The mathematics of financial modeling and investment management:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2004
|
| Series: | The Frank J. Fabozzi series
Wiley finance |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 778 S. graph. Darst. |
| ISBN: | 0471465992 |
Staff View
MARC
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| 245 | 1 | 0 | |a The mathematics of financial modeling and investment management |c Sergio M. Focardi ; Frank J. Fabozzi |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2004 | |
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Record in the Search Index
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|---|---|
| adam_text | Preface xiv
Acknowledgments xvi
About the Authors xviii
Commonly Used Symbols xlx
Abbreviations and Acronyms xx
CHAPTER 1
From Art to Engineering in Finance 1
Investment Management Process 2
Step 1: Setting Investment Objectives 2
Step 2: Establishing an Investment Policy 2
Step 3: Selecting a Portfolio Strategy 6
Step 4: Selecting the Specific Assets 7
Step 5: Measuring and Evaluating Performance 9
Financial Engineering in Historical Perspective 10
The Role of Information Technology 11
Industry s Evaluation of Modeling Tools 13
Integrating Qualitative and Quantitative Information 15
Principles for Engineering a Suite of Models 17
Summary 18
CHAPTER 2
Overview of Financial Markets, Financial Assets, and Market Participants 21
Financial Assets 21
Financial Markets 25
Classification of Financial Markets 25
Economic Functions of Financial Markets 26
Secondary Markets 27
Overview or Market Participants 34
Role of Financial Intermediaries 35
Institutional Investors 37
Insurance Companies 41
Pension Funds 41
Investment Companies 42
Depository Institutions 43
Endowments and Foundations 45
Common Stock 45
iii
Trading Locations 45
Stock Market Indicators 46
Trading Arrangements 48
Bonds 51
Maturity 51
Par Value 52
Coupon Rate 52
Provisions for Paying off Bonds 55
Options Granted to Bondholders 56
Futures and Forward Contracts 57
Futures versus Forward Contracts 58
Risk and Return Characteristics of Futures Contracts 59
Pricing of Futures Contracts 59
The Role of Futures in Financial Markets 63
Options 64
Risk Return for Options 66
The Option Price 66
Swaps 69
Caps and Floors 70 j
Summary 71 f
CHAPTER 3
Milestones in Financial Modeling and Investment Management 75
The Precursors: Pareto, Walras, and the Lausanne School 76
Price Diffusion: Bachelier 78 !
The Ruin Problem in Insurance: Lundberg 80
The Principles of Investment: Markowitz 81
Understanding Value: Modigliani and Miller 83
Modigliani Miller Irrelevance Theorems and the
Absence of Arbitrage 84
Efficient Markets: Fama and Samuelson 85
Capital Asset Pricing Model: Sharpe, Lintner, and Mossin 86
The Multifactor CAPM: Merton 87
Arbitrage Pricing Theory: Ross 88
Arbitrage, Hedging, ana Option Theory:
Black, Scholes, and Merton 89
Summary 90
CHAPTER 4
Principles of Calculus 91
Sets and Set Operations 93
Proper Subsets 93
Empty Sets 95
Union of Sets 95
Intersection of Sets 95
Elementary Properties of Sets 96 |
Distances and Quantities 96 f
n tuples 97
Distance 98
Density of Points 99
Functions 100
Variables 101
Limits 102
Continuity 103
Total Variation 105
Differentiation 106
Commonly Used Rules for Computing Derivatives 107
Higher Order Derivatives 111
Application to Bond Analysis 112
Taylor Series Expansion 121
Application to Bond Analysis 122
Integration 127
Rietnann Integrals 127
Properties ofRiemann Integrals 129
Lebesque Stieltjes Integrals 130
Indefinite and Improper Integrals 131
The Fundamental Theorem of Calculus 132
Integral Transforms 134
Laplace Transform 134
Fourier Transforms 137
Calculus in More than One Variable 138
Summary 139
CHAPTER 5
Matrix Algebra 141
Vectors and Matrices Defined 141
Vectors 141
Matrices 144
Square Matrices 145
Diagonals and Antidiagonals 145
Identity Matrix 146
Diagonal Matrix 146
Upper and Lower Triangular Matrix 148
Determinants 148
Systems of Linear Equations 149
Linear Independence and Rank 151
Hankel Matrix 152
Vector and Matrix Operations 153
Vector Operations 153
Matrix Operations 156
Eigenvalues and Eigenvectors 160
Diagonalization and Similarity 161
Singular Value Decomposition 162
Summary 163
CHAPTER 6
Concepts of Probability 165
Representing Uncertainty with Mathematics 165
Probability in a Nutshell 167
Outcomes and Events 169
Probability 170
Measure 171
Random Variables 172
Integrals 172
Distributions and Distribution Functions 174
Random Vectors 175
Stochastic Processes 178
Probabilistic Representation of Financial Markets 180
Information Structures 181
Filtration 182
Conditional Probability and Conditional Expectation 184
Moments and Correlation 186
Copula Functions 188
Sequences of Random Variables 189
Independent and Identically Distributed Sequences 191
Sum of Variables 191
Gaussian Variables 194
The Regression Function 197
Linear Regression 197 J
Summary 199 i
CHAPTER 7
Optimization 201
Maxima and Minima 202
Lagrange Multipliers 204
Numerical Algorithms 206
Linear Programming 206
Quadratic Programming 211
Calculus of Variations and Optimal Control Theory 212
Stochastic Programming 214
Summary 216
CHAPTER 8
Stochastic Integrals 217
The Intuition Behind Stochastic Integrals 219
Brownian Motion Defined 225
Properties of Brownian Motion 230
Stochastic Integrals Defined 232
Some Properties of Ito Stochastic Integrals 236
Summary 237
CHAPTER 9
Differential Equations and Difference Equations 239
Differential Equations Defined 240
Ordinary Differential Equations 240
Order and Degree of an ODE 241
Solution to an ODE 241
Systems of Ordinary Differential Equations 243
j
Closed Form Solutions of Ordinary Differential Equations 246
Linear Differential Equation 247
Numerical Solutions of Ordinary Differential Equations 249
The Finite Difference Method 249
Nonlinear Dynamics and Chaos 256
Fractals 258
Partial Differential Equations 259
Diffusion Equation 259
Solution of the Diffusion Equation 261
Numerical Solution of PDEs 263
Summary 265
CHAPTER 10
Stochastic Differential Equations 267
The Intuition Behind Stochastic Differential Equations 268
Ito Processes 271
The 1 Dimensional Ito Formula 272
Stochastic Differential Equations 274
Generalization to Several Dimensions 276
Solution of Stochastic Differential Equations 278
The Arithmetic Brownian Motion 280
The Ornstein Uhlenbeck Process 280
The Geometric Brownian Motion 281
Summary 282
CHAPTER 11
Financial Econometrics: Time Series Concepts, Representations, and Models 283
Concepts of Time Series 284
Stylized Facts of Financial Time Series 286
Infinite Moving Average and Autoregressive
Representation of Time Series 288
Univariate Stationary Series 288
The Lag Operator L 289
Stationary Univariate Moving Average 292
Multivariate Stationary Series 293
Nonstationary Series 295
ARMA Representations 297
Stationary Univariate ARMA Models 297
Nonstationary Univariate ARMA Models 300
Stationary Multivariate ARMA Models 301
Nonstationary Multivariate ARMA Models 304
Markov Coefficients and ARMA Models 304
Hankel Matrices and ARMA Models 305
State Space Representation 305
Equivalence of State Space and ARMA Representations 308
Integrated Series and Trends 309
Summary 313
CHAPTER 12
Financial Econometrics: Model Selection, Estimation, and Testing 315
Model Selection 315
Learning and Model Complexity 317
Maximum Likelihood Estimate 319
Linear Models of Financial Time Series 324
Random Walk Models 324
Correlation 327
Random Matrices 329
Multifactor Models 332
CAPM 334
Asset Pricing Theory (APT) Models 335
PCA and Factor Models 335
Vector Autoregressive Models 338
Cointegration 339
State Space Modeling and Cointegration 342
Empirical Evidence of Cointegration in Equity Prices 343
Nonstationary Models of Financial Time Series 345
The ARCH/GARCH Family of Models 346
Markov Switching Models 347
Summary 349
CHAPTER 13
Fat Tails, Scaling, and Stable Laws 351
Scaling, Stable Laws, and Fat Tails 352 }
Fat Tails 352 !
The Class 2 of Fat Tailed Distributions 353 ;
The Law of Large Numbers and the Central Limit Theorem 358
Stable Distributions 360
Extreme Value Theory for IID Processes 362
Maxima 362
Max Stable Distributions 368
Generalized Extreme Value Distributions 368
Order Statistics 369
Point Process of Exceedances or Peaks over Threshold 371
Estimation 373
Eliminating the Assumption of IID Sequences 378
Heavy Tailed ARM A Processes 381
ARCH/GARCH Processes 382
Subordinated Processes 383
Markov Switching Models 384
Estimation 384
Scaling and Self Similarity 385
Evidence of Fat Tails in Financial Variables 388
On the Applicability of Extreme Value Theory in Finance 391
Summary 392
CHAPTER 14
Arbitrage Pricing: Finite State Models 393
The Arbitrage Principle 393
Arbitrage Pricing in a One Period Setting 395
State Prices 397
Risk Neutral Probabilities 398
Complete Markets 399
Arbitrage Pricing in a Multiperiod Finite State Setting 402
Propagation of Information 402
Trading Strategies 403
State Price Deflator 404
Pricing Relationships 405
Equivalent Martingale Measures 414
Risk Neutral Probabilities 416
Path Dependence and Markov Models 423
The Binomial Model 423
Risk Neutral Probabilities for the Binomial Model 426
Valuation of European Simple Derivatives 427
Valuation of American Options 429
Arbitrage Pricing in a Discrete Time, Continuous State Setting 430
APT Models 435
Testing APT 436
Summary 439
CHAPTER 15
Arbitrage Pricing: Continuous State, Continuous Time Models 441
The Arbitrage Principle in Continuous Time 441
Trading Strategies and Trading Gains 443
Arbitrage Pricing in Continuous State, Continuous Time 445
Option Pricing 447
Stock Price Processes 447
Hedging 448
The Black Scholes Option Pricing Formula 449
Generalizing the Pricing of European Options 452
State Price Deflators 454
Equivalent Martingale Measures 457
Equivalent Martingale Measures and Girsanov s Theorem 459
The Diffusion Invariance Principle 461
Application of Girsanov s Theorem to Black Scholes
Option Pricing Formula 462
Equivalent Martingale Measures and Complete Markets 463
Equivalent Martingale Measures and State Prices 464
Arbitrage Pricing with a Payoff Rate 466
Implications of the Absence of Arbitrage 467
Working with Equivalent Martingale Measures 468
Summary 468
CHAPTER 16
Portfolio Selection Using Mean Variance Analysis 471
Diversification as a Central Theme in Finance 472
Markowitz s Mean Variance Analysis 474
Capital Market Line 477
Deriving the Capital Market Line 478
What is Portfolio M? 481
Risk Premium in the CML 482
The CML and the Optimal Portfolio 482
Utility Functions and Indifference Curves 482
Selection of the Optimal Portfolio 484
Extension of the Markowitz Mean Variance Model to
Inequality Constraints 485
A Second Look at Portfolio Choice 487
The Return Forecast 487
The Utility Function 488
Optimizers 490
A Global Probabilistic Framework for Portfolio Selection 490
Relaxing the Assumption of Normality 491
Multiperiod Stochastic Optimization 492
Application to the Asset Allocation Decision 494
The Inputs 495
Portfolio Selection: An Example 500 j
Inclusion of More Asset Classes 503 j
Extensions of the Basic Asset Allocation Model 507 |
Summary 509 ¦
CHAPTER 17
Capital Asset Pricing Model 511
CAPM Assumptions 512
Systematic and Nonsystematic Risk 513
Security Market Line 516
Estimating the Characteristic Line 518
Testing The CAPM 518
Deriving the Empirical Analogue of the CML 518
Empricial Implications 519
General Findings of Empirical Tests of the CAPM 520
A Critique of Tests of the CAPM 520
Merton and Black Modifications of the CAPM 521
CAPM and Random Matrices 522
The Conditional CAPM 523
Beta, Beta Everywhere 524
The Role of the CAPM in Investment Management Applications 525
Summary 526
CHAPTER 18
Muttifactor Models and Common Trends for Common Stocks 529 .
Multifactor Models 530 •
Determination of Factors 532 I
Dynamic Market Models of Returns 537
Estimation of State Space Models 538
Dynamic Models for Prices 538
Estimation and Testing of Cointegrated Systems 543
Cointegration and Financial Time Series 544
Nonlinear Dynamic Models for Prices and Returns 546
Summary 549
CHAPTER 19
Equity Portfolio Management 551
Integrating the Equity Portfolio Management Process 551
Active versus Passive Portfolio Management 552
Tracking Error 553
Backward Looking versus Forward Looking Tracking Error 555
The Impact of Portfolio Size, Benchmark Volatility, and
Portfolio Beta on Tracking Error 556
Equity Style Management 560
Types of Equity Styles 560
Style Classification Systems 562
Passive Strategies 564
Constructing an Indexed Portfolio 564
Index Tracking and Cointegration 565
Active Investing 566
Top Down Approaches to Active Investing 566
Bottom Up Approaches to Active Investing 567
Fundamental Law of Active Management 568
Strategies Based on Technical Analysis 571
Nonlinear Dynamic Models and Chaos 573
Technical Analysis and Statistical Nonlinear
Pattern Recognition 574
Market Neutral Strategies and Statistical Arbitrage 575
Application of Multifactor Risk Models 577
Risk Decomposition 577
Portfolio Construction and Risk Control 582
Assessing the Exposure of a Portfolio 583
Risk Control Against a Stock Market Index 587
Tilting a Portfolio 587
Summary 589
CHAPTER 20
Term Structure Modeling and Valuation of Bonds and Bond Options 593
Basic Principles of Valuation of Debt Instruments 594
Yield to Maturity Measure 596
Premium Par Yield 598
Reinvestment of Cash Flow and Yield 598
The Term Structure of the Interest Rates and the Yield Curve 599
Limitations of Using the Yield to Value a Bond 602
Valuing a Bond as a Package of Cash Flows 603
Obtaining Spot Rates from the Treasury Yield Curve 603
Using Spot Rates to the Arbitrage Free Value of a Bond 606
The Discount Function 606
Forward Rates 607
Swap Curve 608
Classical Economic Theories About the Determinants of the
Shape of the Term Structure 612
Expectations Theories 613
Market Segmentation Theory 618
Bond Valuation Formulas in Continuous Time 618
The Term Structure of Interest Rates in Continuous Time 623
Spot Rates: Continuous Case 624
Forward Rates: Continuous Case 625
Relationships for Bond and Option Valuation 626
The Feynman Kac Formula 627
Multifactor Term Structure Model 632
Arbitrage Free Models versus Equilibrium Models 634
Examples of One Factor Term Structure Models 635
Two Factor Models 638
Pricing of Interest Rate Derivatives 638
The Heath Jarrow Morton Model of the Term Structure 640
The Brace Gatarek Musiela Model 643
Discretization of Ito Processes 644
Summary 646
CHAPTER 21
Bond Portfolio Management 649
Management versus a Bond Market Index 649
Tracking Error and Bond Portfolio Strategies 651
Risk Factors and Portfolio Management Strategies 652
Determinants of Tracking Error 654
Illustration of the Multifactor Risk Model 654
Liability Funding Strategies 661
Cash Flow Matching 664
Portfolio Immunization 667
Scenario Optimization 672
Stochastic Programming 673
Summary 677
CHAPTER 22
Credit Risk Modeling and Credit Default Swaps 679
Credit Default Swaps 679
Single Name Credit Default Swaps 680
Basket Default Swaps 681
Legal Documentation 683
Credit Risk Modeling: Structural Models 683
The Black Scholes Merton Model 685
Geske Compound Option Model 690
Barrier Structural Models 694
Advantages and Drawbacks of Structural Models 696
Credit Risk Modeling: Reduced Form Models 696
The Poisson Process 697
The Jarrow Turnbull Model 698
Transition Matrix 703
The Duffte Singleton Model 706
General Observations on Reduced Form Models 710
Pricing Single Name Credit Default Swaps 710
General Framework 711
Survival Probability and Forward Default Probability:
A Recap 712
Credit Default Swap Value 713
No Need For Stochastic Hazard Rate or Interest Rate 716
Delivery Option in Default Swaps 716
Default Swaps with Counterparty Risk 717
Valuing Basket Default Swaps 718
The Pricing Model 718
How to Model Correlated Default Processes 722
Summary 734
CHAPTER 23
Risk Management 737
Market Completeness 738
The Mathematics of Market Completeness 739
The Economics of Market Completeness 742
Why Manage Risk? 744
Risk Models 745
Market Risk 745
Credit Risk 746
Operational Risk 746
Risk Measures 747
Risk Management in Asset and Portfolio Management 751
Factors Driving Risk Management 752
Risk Measurement in Practice 752
Getting Down to the Lowest Level 753
Regulatory Implications of Risk Measurement 754
Summary 755
INDEX 757
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV017789603 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:21:52Z |
| institution | BVB |
| isbn | 0471465992 |
| language | English |
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| physical | XXII, 778 S. graph. Darst. |
| publishDate | 2004 |
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| publisher | Wiley |
| record_format | marc |
| series2 | The Frank J. Fabozzi series Wiley finance |
| spelling | Focardi, Sergio Verfasser aut The mathematics of financial modeling and investment management Sergio M. Focardi ; Frank J. Fabozzi Hoboken, NJ Wiley 2004 XXII, 778 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Frank J. Fabozzi series Wiley finance Mercado financeiro larpcal Mathematisches Modell Business mathematics Finance Mathematical models Investment analysis Mathematical models Portfolio management Mathematical models Kreditmarkt (DE-588)4073788-3 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s DE-604 Kreditmarkt (DE-588)4073788-3 s DE-188 Fabozzi, Frank J. 1948- Verfasser (DE-588)129772054 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010683099&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Focardi, Sergio Fabozzi, Frank J. 1948- The mathematics of financial modeling and investment management Mercado financeiro larpcal Mathematisches Modell Business mathematics Finance Mathematical models Investment analysis Mathematical models Portfolio management Mathematical models Kreditmarkt (DE-588)4073788-3 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4073788-3 (DE-588)4017195-4 |
| title | The mathematics of financial modeling and investment management |
| title_auth | The mathematics of financial modeling and investment management |
| title_exact_search | The mathematics of financial modeling and investment management |
| title_full | The mathematics of financial modeling and investment management Sergio M. Focardi ; Frank J. Fabozzi |
| title_fullStr | The mathematics of financial modeling and investment management Sergio M. Focardi ; Frank J. Fabozzi |
| title_full_unstemmed | The mathematics of financial modeling and investment management Sergio M. Focardi ; Frank J. Fabozzi |
| title_short | The mathematics of financial modeling and investment management |
| title_sort | the mathematics of financial modeling and investment management |
| topic | Mercado financeiro larpcal Mathematisches Modell Business mathematics Finance Mathematical models Investment analysis Mathematical models Portfolio management Mathematical models Kreditmarkt (DE-588)4073788-3 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Mercado financeiro Mathematisches Modell Business mathematics Finance Mathematical models Investment analysis Mathematical models Portfolio management Mathematical models Kreditmarkt Finanzmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010683099&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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