| Preface | p. 11 |
| Objective | p. 11 |
| History | p. 13 |
| Outline and Readers Guide | p. 15 |
| Acknowledgements | p. 16 |
| A Scientific Perspective | p. 19 |
| Introduction | p. 19 |
| Financial Modeling and Computers | p. 19 |
| Epistemic Uncertainty: Exact and Inexact Models | p. 20 |
| Exact Models, e.g., Financial Statements | p. 22 |
| Inexact Models, e.g., Behavioral Relationships | p. 25 |
| Identification, Simulation and Extrapolation | p. 26 |
| Pro Forma Financial Statement Projections | p. 26 |
| Envisioning Information: Unique Mappings | p. 26 |
| Exercises | p. 28 |
| Bibliography | p. 31 |
| Capital Budgeting and Analytic Formulas | p. 35 |
| Introduction | p. 35 |
| Present and Future Value Calculations | p. 35 |
| Continuous and Discrete Compounding | p. 37 |
| Expansions and Euler Formulas | p. 37 |
| Imaginary and Conjugate Complex Numbers and the Euler Relations | p. 39 |
| Fourier and Wavelet Analysis | p. 43 |
| Fourier Series | p. 43 |
| Fourier Transform | p. 45 |
| Wavelet Transform | p. 45 |
| Multiresolution Analysis | p. 46 |
| Exercises | p. 47 |
| Bibliography | p. 49 |
| Fundamental Security Valuation | p. 51 |
| Introduction | p. 51 |
| Valuation of Bonds | p. 51 |
| Yield Curve and Term Structure Analysis | p. 52 |
| Custom-fitting of Bond Maturities | p. 53 |
| Computing Forward Interest Rates | p. 53 |
| Risk-Based Credit Ratings | p. 53 |
| Valuation of Stocks by Dividend Discount Models | p. 54 |
| Cash Flow and Ratio Analysis | p. 55 |
| Exercises | p. 56 |
| Bibliography | p. 56 |
| Analysis of Exact Data I | p. 57 |
| Introduction | p. 57 |
| First Two Moments | p. 58 |
| Expected Value and Variance | p. 58 |
| Covariance Matrix and Correlations | p. 60 |
| Iso-Information Ellipsoids | p. 61 |
| Iso-Information Ellipsoids and Projections | p. 62 |
| Linear Loci of Certainty | p. 63 |
| Bivariate Least Squares Projections | p. 67 |
| Envisoning Bivariate Modeling Uncertainty | p. 70 |
| Exercises | p. 71 |
| Bibliography | p. 72 |
| Analysis of Inexact Data II | p. 75 |
| Introduction | p. 75 |
| Complete Least Squares Projections | p. 75 |
| Two Important System Identification Theorems | p. 75 |
| Noise and Signal Projections | p. 77 |
| Noise/Data Ratios in Two-Dimensional Data | p. 79 |
| Hypotheses Non Fingo | p. 79 |
| Examples of an Uncertain (n,q) = (3,2) Model | p. 80 |
| Observed Relative Frequencies and Theoretical Distributions | p. 86 |
| Model Quality Measurement by Noise/Data Ratios | p. 87 |
| The Directionless t-Statistic | p. 87 |
| Modeling n-Dimensional Financial Risk | p. 88 |
| Noise/Data Ratios In n-Dimensional Data | p. 88 |
| Modeling 3-Dimensional Uncertainty and Inexactness | p. 89 |
| Stationarity Tests | p. 90 |
| Stationarity Windowing | p. 90 |
| Inertia-Based Prediction | p. 90 |
| Exercises | p. 91 |
| Basic Understanding of CLS | p. 91 |
| Bank Performance Identification From Inexact Data--Trivariate Data Set | p. 92 |
| Identification of 1928 Cobb-Douglas Production Model--Trivariate Data Set | p. 93 |
| Bibliography | p. 95 |
| Optimal Portfolio Formation | p. 99 |
| Introduction | p. 99 |
| Mean-Variance Analysis | p. 99 |
| Efficient Frontier With Two Assets | p. 100 |
| Efficient Frontier With Multiple Assets | p. 102 |
| Value-at-Risk and RiskMetrics | p. 105 |
| Value-at-Risk | p. 105 |
| Singularity Problems of RiskMetrics and CreditMetrics | p. 108 |
| Exercises | p. 110 |
| Bibliography | p. 110 |
| Systematic Financial Risk Analysis | p. 113 |
| Introduction | p. 113 |
| Fundamental Market Model | p. 113 |
| Systematic and Unsystematic Risk | p. 114 |
| Absolute and Relative Risk | p. 114 |
| Sharpe Ratio | p. 115 |
| CAPM, Beta and Epistemic Risk | p. 115 |
| Mutual Funds Selection Based on Beta | p. 117 |
| Related Topics | p. 123 |
| Multi-Factor Models | p. 123 |
| Mdmv Model Comparison Between CAPM and APT | p. 124 |
| Risk Aversion, Neutrality and Gambling | p. 129 |
| Exercises | p. 131 |
| Bibliography | p. 133 |
| Complete Valuation and Dynamic Risk Theory | p. 135 |
| Introduction | p. 135 |
| Expected Return and Risk | p. 138 |
| Complete Capital Market Pricing | p. 142 |
| Risk-Neutral Pricing | p. 144 |
| Single Price Law of Efficient Markets | p. 144 |
| Arbitrage-Free Securities Design | p. 148 |
| Markov State Transition Theory | p. 149 |
| Exact Markov Dynamics | p. 149 |
| Limiting Markov Chain Distribution | p. 150 |
| Ehrenfest's Heat Exchange Example | p. 154 |
| Default and Credit Migration Frequencies | p. 155 |
| Exercises | p. 158 |
| Bibliography | p. 160 |
| Option Pricing I | p. 163 |
| Introduction | p. 163 |
| Pricing By Arbitrage | p. 164 |
| Single-Period Binomial Option Pricing | p. 166 |
| Using Portfolio Theory | p. 167 |
| Pseudo-Probabilities | p. 169 |
| Using CCMP Theory | p. 170 |
| Multi-Period Binomial Option Pricing | p. 171 |
| Put-Call Parity | p. 174 |
| European, American and Asian Options | p. 175 |
| Random Walks and Brownian Motion | p. 178 |
| Exercises | p. 180 |
| Bibliography | p. 181 |
| Option Pricing II | p. 183 |
| Introduction | p. 183 |
| Black-Scholes Option Pricing | p. 185 |
| Non-Dividend-Paying Stock | p. 185 |
| Continuous-Dividend-Paying Stock | p. 190 |
| Historical and Implied Volatility | p. 191 |
| Volatility Computation by "Trial and Error" | p. 191 |
| Volatility Computation by At-the-Money Formula | p. 192 |
| Options' Greek Alphabet | p. 193 |
| Dynamic Hedging Strategies | p. 197 |
| Exercises | p. 198 |
| Bibliography | p. 199 |
| Bond Portfolio Valuation and Management | p. 201 |
| Introduction | p. 201 |
| Bond Price Volatility | p. 201 |
| Risks in Fixed Income Securities | p. 201 |
| Measures of Interest Rate Risk | p. 202 |
| Macauley and Modified Durations | p. 204 |
| Modified Duration | p. 204 |
| Interpretation and Various Definitions | p. 204 |
| Macauley Duration | p. 205 |
| Dollar Duration | p. 207 |
| Effective Duration | p. 207 |
| Option-Adjusted Spreads and Imbedded Options | p. 207 |
| Convexity | p. 210 |
| Definition of Convexity | p. 211 |
| Positive and Negative Convexity | p. 211 |
| Default Risk and Effective Duration of Bonds | p. 211 |
| Bond Portfolio Immunization | p. 213 |
| Duration of Common Stocks | p. 215 |
| Interest Rate Risk Management | p. 216 |
| Horizon Hedging | p. 217 |
| Exercises | p. 219 |
| Bibliography | p. 220 |
| Forwards and Futures | p. 223 |
| Introduction | p. 223 |
| Forwards and Futures Valuation | p. 223 |
| Forwards and Futures Pricing | p. 224 |
| Foreign Exchange Futures | p. 226 |
| Risks in the Futures Markets | p. 227 |
| Basis Risk | p. 227 |
| Calendar Spread Risk | p. 228 |
| Hedging with Futures | p. 228 |
| Imperfect Insurance | p. 230 |
| Portfolio Insurance? | p. 232 |
| Exercises | p. 234 |
| Bibliography | p. 235 |
| Swaps | p. 237 |
| Introduction | p. 237 |
| Reasons for Using Swaps | p. 237 |
| Valuation of Interest Rate Swaps | p. 238 |
| Interest Rate Swaps | p. 238 |
| Valuation of Interest Rate Swaps | p. 239 |
| Constructing a Swap Yield Curve | p. 243 |
| Computing the Discount Function | p. 245 |
| Valuation of Currency Swaps | p. 246 |
| Quoting Conventions | p. 246 |
| Valuation of Currency Swaps | p. 248 |
| Risks of Swaps Contracts | p. 250 |
| Market and Credit Risk | p. 250 |
| Duration of a Swap | p. 251 |
| Exercises | p. 251 |
| Bibliography | p. 252 |
| Multi-Currency Investments and Exact Performance Attribution | p. 253 |
| Introduction | p. 253 |
| Multi-Currency Investment Return Accounting | p. 255 |
| Investment Strategy Return Attribution | p. 255 |
| Exact Cash Growth Accounting | p. 256 |
| Strategy Return Matrices | p. 257 |
| Portfolio of Multi-Currency Investment Strategies | p. 259 |
| Growth Accounting of Portfolio Investments | p. 259 |
| Vectorization of Sequence of Strategy Matrices | p. 260 |
| Strategy Risk Matrices | p. 263 |
| Singularity of Strategy Risk Matrix | p. 266 |
| Multi-Currency Portfolio Optimization | p. 267 |
| Extended Markowitz Procedure | p. 267 |
| Exact Investment Performance Attribution | p. 272 |
| Exercises | p. 278 |
| Bibliography | p. 280 |
| Algebraic Geometric Measurements of the Bivariate Model | p. 283 |
| Flow Chart of Linear Model Identification | p. 287 |
| 3D Noise/Signal Ratio | p. 289 |
| Bibliography | p. 290 |
| 1986 Manifesto for Identification of Models From Inexact Data | p. 291 |
| Background | p. 291 |
| Proposed Research Path | p. 292 |
| Biographical Background | p. 292 |
| List of (Computational) Finance Journals on the Internet | p. 293 |
| Electronic Journals | p. 293 |
| Index | p. 295 |
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