COMPUTATIONAL FINANCE

A Scientific Perspective

By: LOS CORNELIS A

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Paperback | 7 December 2000

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Computational finance deals with the mathematics of computer programs that realize financial models or systems. This book outlines the epistemic risks associated with the current valuations of different financial instruments and discusses the corresponding risk management strategies. It covers most of the research and practical areas in computational finance. Starting from traditional fundamental analysis and using algebraic and geometric tools, it is guided by the logic of science to explore information from financial data without prejudice. In fact, this book has the unique feature that it is structured around the simple requirement of objective science: the geometric structure of the data = the information contained in the data.

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Non-Fiction Computing & I.T.Business Applications Accounting Software Mathematics Accounting & Finance Finance Banking Business & Management Business Mathematics & Systems Booktopia Publisher Services World Scientific Publishing

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Hardcover

Published: 7th December 2000

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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
Table of Contents provided by Syndetics. All Rights Reserved.

COMPUTATIONAL FINANCE

A Scientific Perspective

At a Glance

Paperback

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Hardcover

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