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Methods and Applications of
Statistics in Business, Finance,and Management Science
N. Balakrishnan
McMaster UniversityDepartment ofStatistics
Hamilton, Ontario, Canada
4 WILEY
A JOHN WILEY & SONS, INC., PUBLICATION
Contents
Preface v
Contributors vii
1 Alternatives to Black-Scholes Formulation in Finance 1
1.1 Introduction 1
1.2 Motivation for Alternative Models 2
1.3 Methods of Valuation 3
1.4 Stochastic Interest-Rate Models 7
1.5 Stochastic Volatility Models 11
1.6 Models with Levy Processes 16
References 22
2 Analytical Methods for Risk Management: An Engineering Systems
Perspective 25
2.1 Introduction 25
2.2 Risk Management in Engineering Systems 26
2.3 Risk Assessment and Analysis 31
2.4 Allocating Resources 51
2.5 Conclusion 53
References and Relevant Literature 55
3 ARCH and GARCH Models 59
3.1 Introduction 59
3.2 Volatility Clustering 59
3.3 GARCH 62
3.4 IGARCH 65
3.5 EGARCH 65
3.6 Alternative Parameterizations 66
3.7 Time-Varying Parameter and Bilinear Models 66
3.8 Estimation and Inference 66
3.9 Testing 67
3.10 Empirical Example 67
3.11 Future Developments 68
xi
XU Contents
References 69
4 Bayesian Forecasting 72
4.1 Introduction 72
4.2 Background 72
4.3 Dynamic Bayesian Models 73
4.4 Normal Dynamic Linear Models 74
4.5 Component Dynamic Linear Models 76
4.6 Discounting 77
4.7 Intervention 77
4.8 Monitoring and Adaptation 78
4.9 Mixtures of Dynamic Models 78
4.10 Non-normal Nonlinear Models 79
4.11 Multivariate Models 80
4.12 Computation and Simulation 80
4.13 Related Areas 81
References 81
5 Bayesian Networks 85
5.1 Examples and Definitions 85
5.2 Constructing Bayesian-Network Models 90
5.3 Models Specified by Input Lists 90
5.4 Graphically Specified Models 91
5.5 Conditionally Specified Models 91
5.6 Learning Models from Data 91
5.7 Propagation in Bayesian Networks 92
5.8 Available Software 95
References 95
6 Box-Jenkins Model 98
6.1 Introduction 98
References 103
7 Business Forecasting Methods 104
7.1 Introduction 104
7.2 Trend Curves 105
7.3 Exponential Smoothing 106
7.4 Exponential Smoothing and Arima Model Building 108
7.5 Regression and Econometric Methods 109
7.6 Regression and Time-Series Principles 110
7.7 Combination of Forecasts Ill
7.8 Evaluation of Forecasts 112
7.9 Summary 114
References 114
Contents Xlll
8 Combination of Forecasts 116
8.1 Introduction 116
8.2 The Theory of Combining 116
8.3 Estimators of the Weights 118
8.4 An Example 120
8.5 Further Extensions 120
References 120
9 Decision Theory 122
9.1 Introduction 122
9.2 Parameters, Decisions, and Consequences 122
9.3 Utility 123
9.4 Components of a Decision Problem 123
9.5 Subjective Probability 124
9.6 Decision Analysis 124
9.7 Statistical Decision Problems 125
9.8 Conjugate Families of Prior Distributions 126
9.9 Improper Prior Distributions 127
9.10 Estimation and Tests of Hypothesis 129
9.11 Sequential Decision Problems 130
References 131
10 Dynamic Programming 133
10.1 Introduction 133
10.2 Definitions and Examples 133
10.3 Some Fundamental Principles 135
10.4 The Optimality Equation and Backward Induction 136
10.5 Stationary Plans 137
References 138
11 Estimation of Travel Distance 139
11.1 Introduction 139
11.2 Distance Functions 141
11.3 Goodness-of-Fit Criteria 145
11.4 Areas of Future Research 152
References 155
12 Financial Time Series 158
12.1 Asset Price and Return 158
12.2 Fundamental and Technical Analyses 161
12.3 Volatility Model 162
12.4 High-Frequency Data 166
12.5 Continuous-Time Model 167
References 170
XIV Contents
13 Forecasting 172
13.1 Introduction 172
13.2 Model Components 173
13.3 Model Fitting for Forecasting 175
13.4 Forecasting Methods 176
13.5 Forecast Quality 177
References 178
14 Foundations of Risk Measurement 180
14.1 Introduction 180
References 183
15 Functional Networks 185
15.1 Introduction 185
15.2 Elements of Functional Networks 185
15.3 Differences Between Standard NNs and FNs 187
15.4 Development and Implementation of FNs 188
15.5 An Example of Application 193
References 196
16 Game Theory 199
16.1 Introduction 199
16.2 Strategies and Payoffs 200
16.3 Applications to Statistics 208
References 209
Additional Reading 209
17 Intervention Model Analysis 211
17.1 Introduction 211
17.2 Time-Series and Intervention Models 211
17.3 Applications and Extensions 215
References 216
18 Inventory Theory 217
18.1 Introduction 217
18.2 Historical Background 217
18.3 Models with Known Demand 218
18.4 Models with Uncertain Demand 219
18.5 Conclusion 224
References 224
19 Manpower Planning 226
19.1 Introduction 226
19.2 Statistical Analysis of Wastage 226
19.3 Markov Models for Graded Systems 227
19.4 Renewal Models for Graded Systems 228
19.5 Literature 228
References 229
Contents XV
20 Markov Networks 230
20.1 Statement of the Problem 230
20.2 Some Basic Concepts of Graphs 230
20.3 Constructing Markov Network Models 238
20.4 Propagation in Markov Networks 240
20.5 Available Software 242
References 242
21 Methods of Estimation of Risks and Analysis of Business Processes 245
21.1 Introduction 245
21.2 Mathematical Models of Economic Systems in the Form of the Business
Processes Portfolio 247
21.3 Risks of Economic Systems 255
21.4 Economic Systems Factors Analysis 263
References 269
22 Mining Functional Data in Prediction Markets 273
22.1 Introduction 273
22.2 Prediction Markets 274
22.3 Data 276
22.4 Functional Data Analysis 277
22.5 Discussion 289
References 291
23 Models for Bid Arrivals and Bidder Arrivals in Online Auctions 293
23.1 Introduction 293
23.2 Motivation 293
23.3 Features of Bid Arrivals 295
23.4 The BARISTA: A Three-Stage Nonhornogeneous Poisson Process... 297
23.5 Relating Bidder Arrivals and Bid Arrivals 303
References 308
24 Multiserver Queues 310
24.1 Introduction 310
24.2 Markovian Queues 310
24.3 Non-Markovian Queues 312
24.4 Other Methods 313
References 314
25 Multivariate Time-Series Analysis 317
25.1 Introduction 317
25.2 Stationary Multivariate Time Series and Their Covariance Properties .317
25.3 Some Spectral Characteristics for Stationary Vector Processes 319
25.4 Linear Filtering Relations for Stationary Vector Processes 320
25.5 Linear Model Representations for Stationary Vector Processes 321
25.6 Vector Autoregressive Moving Average (ARMA) Model Representations 321
25.7 Nonstationary Vector Autoregressive Moving-Average Models 325
25.8 Forecasting for Vector Autoregressive Moving-Average Processes....
326
XVI Contents
25.9 Statistical Analysis of Vector Autoregressive Moving-Average Models. 327
References 329
26 Network Analysis 332
26.1 Introduction 332
27 Network of Queues 338
27.1 Introduction 338
27.2 Some Background 338
27.3 Some Results 339
27.4 More General Networks 341
27.5 Sojourn Times in Queueing Networks 341
27.6 Customer Flow in Networks 342
27.7 Other Approaches and Topics 342
References 345
28 Neural Networks 347
28.1 Introduction 347
28.2 Feed-Forward Networks 347
28.3 Recurrent Networks 351
28.4 Associative-Memory Networks and Boltzmaim Machines 351
28.5 Networks Trained by Unsupervised Learning 352
28.6 Use of the Bayesian Approach 353
28.7 Conclusion 355
References 355
Further Reading 357
29 Newsboy Inventory Problem 358
29.1 Introduction 358
References 364
30 Nonlinear Time Series 365
30.1 Introduction 365
30.2 Review of Linear Time Series 365
30.3 Nonparanietric Methods 366
30.4 Parametric Models 367
30.5 Other Surveys and Comparisons 371
References 372
31 Nonstationary Time Series 375
31.1 Introduction 375
31.2 Removing Nonstationary Means and Variances 375
31.3 Extensions 376
31.4 Homogeneous and Explosive Nonstationarity 381
31.5 Differencing 381
31.6 Starting Values and Nonstationarity 382
31.7 ARIMA Models 382
31.8 Sample Autocorrelations—Identifying the Degree of Differencing .... 382
Contents XVU
31.9 Estimation of Unit and Explosive Roots 383
31.10 Forecasting 383
31.11 Variations and Extensions 385
31.12 Nonstationary Spectral Analysis 385
References 387
32 PERT 389
32.1 Introduction 389
32.2 Finding the Expected Critical Path Length 390
32.3 Simulation and Statistical Computations 392
32.4 Estimation of Individual Activity Times 393
32.5 Conclusions 394
References 395
33 Prediction and Forecasting 396
33.1 Introduction 396
33.2 Regression Models 396
33.3 Regression and Smoothing Methods for Extrapolating a Single Time Series397
33.4 Forecasts from Univariate Time-Series Models 399
33.5 Forecasts from Multivariate Time-Series Models 401
33.6 State-Space Models, Kalman Filtering, and Bayesian Forecasting .... 402
33.7 Econometric Models 403
33.8 Input-Output Tables 404
33.9 Turning Points and Business Cycle Indicators 404
33.10 Surveys of Anticipations and Intentions 404
33.11 Combination of Forecasts 405
33.12 Prediction of Qualitative Characteristics 405
33.13 Forecast Quality and the Evaluation of Forecasts 405
References 406
34 Pricing Foreign Exchange Options with Stochastic Volatility 408
34.1 Introduction 408
34.2 Arbitrage-Free Cross-Currency Markets 410
34.3 Stein and Stein Stochastic Volatility Model with Vasicek Interest Rates 413
34.4 Heston's Stochastic Volatility Model with CIR Interest Rates 417
34.5 Foreign Exchange Option under Heston Volatility with Constant Interest
Rates 429
34.6 Concluding Remarks 430
References 432
35 Probabilistic Expert Systems 434
35.1 Introduction 434
35.2 Graph Types 438
35.3 Conditional Independence and Markov Properties 438
35.4 Specification of Joint Distribution 440
35.5 Local Computation Algorithm 442
35.6 Extensions 443
References 443
XVl'ii Contents
36 Problem Solving in Statistics 445
36.1 Introduction 445
36.2 Phase 1: Study Design 145
36.3 Phase 2: Data Collection 448
36.4 Phase 3: Data Analysis 450
36.5 Poslprocess Responsibilities 452
36.6 Conclusions 452
References 452
37 Queueing Theory 455
37.1 Introduction 455
37.2 Subsequent Development of the Simple Queue Model 456
37.3 Variants of the Simple Queueing Model 458
37.4 Concluding Remarks 458
References 459
38 Queues and Networks 463
38.1 Introduction 463
38.2 A Glimpse on Queueing Theory by Example 464
38.3 The Vocabulary of Queueing Theory 467
38.4 Little's Formulas 469
38.5 Markovian Queueing Systems of BD Type 471
38.6 General Service Times: The System M/G/l 477
38.7 The Systems M/G/c and G/G/c 479
38.8 Networks of Queues 480
38.9 Approximations and Numerical Methods 488
38.10 Simulation 489
References 490
39 Ranking and Selection Among Mutual Funds 493
39.1 Introduction 493
39.2 Statistical Underpinnings of Data Mining Using Combinatorial Fusion
Algorithm 498
39.3 Stochastic Dominance and Asymmetric Attitude Towards Risk 505
39.4 Summary and Final Remarks 505
References 506
40 Risk Theory 508
40.1 Introduction 508
References 512
41 Statistical Consulting 514
41.1 Definition 514
41.2 What Consultants Do 514
41.3 Historical Perspective 516
41.4 Skills Needed by a Consultant 518
41.5 Consulting and Communication 519
41.6 Computers and Consultants 519
Contents XIX
41.7 Keeping Up with Statistics 520
41.8 Ethics 520
41.9 Teaching Consulting 521
41.10 Rewards of Consulting 522
References 523
42 Statistical Methods in Inventory Effect and Analysis 524
42.1 Introduction 524
42.2 Futures Markets 525
42.3 Backwardation and Inventory Effect 526
42.4 Inventory Effect: A Preliminary Analysis 527
42.5 Ordered Bivariate Normal Distribution 529
42.6 Bivariate Lognorinal Distribution 532
42.7 Ordered Bivariate Lognormal Distribution 530
42.8 Conclusions 537
References 539
43 Statistical Methods in Risk Management by Futures Clearinghouses 541
43.1 Introduction 541
43.2 Margin Requirements 545
43.3 Settlement Frequency 557
43.4 Capital Requirements 560
43.5 Price Limits 562
43.6 Position Limits 564
43.7 Conclusion 565
References 566
44 Statistics in Auditing 568
44.1 Introduction 568
44.2 Study of Internal Control System 568
44.3 Study of Account Balances 568
44.4 Analytical Review 570
References 571
45 Statistics in Banking 572
45.1 Introduction 572
45.2 Further Reading 576
References 576
46 Statistics in Finance 578
46.1 Introduction 578
46.2 Regression Analysis and the Market Model 578
46.3 Factor, Multiple Discriminant, and Logit Applications 580
46.4 Time-Series Analyses of Financial Information 582
46.5 Statistical Decision Theory and Finance 583
References 584
XX Contents
47 Statistics in Management Science 586
47.1 Introduction 586
47.2 Using Regression to Estimate Managerial Decision Rules 587
47.3 Using Regression for Input Data in Modeling 588
47.4 Construction of Causal Models by Regression 589
47.5 Statistical Analysis of Algorithmic Performance Data 590
47. fi Sampling Theory 591
47.7 Other Statistical Tools 592
References 592
48 Statistics in Marketing 594
48.1 Introduction 594
48.2 Some Early Contributions 594
48.3 The Uses of Statistics in Marketing Research 597
48.4 Sample Survey Methods 597
48.5 Multivariate Techniques 598
48. fi Forecasting Methods 601
48.7 Psychometric Methods in the Measurement of Consumer Perceptions and
Preferences 603
48.8 Experimentation 607
48.9 Probability Models 609
References 610
49 Statistics of Risk Management 618
49.1 Introduction 618
49.2 General Concept of Risk
Management and
Monitoring 618
49.3 Scope 618
49.4 Evolution of Risk Management 619
49.5 Insurance 619
49.6 Gambling, Capital Budgeting, and Investments 619
49.7 Technological Risk Management 620
49.8 Low-Probability-High-Consequence Risk Management 621
49.9 Environmental Risk and
Monitoring Systems 622
49.10 Epidemiology and Disease Detection 623
49.11 Principles of Statistical Monitoring 623
References 624
50 Stochastic Differential Equations: Applications in Economics and Man¬
agement Science 626
50.1 Introduction 626
50.2 Option Pricing 627
50.3 Stochastic Optimal Control 629
50.4 Final Remarks 632
References 632
•
Contents XXI
51 Stochastic Games 634
51.1 Introduction 6.34
51.2 Special Cases 635
51.3 Computation 637
References 638
52 Stock Market Price Indexes 639
52.1 Introduction 639
52.2 Definition and Uses 639
52.3 Brief History 640
52.4 Main Issues 640
52.5 A Numerical Example 645
52.6 Two Major Stock Market Price Indexes 645
52.7 The S&P 500 649
52.8 Comparison of Four International Indexes 651
52.9 Stock Market Indexes and Portfolio Analysis 653
52.10 Summary 656
References 657
53 The Black-Scholes Formula and Its Applications in Finance 660
53.1 Introduction 660
53.2 The Black-Scholes Model 661
53.3 European Call and Put Options 665
53.4 Some Exotic Options 673
53.5 American Options 677
53.6 Application to the Modeling of Credit Risk 679
53.7 Real Options 684
References 685
54 Time Series 687
54.1 Introduction 687
54.2 Examples of Time Series 688
54.3 A Historical Perspective 691
54.4 Stationarity 691
54.5 The Frequency Domain 692
54.6 The Time Domain 692
54.7 State-Space Models 693
54.8 Transfer Functions and Interventions 694
54.9 Other Topics 694
54.10 Literature 695
54.11 Computer Programs 695
54.12 Future Developments 695
References 696
Index 698