Stochastic Volatility Option Pricing Models 504
32.1 Introduction 504
32.2 Nonclosed-Form Type of Option Pricing Model 504
32.3 Review of Characteristic Function 508
32.4 Closed-Form Type of Option Pricing Model 508
32.4.1 The Heston Model 510
32.5 Conclusion 512
References 512
Appendix 32A The Market Price of the Risk 512
Chapter 33 Derivations and Applications of Greek Letters: Review and Integration 514
33.1 Introduction 514
33.2 Delta ( ) 514
33.2.1 Derivation of Delta for Different Kinds of Stock Options 514
33.2.2 Application of Delta 516
33.3 Theta () 517
33.3.1 Derivation of Theta for Different Kinds of Stock Options 517
33.3.2 Application of Theta () 519
33.4 Gamma ( ) 519
33.4.1 Derivation of Gamma for Different Kinds of Stock Options 519
33.4.2 Application of Gamma ( ) 520
33.5 Vega ( ) 521
33.5.1 Derivation of Vega for Different Kinds of Stock Options 521
33.5.2 Application of Vega ( ) 522
33.6 Rho (.) 523
33.6.1 Derivation of Rho for Different Kinds of Stock Options 523
33.6.2 Application of Rho (.) 524
33.7 Derivation of Sensitivity for Stock Options Respective with Exercise Price 524
33.8 Relationship Between Delta, Theta, and Gamma 525
33.9 Conclusion 526
References 526
Chapter 34 A Further Analysis of the Convergence Rates and Patterns of the Binomial Models 527
34.1 Brief Review of the Binomial Models 527
34.2 The Importance of Node Positioning for Monotonic Convergence 528
34.3 The Flexibility of GCRR Model for Node Positioning 529
34.4 Numerical Results of Various GCRR Models 529
34.5 Conclusion 532
References 535
Appendix 34A Extrapolation Formulas for Various GCRR Models 535
Chapter 35 Estimating Implied Probabilities from Option Prices and the Underlying 536
35.1 Introduction 536
35.2 Black Scholes Baseline 537
35.2.1 The BS Differential Equation 537
35.2.2 A Probability Density Approach 537
35.3 Empirical Departures from Black Scholes 538
35.4 Beyond Black Scholes 539
35.4.1 How Volatility Varies with the Strike 539
35.4.2 The Kolmogorov Equation 539
35.5 Histogram Estimators 539
35.5.1 A Crude Histogram Estimator 539
35.5.2 An Improved Histogram Estimator 540
35.6 Tree Methods 541
35.6.1 A Standard Tree 541
35.6.2 Implied Binomial Trees 541
35.6.3 Numerical Example 542
35.7 Local Volatility Functions 543
35.8 PDF Approaches 543
35.8.1 Mixture-of-Log-Normals Specification 543
35.8.2 Data and Estimation Results 544
35.9 Inferences from the Mixture Model 545
35.9.1 Tests of the Adequacy of BlackScholes 545
35.9.2 Hypothesis Tests on the Forecast Intervals 546
35.9.3 Comparing the Entire Density 546
35.10 Jump Processes 547
35.10.1 Merton Model 547
35.10.2 Bipower Variation 547
35.10.3 An Application 548
35.11 Conclusion 549
References 549
Chapter 36 Are Tails Fat Enough to Explain Smile 551
36.1 Introduction 551
36.2 Literature Review 552
36.3 The Models 553
36.3.1 The Black-Scholes Model 553
36.3.2 The Static Lognormal Model 554
36.3.3 The \Risk-Neutral\ Empirical Model 555
36.3.4 The Static Empirical Model 556
36.4 Data and Empirical Results 557
36.5 Conclusion 561
References 561
Appendix 36A 562
Chapter 37 Option Pricing and Hedging Performance Under Stochastic Volatility and Stochastic Interest Rates 566
37.1 Introduction 566
37.2 The Option Pricing Model 568
37.2.1 Pricing Formula for European Options 569
37.2.2 Hedging and Hedge Ratios 571
37.2.3 Implementation 574
37.3 Data Description 575
37.4 Empirical Tests 576
37.4.1 Static Performance 577
37.4.2 Dynamic Hedging Performance 579
37.4.3 Regression Analysis of Option Pricing and Hedging Errors 583
37.4.4 Robustness of Empirical Results 586
37.5 Conclusions 590
References 590
Appendix 37A 591
Chapter 38 Application of the Characteristic Function in Financial Research 594
38.1 Introduction 594
38.2 The Characteristic Functions 594
38.3 CEV Option Pricing Model 595
38.4 Options with Stochastic Volatility 596
38.5 Conclusion 600
References 600
Chapter 39 Asian Options 601
39.1 Introduction 601
39.2 Valuation 602
39.2.1 Monte Carlo Simulations 602
39.2.2 Approximations 602
39.2.3 Other Mathematical and Numerical Methods 603
39.2.4 Binomial Models 603
39.2.5 Applying Insurance Models 604
39.3 Conclusion 604
References 604
Chapter 40 Numerical Valuation of Asian Options with Higher Moments in the Underlying Distribution 605
40.1 Introduction 605
40.2 Definitions and the Basic Binomial Model 606
40.3 Edgeworth Binomial Model for Asian Option Valuation 607
40.4 Upper Bound and Lower Bound for European Asian Options 609
40.5 Upper Bound and Lower Bound for American Asian Options 611
40.6 Numerical Examples 612
40.6.1 Pricing European Asian Options Under Lognormal Distribution 612
40.6.2 Pricing American Asian Options Under Lognormal Distribution 616
40.6.3 Pricing European Asian Options Under Distributions with Higher Moments 618
40.6.4 Pricing American Asian Options Under Distributions with Higher Moments 619
40.7 Conclusion 620
References 620
Chapter 41 The Valuation of Uncertain Income Streams and the Pricing of Options* 622
41.1 Introduction 622
41.2 Uncertain Income Streams: General Case 623
41.3 Uncertain Income Streams: Special Case 625
41.4 Options 628
41.5 Conclusion 630
References 630
Appendix 41A The Bivariate Normal Density Function 631
Chapter 42 Binomial OPM, Black-Scholes OPM and Their Relationship: Decision Tree and Microsoft Excel Approach 634
42.1 Introduction 634
42.2 Call and Put Options 634
42.3 One Period Option Pricing Model 635
42.4 Two-Period Option Pricing Model 638
42.5 Using Microsoft Excel to Create the Binomial Option Trees 639
42.6 Black-Scholes Option Pricing Model 641
42.7 Relationship Between the Binomial OPM and the Black-Scholes OPM 642
42.8 Decision Tree Black-Scholes Calculation 643
42.9 Conclusion 643
References 644
Appendix 42A Excel VBA CodeBinomial Option Pricing Model 644
Chapter 43 Combinatorial Methods for Constructing Credit Risk Ratings 654
43.1 Introduction 654
43.1.1 Importance of Credit Risk Ratings 654
43.1.2 Contribution and Structure 655
43.2 Logical Analysis of Data: An Overview3 656
43.3 Absolute Creditworthiness: Credit Risk Ratings of Financial Institutions4 658
43.3.1 Problem Description 658
43.3.2 Data 659
43.3.3 LAD Model for Bank Ratings 660
43.3.4 LAD Model Evaluation 661
43.3.5 Remarks on Reverse-Engineering Bank Ratings 662
43.4 Relative Creditworthiness: Country Risk Ratings5 663
43.4.1 Problem Description 663
43.4.2 Data 663
43.4.3 Rating Methodologies 664
43.4.4 Evaluation of the Results 670
43.4.5 Importance of Variables 674
43.5 Conclusions 674
References 675
Appendix 43A 677
Chapter 44 The Structural Approach to Modeling Credit Risk 680
44.1 Introduction 680
44.2 Structural Credit Risk Models 680
44.2.1 The Merton (1974) Model 680
44.2.2 Extensions of the Merton (1974) Model 681
44.2.3 Models of Default Probabilities 683
44.3 Empirical Evidence 683
44.3.1 Evidence from the Corporate Bond Market 683
44.3.2 Evidence from the Real Default Rates 684
44.3.3 The Credit Spread Puzzle and Its Implications 684
44.3.4 Evidence from the CDS Market 685
44.4 Conclusion 686
References 686
Chapter 45 An Empirical Investigation of the Rationales for Integrated Risk-Management Behavior 689
45.1 Introduction 689
45.2 Theories of Risk-Management, Previous Research, and Testable Hypotheses 691
45.2.1 Brief Review of Main Theories of Corporate Hedging 691
45.2.2 Review of Related Banking Theory 692
45.2.3 Relation to Previous Empirical Research 692
45.2.4 Hypotheses 694
45.2.5 Control Variables 698
45.3 Data, Sample Selection, and Empirical Methodology 699
45.3.1 Data 699
45.3.2 Sample Selection 700
45.3.3 Our Measures of Bank Risk-Taking 700
45.3.4 The Empirical Model 700
45.3.5 Accounting for Nonlinearities and Inter-relations Between Independent Variables 702
45.4 Empirical Results 703
45.4.1 Descriptive Statistics and Industry Trends 703
45.4.2 Multivariate Analysis for Interest Rate Risk 703
45.4.3 Multivariate Analysis for Total Risk 706
45.5 Conclusion 708
References 708
Chapter 46 Copula, Correlated Defaults, and Credit VaR 710
46.1 Introduction 710
46.2 Methodology 711
46.2.1 CreditMetricsTM 711
46.2.2 Copula Function 714
46.2.3 Factor Copula Model 715
46.3 Experimental Results 716
46.3.1 Data 716
46.3.2 Simulation 718
46.3.3 Discussion 718
46.4 Conclusion 723
References 724
Chapter 47 Unspanned Stochastic Volatilities and Interest Rate Derivatives Pricing 725
47.1 Introduction 725
47.2 Term Structure Models with Spanned Stochastic Volatility 728
47.3 LIBOR Market Models with Stochastic Volatility and Jumps: Theory and Estimation 735
47.3.1 Specification of the LIBOR Market Models 735
47.3.2 Estimation Method and Results 739
47.4 Nonparametric Estimation of the Forward Density 746
47.4.1 Nonparametric Method 749
47.4.2 Empirical Results 750
47.5 Conclusion 758
References 758
Appendix 47A The Derivation for QTSMs 760
Appendix 47B The Implementation of the Kalman Filter 762
Appendix 47C Derivation of the Characteristic Function 763
Chapter 48 Catastrophic Losses and Alternative Risk Transfer Instruments 764
48.1 Introduction 764
48.2 Catastrophe Bonds 764
48.2.1 CAT Bond Valuation Models 765
48.3 Catastrophe Equity Puts 768
48.3.1 Catastrophe Equity Put Valuation Models 768
48.4 Catastrophe Derivatives 771
48.4.1 Catastrophe Derivatives Valuation Models 772
48.5 Reinsurance with CAT-Linked Securities 774
48.6 Conclusion 775
References 777
Chapter 49 A Real Option Approach to the Comprehensive Analysis of Bank Consolidation Values 778
49.1 Introduction 778
49.2 The Model 779
49.2.1 The Premerger Bank Model 779
49.2.2 The Bank Consolidation Model 781
49.3 Case Study 782
49.3.1 An Introduction to the Case Study 782
49.3.2 Estimating the Parameters 782
49.4 Results 786
49.4.1 The Fair Transaction Value of the Banks 786
49.4.2 Bankruptcy and Stopping Points 786
49.4.3 Sensitivity Analysis 787
49.5 Conclusions 788
References 788
Appendix 49A The Correlations Between the Standard Wiener Process Generated from a Banks Net Interest Income 789
Appendix 49B The Risk-Adjusted Processes 789
Appendix 49C The Discrete Version of the Risk-Adjusted Process 789
Chapter 50 Dynamic Econometric Loss Model: A Default Study of US Subprime Markets 790
50.1 Introduction 790
50.2 Model Framework 791
50.3 Default Modeling 793
50.3.1 Seasoning 793
50.3.2 Payment Shock Interest Only (IO) 794
50.3.3 Combined Loan-to-Value (CLTV) 794
50.3.4 FICO 794
50.3.5 Debt-to-Income Ratio (DTI) and Loan Documentation (DOC) 795
50.3.6 Loan Size 797
50.3.7 Lien 798
50.3.8 Occupancy 798
50.3.9 Purpose 799
50.3.10 Dynamic Factors: Macroeconomic Variables 799
50.3.11 House Price Appreciation (HPA) 800
50.4 Prepayment Modeling 803
50.4.1 Housing Turnover and Seasoning 803
50.4.2 Seasoning 804
50.4.3 Teaser Effect 804
50.4.4 Interest Only (IO) Effect 805
50.4.5 Re nance 805
50.4.6 Burnout Effect 805
50.4.7 CLTV Wealth Effect 806
50.4.8 FICO Credit Effect 806
50.4.9 Prepayment Penalty 807
50.4.10 Interaction Between Prepayment and Default 807
50.5 Delinquency Study 808
50.5.1 Delinquency, the Leading Indicator 808
50.5.2 Analysis Among Delinquency Spectrum 808
50.5.3 A Delinquency Error Correction Default Model 808
50.6 Conclusion 811
50.6.1 Traditional Models 811
50.6.2 Innovation 811
50.6.3 Advantages 812
50.6.4 Findings 812
50.6.5 Future Improvements 812
References 813
Appendix 50A Default and Prepayment Definition 813
Appendix 50B General Model Framework 814
Appendix 50C Default Specification 814
RATE Effect 815
Occupancy 815
Loan Purpose 815
Lien 815
Loan Document 815
Appendix 50D Prepayment Specification Single Monthly Mortality (SMM) Rate Function 816
Chapter 51 The Effect of Default Risk on Equity Liquidity: Evidence Based on the Panel Threshold Model 817
51.1 Introduction 817
51.2 Data and Methodology 818
51.2.1 Data 818
51.2.2 Methodology 819
51.3 Empirical Results 822
51.3.1 Descriptive Statistics 822
51.3.2 Results of Panel Data Regression 822
51.3.3 Results of Panel Threshold Regression 824
51.4 Conclusion 825
References 825
Appendix 51A 826
Chapter 52 Put Option Approach to Determine Bank Risk Premium 829
52.1 Introduction 829
52.2 Evaluating Insurers Liability by Option Pricing Model: Merton (1977) 830
52.3 Extensions of Merton (1977) 830
52.3.1 The Consideration of Surveillance Costs 831
52.3.2 Incorporating Forbearance 831
52.3.3 The Consideration of Interest Rate Risk 832
52.3.4 Utilization of GARCH Option Pricing 833
52.4 Applications for Merton (1977) 833
52.4.1 Marcus and Shaked (1984) 833
52.4.2 Ronn and Verma (1986) 834
52.4.3 Pennacchi (1987) 834
52.4.4 Flannery (1991) 835
52.5 Conclusion 835
References 836
Appendix 52A 836
Appendix 52B 837
Chapter 53 Keiretsu Style Main Bank Relationships, R&D Investment, Leverage, and Firm Value: Quantile Regression Approach 838
53.1 Introduction 838
53.2 Literature Review 840
53.3 Data and Sample 840
53.3.1 Data Source and Sample Description 840
53.3.2 Keiretsu and Main Bank Sample 842
53.3.3 Model Specification 843
53.4 Empirical Results and Analysis 845
53.4.1 Quantile Regression and Bootstrapping Analysis 845
53.4.2 Analysis of Results of Quantile Regression and OLS 845
53.5 Conclusions and Discussion 849
References 850
Chapter 54 On the Feasibility of Laddering 851
54.1 Introduction 851
54.2 The Model 853
54.2.1 IPO Pricing and Overallotments 855
54.2.2 Laddering 855
54.3 Results 857
54.4 Conclusion 859
References 859
Chapter 55 Stock Returns, Extreme Values, and Conditional Skewed Distribution 860
55.1 Introduction 860
55.2 The AGARCH Model Based on the EGB2 Distribution 861
55.3 Data 862
55.4 Empirical Evidence 863
55.4.1 GARCH(1,1) Model: The Normal Distribution 863
55.4.2 AGARCH(1,1): The EGB2 Distribution Model 866
55.5 Distributional Fit Test 866
55.6 The Implication of the EGB2 Distribution 866
55.7 Conclusion 868
References 869
Chapter 56 Capital Structure in Asia and CEO Entrenchment 870
56.1 Introduction 870
56.2 Prior Research and Hypothesis 871
56.2.1 CEO Entrenchment and Leverage 871
56.2.2 Free Cash Flow, CEO Entrenchment, and Leverage 872
56.2.3 Institutional Ownership, CEO Entrenchment, and Leverage 872
56.3 Data and Method 872
56.3.1 Sample Construction 872
56.3.2 Empirical Model 873
56.4 Results 874
56.4.1 Descriptive Statistics 874
56.4.2 Leverage Levels 874
56.4.3 Changes in Leverage 876
56.4.4 Financing De cit 876
56.5 Conclusion 878
References 878
Appendix 56A Variables Definition 879
Chapter 57 A Generalized Model for Optimum Futures Hedge Ratio 880
57.1 Introduction 880
57.2 GIG and GH Distributions 883
57.2.1 The Generalized Hyperbolic Distributions 883
57.2.2 Multivariate Modeling 884
57.3 Futures Hedge Ratios 884
57.3.1 Minimum Variance Hedge Ratio 884
57.3.2 Sharpe Hedge Ratio 885
57.3.3 Minimum Generalized Semivariance Hedge Ratio 886
57.4 Estimation and Simulation 886
57.4.1 Kernel Density Estimators 886
57.4.2 Maximum Likelihood Estimation 886
57.4.3 Simulation of Generalized Hyperbolic Random Variables 887
57.5 Conclusion 887
References 887
Appendix 57A 888
Chapter 58 The Sensitivity of Corporate Bond Volatility to Macroeconomic Announcements 890
58.1 Introduction 890
58.2 Theory and Hypotheses 891
58.3 Data and Return Computations 893
58.4 Descriptive Statistics of Daily Excess Returns 893
58.4.1 Full Sample of Announcement and Nonannouncement Days 903
58.4.2 Announcement Versus Nonannouncement Days 903
58.5 OLS Regressions of Volatility and Excess Returns 904
58.5.1 Volatility Measure Regressions 904
58.5.2 Excess Return Regressions 906
58.6 Conditional Variance Models 906
58.7 Alternative GARCH Models 910
58.7.1 Component GARCH 910
58.7.2 Filter GARCHs 911
58.7.3 A Modi ed Filter GARCH 914
58.7.4 Tests for Asymmetric Volatility 916
58.8 Conclusion 917
References 919
Appendix 58A 920
Chapter 59 Raw Material Convenience Yields and Business Cycle 921
59.1 Introduction 921
59.2 Characteristics of Study Commodities 923
59.2.1 Agricultural Commodities 923
59.2.2 Crude Oil 924
59.3 The Model 925
59.4 Data 927
59.5 Empirical Results 928
59.6 Conclusion 936
References 937
Chapter 60 Alternative Methods to Determine Optimal Capital Structure: Theory and Application 938
60.1 Introduction 938
60.2 The Traditional Theory of Optimal Capital Structure5 939
60.2.1 Bankruptcy Costs 939
60.2.2 Agency Costs 941
60.3 Optimal Capital Structure in the Contingent Claims Framework 941
60.3.1 The Leland (1994) Model 942
60.3.2 The Leland and Toft (1996) Model 944
60.4 Recent Development of Capital Structure Models 946
60.4.1 The Fan and Sundaresan (2000) Model 947
60.4.2 The Goldstein et al. (2001) Model 948
60.4.3 Other Important Extensions 951
60.5 Application and Empirical Evidence of Capital Structure Models 953
60.6 Conclusion 955
References 955
Chapter 61 Actuarial Mathematics and Its Applications in Quantitative Finance 957
61.1 Introduction 957
61.2 Actuarial Discount and Accumulation Functions 957
61.3 Actuarial Mathematics of Insurance 959
61.4 Actuarial Mathematics of Annuity 962
61.5 Actuarial Premiums and Actuarial Reserves 963
61.5.1 Actuarial Premiums 963
61.5.2 Actuarial Reserve 964
61.6 Applications in Quantitative Finance 965
61.7 Conclusion 967
References 967
Chapter 62 The Prediction of Default with Outliers: Robust Logistic Regression 968
62.1 Introduction 968
62.2 Literature Review of Outliers in Conventional and in Logit Regression 969
62.2.1 Outliers in Conventional Regression 969
62.2.2 Outliers in Logit Regression: Robust Logistic Regression 969
62.3 Five Validation Tests 970
62.3.1 Contingency Table (Cross-Classification Table) 970
62.3.2 Cumulative Accuracy Pro le (CAP) 970
62.3.3 Receiver Operating Characteristic (ROC) 971
62.3.4 Kolmogorov-Smirnov (KS) 971
62.3.5 Brier Score 971
62.4 SourceofDataandEmpiricalModel 972
62.4.1 Source of Data 972
62.4.2 Empirical Model 972
62.5 Empirical Results 972
62.6 Conclusion 976
References 979
Chapter 63 Term Structure of Default-Free and Defaultable Securities: Theory and Empirical Evidence 981
63.1 Introduction 981
63.2 Definitions and Notations 982
63.2.1 Zero-Coupon Bonds 982
63.2.2 Term Structure of Interest Rates 982
63.2.3 Instantaneous Interest Rate 982
63.2.4 Forward Rate 982
63.2.5 Instantaneous Forward Rate 982
63.3 Bond Pricing in Dynamic Term Structure Model Framework 982
63.3.1 Spot Rate Approach 982
63.3.2 Forward Rate Approach 983
63.4 Dynamic Term Structure Models 983
63.4.1 Af ne DTSMs 983
63.4.2 Quadratic DTSMs 985
63.4.3 DTSMs with Jumps 986
63.4.4 DTSMs with a Regime Switching 986
63.4.5 DTSMs with Stochastic Volatility 987
63.4.6 Other Non-af ne DTSMs 987
63.4.7 Empirical Performance 988
63.5 Models of Defaultable Bonds 990
63.5.1 Structural Models 990
63.5.2 Reduced-Form Models 990
63.5.3 Empirical Issues 997
63.6 Interest Rate and Credit Default Swaps 998
63.6.1 Valuation of Interest Rate Swap 998
63.6.2 Valuation of Credit Default Swaps 999
63.6.3 Empirical Issues 1001
63.7 Concluding Remarks 1003
References 1003
Chapter 64 Liquidity Risk and Arbitrage Pricing Theory 1008
64.1 Introduction 1008
64.2 The Model 1010
64.2.1 Supply Curve 1010
64.2.2 Trading Strategies 1011
64.2.3 The Marked-to-Market Value of a s.f.t.s. and Its Liquidity Cost 1012
64.3 The Extended First Fundamental Theorem 1012
64.4 The Extended Second Fundamental Theorem 1013
64.5 Example (Extended BlackScholes Economy) 1016
64.5.1 The Economy 1016
64.5.2 Call Option Valuation 1017
64.6 Discontinuous Supply Curve Evolutions 1017
64.6.1 The Supply Curve and s.f.t.s.s 1017
64.6.2 The Extended First Fundamental Theorem 1018
64.6.3 The Extended Second Fundamental Theorem 1018
64.7 Conclusion 1018
References 1018
Appendix 64A 1019
Chapter 65 An Integrated Model of Debt Issuance, Refunding, and Maturity 1026
65.1 Introduction 1026
65.2 The Model 1027
65.2.1 Cost Factors 1027
65.2.2 Development of the Model 1028
65.3 Operationalizing the Model 1030
65.3.1 Information Required 1030
65.3.2 Outputs 1031
65.3.3 Optimization 1031
65.3.4 Solution 1032
65.4 Numerical Illustration 1033
65.4.1 Methodology 1034
65.4.2 Results 1035
65.4.3 Optimal Policy Decisions 1035
65.4.4 Cost Information 1035
65.4.5 Moving Horizon 1036
65.4.6 Economic Implications and Future Research 1036
65.5 Conclusions 1037
References 1038
Chapter 66 Business Models: Applications to Capital Budgeting, Equity Value, and Return Attribution 1040
66.1 Introduction 1040
66.2 The Model Assumptions 1041
66.3 Simulation Results of the Capital Budgeting Decisions 1044
66.4 Relative Valuation of Equity 1047
66.5 Equity Return Attribution 1049
66.6 Conclusion 1050
References 1050
Appendix 66A Derivation of the Risk Neutral Probability 1051
Appendix 66B The Model for the Fixed OperatingCostatTimeT 1051
Appendix 66C The Valuation Model Using the Recombining Lattice 1052
Appendix 66D Input Data of the Model 1053
Chapter 67 Dividends Versus Reinvestments in Continuous Time: A More General Model 1054
67.1 Introduction 1054
67.2 The Model 1054
67.3 The Solution 1056
67.4 Expected Bankruptcy Time 1057
67.5 Further Remarks 1058
67.6 Conclusion 1058
References 1059
Chapter 68 Segmenting Financial Services Market: An Empirical Study of Statistical and Non-parametric Methods 1060
68.1 Introduction 1060
68.2 Methodology 1061
68.2.1 Linear Discrimination by the Mahalanobis Method 1061
68.2.2 Linear Discrimination by Logit Regression 1061
68.2.3 Mathematical Programming 1062
68.3 Evaluating the Classification Function 1063
68.4 Experimental Design 1064
68.5 Results 1064
68.6 Conclusions 1065
References 1065
Chapter 69 Spurious Regression and Data Mining in Conditional Asset Pricing Models 1066
69.1 Introduction 1066
69.2 Spurious Regression and Data Mining in Predictive Regressions 1067
69.3 Spurious Regression, Data Mining, and Conditional Asset Pricing 1068
69.4 The Data 1068
69.5 The Models 1070
69.5.1 Predictive Regressions 1070
69.5.2 Conditional Asset Pricing Models 1071
69.6 Results for Predictive Regressions 1072
69.6.1 Pure Spurious Regression 1072
69.6.2 Spurious Regression and Data Mining 1075
69.7 Results for Conditional Asset Pricing Models 1079
69.7.1 Cases with Small Amounts of Persistence 1079
69.7.2 Cases with Persistence 1079
69.7.3 Suppressing Time-Varying Alphas 1081
69.7.4 Suppressing Time-Varying Betas 1081
69.7.5 A Cross-Section of Asset Returns 1082
69.7.6 Revisiting Previous Evidence 1084
69.8 Solutions to the Problems of Spurious Regression and Data Mining 1085
69.8.1 Solutions in Predictive Regressions 1085
69.8.2 Solutions in Conditional Asset Pricing Models 1086
69.9 Robustness of the Asset Pricing Results 1086
69.9.1 Multiple Instruments 1087
69.9.2 Multiple-Beta Models 1087
69.9.3 Predicting the Market Return 1087
69.9.4 Simulations Under the Alternative Hypothesis 1087
69.10 Conclusions 1087
References 1088
Chapter 70 Issues Related to the Errors-in-Variables Problems in Asset Pricing Tests 1090
70.1 Introduction 1090
70.2 The Errors-in-Variables Problem 1091
70.3 A Correction for the Errors-in-Variables Bias 1093
70.3.1 Homoscedastic Market Model Disturbances 1094
70.3.2 Sensitivity of the EIV Correction to the Factors 1096
70.3.3 Heteroscedastic Market Model Disturbances 1097
70.3.4 Simulation Evidence 1097
70.4 Results 1098
70.4.1 Data 1098
70.4.2 Cross-Sectional Dependence Between Residuals 1100
70.4.3 Beta Risk Price Estimates After the EIV Correction 1101
70.4.4 Estimation Efficiency of the Beta Risk Price Estimates 1106
70.5 Conclusions 1107
References 1107
Chapter 71 McMC Estimation of Multiscale Stochastic Volatility Models 1108
71.1 Introduction 1108
71.2 Multiscale Modeling and McMC Estimation 1109
71.2.1 Continuous Time Model 1109
71.2.2 Discretization of the Model 1109
71.2.3 Discrete Time Model Specification 1110
71.2.4 Prior Specification 1111
71.2.5 Estimation 1111
71.3 Simulation Study 1112
71.4 Empirical Application: FX Data 1112
71.5 Implication on Derivatives Pricing and Hedging 1117
71.6 Conclusions 1117
References 1118
Appendix 71A Proof of Independent Factor Equivalence 1118
Appendix 71B Full Conditionals 1119
Chapter 72 Regime Shifts and the Term Structure of Interest Rates 1120
72.1 Introduction 1120
72.2 Regime-Switching and Short-Term Interest Rate 1121
72.2.1 Short-Term Interest Rate Models 1121
72.2.2 Regime-switching 1122
72.3 Regime-Switching Term Structure Models in Discreet Time 1125
72.3.1 State Variables 1125
72.3.2 The Stochastic Discount Factor 1125
72.3.3 Solving for the Term Structure of Interest Rates 1126
72.4 Regime-Switching Term Structure Models in Continuous Time 1127
72.4.1 A Useful Representation for Regime Shift 1128
72.4.2 Regime-Dependent Jump Diffusion Model for the Term Structure of Interest Rates 1129
72.5 Conclusion 1132
References 1132
Chapter 73 ARM Processes and Their Modeling and Forecasting Methodology 1134
73.1 Introduction 1134
73.2 Overview of ARM Processes 1135
73.2.1 Background ARM Processes 1135
73.2.2 Foreground ARM Processes 1136
73.2.3 Transition Functions of Background ARM Processes 1136
73.2.4 Autocorrelation Functions of Foreground ARM Processes 1137
73.2.5 Empirical Distributions 1138
73.2.6 Stitching Transformations 1138
73.3 The ARM Modeling Methodology 1138
73.4 The ARM Forecasting Methodology 1139
73.4.1 Selection of the Mixing Parameter 1140
73.4.2 Computation of Conditional Expectations 1141
73.4.3 Computation of Conditional Distributions 1142
73.5 Example: ARM Modeling of an S&P 500 Time Series 1144
73.6 Summary 1147
References 1148
Chapter 74 Alternative Econometric Methods for Information-based Equity-selling Mechanisms 1149
74.1 Introduction 1149
74.2 The Information Contents of Equity-Selling Mechanisms 1150
74.3 Alternative Econometric Methods for Information-Based Equity-Selling Mechanisms 1151
74.3.1 The Two-Stage Estimation Approach 1152
74.3.2 The Conditional Correlation Approach 1153
74.3.3 The Nonparametric Approach 1158
74.4 Conclusions 1159
References 1160
Chapter 75 Implementation Problems and Solutions in Stochastic Volatility Models of the Heston Type 1162
75.1 Introduction 1162
75.2 The Transform-Based Solution for Hestons Stochastic Volatility Model 1162
75.2.1 Call Option 1163
75.2.2 Put Option 1164
75.2.3 Digital Call 1164
75.2.4 Cash-Secured Put 1164
75.3 Solutions to the Discontinuity Problem of Hestons Formula 1165
75.3.1 Rotation-Corrected Angle 1165
75.3.2 Direct Integration 1166
75.3.3 Simple Adjusted Formula 1166
75.4 Conclusion 1167
References 1168
Chapter 76 Revisiting Volume vs. GARCH Effects Using Univariate and Bivariate GARCH Models: Evidence from U.S. Stock Markets 1169
76.1 Introduction 1169
76.2 The Mixture of Distribution Hypothesis 1171
76.3 Data and Methodology 1171
76.4 Empirical Findings in NYSE 1172
76.5 Conclusion 1174
References 1175
Appendix 76A 1176
Chapter 77 Application of Fuzzy Set Theory to Finance Research: Method and Application 1178
77.1 Introduction 1178
77.2 Fuzzy Set 1179
77.2.1 The Definition of Fuzzy Set 1179
77.2.2 Membership Function 1180
77.2.3 Fuzzy Logic 1182
77.2.4 The Operations of Fuzzy Set 1182
77.2.5 Defuzzify 1183
77.2.6 Fuzzy Decision 1185
77.3 Applications of Fuzzy Set Theory 1185
77.3.1 A Example of Option 1185
77.3.2 The B-S Model Under Fuzzy Environment 1186
77.3.3 The derivation of fuzzy B-S OPM 1188
77.3.4 General Inference 1188
77.4 A Example of Fuzzy Binomial OPM 1189
77.4.1 One-Step Fuzzy Binomial OPM 1189
77.4.2 Two-Step Fuzzy Binomial OPM 1190
77.4.3 N-Step Fuzzy Binomial OPM 1190
77.5 An Example of Real Options 1191
77.6 Fuzzy Regression 1192
77.7 Conclusion 1193
References 1194
Chapter 78 Hedonic Regression Analysis in Real Estate Markets: A Primer 1195
78.1 Introduction 1195
78.2 The Theoretical Foundation 1195
78.3 The Data 1196
78.4 The Linear Model 1196
78.5 Empirical Specification 1197
78.5.1 The Dependent Variable 1197
78.5.2 Independent Variables 1197
78.5.3 Example Using the Linear Model 1197
78.6 The Semi-Log Model 1198
78.6.1 Example Using the Semi-Log Model 1198
78.7 The Box-Cox Model 1199
78.7.1 Example Using the Box-Cox Model 1199
78.8 Problems with Hedonic Modeling 1199
78.8.1 The Identi cation Problem 1199
78.8.2 The Equilibrium Pricing Problem 1200
78.9 Recent Developments 1200
78.10 Conclusion 1201
References 1201
Chapter 79 Numerical Solutions of Financial Partial Differential Equations 1202
79.1 Introduction 1202
79.2 The Model 1202
79.3 Discretization 1203
79.4 Finite Difference 1203
79.4.1 Explicit Method 1203
79.4.2 Implicit Method 1205
79.4.3 CrankNicolson Method 1208
79.5 Finite Volume 1210
79.6 Finite Element 1211
79.7 Empirical Result 1212
79.8 Conclusion 1213
References 1213
Further Reading 1214
Chapter 80 A Primer on the Implicit Financing Assumptions of Traditional Capital Budgeting Approaches 1215
80.1 Introduction 1215
80.2 Textbook Approaches to NPV 1216
80.3 Theoretical Valuation of Cash Flows 1218
80.4 An Example 1220
80.5 Personal Tax and Miller Equilibrium 1221
80.6 Conclusion 1223
References 1224
Chapter 81 Determinants of Flows into U.S.-Based International Mutual Funds 1226
81.1 Introduction 1226
81.2 Motivation and Hypotheses 1227
81.3 Data 1228
81.4 Methodology and Empirical Results 1229
81.4.1 Diversification and International Mutual Fund Flows 1232
81.4.2 Information Asymmetry, Return Chasing, and International Mutual Fund Flows 1238
81.4.3 Home Bias and International Mutual Fund Flows 1238
81.4.4 Monthly International Mutual Fund Flows 1238
81.5 Conclusion 1238
References 1244
Appendix 81A Econometric Analysis of Panel Data 1244
Data Appendix 1245
Chapter 82 Predicting Bond Yields Using Defensive Forecasting 1247
82.1 Introduction 1247
82.1.1 On-Line Prediction 1247
82.1.2 Applying the Framework to Finance 1248
82.1.3 Probability Forecasting 1249
82.2 Game-Theoretic Probability 1250
82.2.1 Villes Theorem 1250
82.2.2 Martingales in Villes Picture 1251
82.2.3 Borels Strong Law in Game-Theoretic Form 1252
82.2.4 Bernoullis Theorem in Game-Theoretic Form 1253
82.2.5 Bounded Forecasting 1254
82.3 Defensive Forecasting 1255
82.3.1 Defeating a Continuous Strategy for Skeptic 1255
82.3.2 Calibration 1256
82.3.3 Resolution 1258
82.3.4 Defensive Forecasting of Prices 1259
82.4 Predicting Bond Yields 1259
82.4.1 Data 1260
82.4.2 Implementation 1260
82.4.3 Empirical Results 1261
82.5 Conclusion 1261
References 1261
Chapter 83 Range Volatility Models and Their Applications in Finance 1263
83.1 Introduction 1263
83.2 The Price Range Estimators 1264
83.3 The Range-Based Volatility Models 1266
83.3.1 The Random Walk Model 1266
83.3.2 The MA Model 1266
83.3.3 The EWMA Model 1266
83.3.4 The AR Model 1266
83.3.5 The Discrete-Time Range-Based SV Model 1266
83.3.6 The Range-Based EGARCH Model 1267
83.3.7 The CARR Model 1267
83.3.8 The Range-Based DCC Model 1268
83.4 The Realized Range Volatility 1268
83.5 The Financial Applications and Limitations of the Range Volatility 1269
83.6 Conclusion 1269
References 1270
Chapter 84 Examining the Impact of the U.S. IT Stock Market on Other IT Stock Markets 1272
84.1 Introduction 1272
84.2 Data and Methodology 1273
84.3 Empirical Results 1274
84.4 Conclusions 1278
References 1278
Appendix 84A 1279
Chapter 85 Application of Alternative ODE in Finance and Economics Research 1281
85.1 Introduction 1281
85.2 Ordinary Differential Equation 1282
85.2.1 Classical Techniques 1282
85.2.2 Laplace Transformation 1282
85.2.3 EulerLagrange Equation 1283
85.3 Applications of ODE in Deterministic System 1283
85.3.1 Gross Domestic Product 1283
85.3.2 Investment of the Firm 1284
85.4 Applications of ODE in Stochastic System 1285
85.4.1 Preliminary 1285
85.4.2 Application in Capital Structure Management 1287
85.5 Conclusion 1288
References 1288
Chapter 86 Application of Simultaneous Equation in Finance Research 1289
86.1 Introduction 1289
86.2 Two-Stage and Three-Stage Least Squares Method 1290
86.2.1 Identi cation Problem 1290
86.2.2 Two-Stage Least Squares 1292
86.2.3 Three-Stage Least Squares 1292
86.3 Application of Simultaneous Equation in Finance Research 1293
86.4 Conclusion 1293
References 1294
Chapter 87 The Fuzzy Set and Data Mining Applications in Accounting and Finance 1295
87.1 Introduction 1295
87.2 A Fuzzy Approach to International Transfer Pricing 1295
87.3 A Fuzzy Set Approach to Human Resource Allocation of a CPA Firm 1300
87.4 A Fuzzy Set Approach to Accounting Information System Selection 1304
87.5 Fuzzy Set Formulation to Capital Budgeting 1307
87.6 A Data Mining Approach to Firm Bankruptcy Predictions 1312
87.7 Conclusion 1317
References 1317
Chapter 88 Forecasting S&P 100 Volatility: The Incremental Information Content of Implied Volatilities and High-Frequency Index Returns 1320
88.1 Introduction 1320
88.2 Data 1321
88.2.1 Daily Index Returns 1321
88.2.2 Implied Volatilities 1321
88.2.3 High-Frequency Stock Returns 1322
88.3 Methodology for Forecasting Volatility 1323
88.3.1 In-Sample Models 1323
88.3.2 Forecasting Methods 1323
88.3.3 Forecast Evaluation 1325
88.4 Results 1325
88.4.1 In-Sample ARCH Results 1325
88.4.2 Out-of-Sample Forecasting 1327
88.5 Conclusion 1330
References 1331
Chapter 89 Detecting Structural Instability in Financial Time Series 1332
89.1 Introduction 1332
89.2 Genesis of the Literature 1332
89.3 Problems of Multiple Change Points 1334
89.4 Here Came the GARCH and Its Brethrens 1335
89.5 Examples of Structural Shift Analysis in Financial Time Series 1336
89.5.1 Analysis of Volatility in Emerging and Developed Stock Markets 1336
89.5.2 Detecting Volatility Changes Across the Oil Sector 1338
89.5.3 Other Recent Applications of Variance Shift Detection 1339
89.6 Implications of Structural Instability to Financial Theories and Practice 1339
89.7 Direction of Future Research and Developments 1340
89.8 Epilogue 1341
References 1341
Chapter 90 The Instrument Variable Approach to Correct for Endogeneity in Finance 1343
90.1 Introduction 1343
90.2 Endogeneity: The Statistical Issue 1344
90.3 Instrumental Variables Approach to Endogeneity 1344
90.3.1 Instrumental Variables and Two-Stage Least Square (2SLS) 1344
90.3.2 Hypothesis Testing with 2SLS 1345
90.3.3 Instrumental Variables and Generalized Method of Moments 1346
90.3.4 Hypothesis Testing Using GMM 1347
90.4 Validity of Instrumental Variables 1347
90.4.1 Test for Exogeneity of Instruments 1347
90.4.2 Whether IV Estimator Is Really Needed 1348
90.5 Identi cation and Inferences with Weak Instruments 1350
90.5.1 Problems with Weak Instruments and Diagnosis 1350
90.5.2 Possible Cures and Inferences with Weak Instruments 1351
90.6 Empirical Applications in Corporate Finance 1352
90.7 Conclusion 1354
References 1354
Chapter 91 Bayesian Inference of Financial Models Using MCMC Algorithms 1356
91.1 Introduction 1356
91.2 Bayesian Inference and MCMC Algorithms 1356
91.2.1 Bayes Theorem 1356
91.2.2 Markov Chain Monte Carlo Algorithms 1357
91.3 CKLS Model with ARMA-GARCH Errors 1359
91.4 Copula Model for FTSE100 and S&P500 1361
91.5 Conclusion 1364
References 1365
Chapter 92 On Capital Structure and Entry Deterrence 1366
92.1 Introduction 1366
92.2 The Setting 1367
92.3 Equilibrium 1369
92.4 Capital Structure and Entry Deterrence 1371
92.5 Conclusion 1373
References 1374
Chapter 93 VAR Models: Estimation, Inferences, and Applications 1375
93.1 Introduction 1375
93.2 A Brief Discussion of VAR Models 1375
93.2.1 Estimation 1375
93.2.2 Inferences 1376
93.3 Applications of VARs in Finance 1377
93.3.1 Stock Return Predictability and Optimal Asset Allocation 1377
93.3.2 Exchange Rate Prediction 1378
93.3.3 Measuring Market Quality and Informational Content of Stock Trades 1379
93.3.4 Relative Informational Efficiency 1380
93.4 Conclusion 1381
References 1381
Chapter 94 Signaling Models and Product Market Games in Finance: Do We Know What We Know?* 1383
94.1 Introduction 1383
94.2 Supermodularity: Definitions 1384
94.3 Supermodularity in Signaling Models 1384
94.3.1 Dividend Signaling 1385
94.3.2 An Example 1386
94.4 Supermodularity in Product Market Games 1387
94.4.1 Effect of Leverage Decisions
94.4.2 Loan Commitments in a Duopoly
94.5 Empirical Evidence 1390
94.6 Conclusion 1391
References 1391
Chapter 95 Estimation of Shortand Long-Term VaR for Long-Memory Stochastic Volatility Models 1393
95.1 Introduction 1393
95.2 Long Memory in Stochastic Volatility 1394
95.3 VaR Calculation 1395
95.3.1 Daily VaR 1395
95.3.2 Long-Term VaR 1396
95.3.3 Implementation 1397
95.4 Conclusions 1398
References 1398
Chapter 96 Time Series Modeling and Forecasting of the Volatilities of Asset Returns 1400
96.1 Introduction 1400
96.2 Conditional Heteroskedasticity Models 1400
96.2.1 Stylized Facts on Time Series of Asset Returns 1400
96.2.2 Historic Volatility and Exponentially Weighted Moving Averages 1401
96.2.3 The GARCH Model 1401
96.2.4 The Exponential GARCH Model 1402
96.2.5 ARMA-GARCH and ARMA-EGARCH Models 1402
96.2.6 Volatility Persistence and Integrated GARCH Models 1402
96.2.7 Stochastic Volatility Models 1403
96.3 Regime-Switching, Change-Point and Spline-GARCH Models of Volatility 1404
96.3.1 Regime-Switching Volatility Models 1404
96.3.2 Spline-GARCH Models 1405
96.3.3 Stochastic Change-Point ARX-GARCH Models 1405
96.4 Multivariate Volatility Models and Applications to MeanVariance Portfolio Optimization 1407
96.4.1 Multivariate GARCH Models 1407
96.4.2 A New Approach and Its Application to MeanVariance Portfolio Optimization 1407
96.5 Conclusion 1408
References 1408
Chapter 97 Listing Effects and the Private Company Discount in Bank Acquisitions 1410
97.1 Introduction 1410
97.2 Why Acquiring Firms May Pay Less for Unlisted Targets 1411
97.2.1 Motivations of the Acquiring Firm 1411
97.2.2 Motivations of Owners of Unlisted Targets 1412
97.2.3 Why Study Acquisitions in the Commercial Banking Industry? 1412
97.3 Sample Characteristics 1413
97.3.1 Sample Selection 1413
97.3.2 Selected Sample Characteristics 1413
97.4 Event Study Analysis 1414
97.4.1 Event Study Approach 1414
97.4.2 Gains to Acquiring Firms for Listed and Unlisted Targets 1416
97.5 Findings Based on Multiples 1416
97.5.1 Acquisition Multiples 1416
97.5.2 Summary Statistics for Multiples 1416
97.5.3 Relating Acquisition Multiples to Firm and Deal Characteristics 1418
97.6 Cross-Sectional Analysis 1422
97.6.1 Regression Specification 1422
97.6.2 Regression Results 1422
97.6.3 Acquisition Discounts 1425
97.7 Conclusions 1425
References 1426
Chapter 98 An ODE Approach for the Expected Discounted Penalty at Ruin in Jump Diffusion Model (Reprint)* 1427
98.1 Introduction 1427
98.2 Integro-Differential Equation 1428
98.3 Explicit Formula for ODE Method 1430
98.4 The Constant Vector Q: Second Method 1435
98.5 Conclusion 1439
References 1440
Appendix 98A Proofs 1440
Appendix 98B Toolbox for Phase-Type Distributions 1444
Appendix 98C First Order Derivative of at Zero 1444
Chapter 99 Alternative Models for Estimating the Cost of Equity Capital for Property/Casualty Insurers* 1447
99.1 Introduction 1447
99.2 Prior Work 1448
99.3 Model-Specification and Estimation 1449
99.3.1 CAPM 1449
99.3.2 APT 1450
99.3.3 Uni cation of the CAPM and APT 1451
99.4 Data Description and Cost of Equity Capital Estimates 1452
99.4.1 Data 1452
99.4.2 Empirical Results 1453
99.5 Evaluations of Simulations and Estimates 1458
99.5.1 MSE Method 1458
99.5.2 Theil U 2 1459
99.5.3 Conditional Efficiency Method 1459
99.5.4 Comparison of Alternative Testing Results 1460
99.6 Summary and Conclusion 1462
References 1463
Chapter 100 Implementing a Multifactor Term Structure Model 1465
100.1 Introduction 1465
100.2 A Multifactor Term Structure Model 1465
100.3 Pricing Options in the Multifactor Model 1467
100.4 Calibrating a Multifactor Model 1469
100.5 Conclusion 1470
References 1470
Chapter 101 Taking Positive Interest Rates Seriously* 1471
101.1 Introduction 1471
101.2 Background 1472
101.3 The Model 1473
101.4 The Hump-Shaped Forward Rate Curve 1476
101.5 Fitting the US Treasury Yields and US Dollar Swap Rates 1477
101.5.1 Data and Estimation 1477
101.5.2 Model Performance 1477
101.5.3 The Time Series Behavior of the Interest-Rate Factors 1478
101.6 Extensions: Jumps in Interest Rates 1480
101.7 Conclusion 1482
References 1482
Appendix 101A Factor Representation 1483
Appendix 101B Extended Kalman Filter and Quasilikelihood 1484
Chapter 102 Positive Interest Rates and Yields: Additional Serious Considerations* 1485
102.1 Introduction 1485
102.2 A Non-Zero Bound for Interest Rates 1485
102.3 The CoxIngersollRoss and PanWu Term Structure Models 1486
102.4 Bubble-Free Prices 1488
102.5 Multivariate Af ne Term-Structure Models with Zero Bounds on Yields 1493
102.6 Non-Af ne Term Structures with Yields Bounded at Zero 1496
102.7 Non-Zero Bounds for Yields 1498
102.8 Conclusion 1499
References 1499
Appendix 102A 1499
Chapter 103 Functional Forms for Performance Evaluation: Evidence from Closed-End Country Funds* 1505
103.1 Introduction and Motivation 1505
103.2 Literature Review 1506
103.2.1 CES Functional Form of the CAPM 1506
103.2.2 Generalized Functional Form of the CAPM 1507
103.2.3 Translog Functional Form of the CAPM 1508
103.3 Model Estimation 1508
103.3.1 Generalized Functional Form Model for Closed-End Fund 1508
103.3.2 Functional Form of the International Closed-End Country Fund Model 1509
103.4 Data and Methodology 1509
103.4.1 Data 1509
103.4.2 Methodology 1515
103.5 Empirical Results 1516
103.5.1 Generalized Functional Form for International Closed-End Fund 1516
103.5.2 Generalized Global Model for International Closed-End Fund 1519
103.5.3 Comparison of Functional Form Model Between Developed Market Funds and Emerging Market Funds, Between Regional Funds and 1519
103.5.4 Performance Evaluation 1527
103.6 Conclusion 1527
References 1535
Chapter 104 A Semimartingale BSDE Related to the Minimal Entropy Martingale Measure* 1536
104.1 Introduction 1536
104.2 Some Basic Definitions, Conditions, and Auxiliary Facts 1537
104.3 Backward Semimartingale Equation for the Value Process 1539
104.4 Conclusions 1545
References 1546
Chapter 105 The Density Process of the Minimal Entropy Martingale Measure in a Stochastic Volatility Model with Jumps (Reprint)* 1547
105.1 Introduction 1547
105.2 The Market 1548
105.3 The Minimal Entropy Martingale Measure 1549
105.4 The Density Process 1551
105.5 The Entropy Price of Derivatives and Integro-Partial Differential Equations 1553
105.6 Conclusions 1554
References 1555
Chapter 106 Arbitrage Detection from Stock Data: An Empirical Study 1556
106.1 Introduction 1556
106.1.1 Background 1556
106.1.2 Previous Studies in Arbitrage Detection 1556
106.1.3 The Use of HilbertHuang Transformation on Arbitrage Detection 1557
106.2 Arbitrage Detection: Volatility Change 1558
106.2.1 Volatility Change in Normal Distribution Models 1558
106.2.2 Volatility Change in Geometric Brownian Motion Models 1560
106.2.3 Volatility Change in Markov Switch Models 1560
106.2.4 A Brief Summary 1561
106.3 Arbitrage Detection: Mean Change 1562
106.3.1 Mean Change in Normal Distribution Models 1562
106.3.2 Mean Change in Brownian Motion Models 1562
106.3.3 A Brief Summary 1563
106.4 Empirical Studies 1565
106.4.1 Volatility Change Data (Subprime Mortgage Crisis in 2007) 1566
106.4.2 Volatility Change Data (Dot-Com Bubble in 2000) 1568
106.4.3 A Brief Summary 1568
106.5 Conclusions and Further Researches 1569
106.5.1 Conclusions 1569
106.5.2 Further Research 1570
References 1570
Chapter 107 Detecting Corporate Failure 1571
107.1 Introduction 1571
107.2 The Possible Causes of Bankruptcy 1572
107.3 The Methods of Bankruptcy 1572
107.3.1 Company Voluntary Arrangements 1572
107.3.2 Administration Order 1573
107.3.3 Administrative Receivership 1573
107.3.4 Creditors Voluntary Liquidation 1573
107.3.5 Members Voluntary Liquidation 1573
107.3.6 Compulsory Liquidation 1573
107.4 Prediction Model for Corporate Failure 1574
107.4.1 Financial Ratio Analysis and Discriminant Analysis 1574
107.4.2 Conditional Probability Analysis 1576
107.4.3 Three CPA Models: LP, PM, and LM 1577
107.4.4 Time Series Analysis: CUSUM Model 1578
107.4.5 Merton Model 1579
107.5 The Selection of Optimal Cutoff Point 1581
107.6 Recent Development 1582
107.7 Conclusion 1582
References 1582
Chapter 108 Genetic Programming for Option Pricing 1585
108.1 Introduction 1585
108.2 Genetic Program Elements 1586
108.2.1 Basic Approach 1586
108.2.2 Fitness and Selection Criteria 1588
108.2.3 Advantages of Genetic Programming 1588
108.2.4 Convergence Characteristics of Genetic Algorithms and Programs 1588
108.3 BlackScholes Example 1589
108.4 Extensions 1591
108.5 Conclusion 1591
References 1592
Chapter 109 A Constant Elasticity of Variance (CEV) Family of Stock Price Distributions in Option Pricing, Review, and Integration 1593
109.1 Introduction 1593
109.2 The CEV Diffusion and Its Transition Density 1594
109.3 The CEV Option Pricing Models 1597
109.4 Computing the Non-Central Chi-Square Probabilities 1600
109.4.1 A Formula for Non-Central Chi-Square Distribution, An Infinite Sum of Poisson-Weighted Central Chi-Squares 1600
109.4.2 Various Approximation Formulas 1600
109.5 Conclusion 1601
Appendix 109A 1601
References 1603
References 1604
Author Index 1662
Subject Index 1686