Computational Finance: A Scientific Perspective / Edition 1

by Cornelis A Los

Overview

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.

Product Details

ISBN-13:	9789810244965
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	12/07/2000
Pages:	340
Product dimensions:	6.38(w) x 8.80(h) x 0.90(d)

About the Author

Currently Dr. Los is an Associate Professor of Finance in the College of Business Administration and the Graduate School of Management at Kent State University in Kent, OH, USA. His interests are in financial econometrics and financial engineering, portfolio theory and management, international financial markets and bank risk management. An author of more than 100 articles, book chapters, refereed conference papers, etc., Professor Los has written for numerous international publications. As a financial modeler, interested in financial risk measurement and analysis, like in inverse problems of non-stationary dependent data series, Prof. Los measures and analyzes the degrees of efficiency of financial markets, in particular, of FX and stock markets in Asia, Latin America and in Europe. He studies their long-term dependence characteristics, via the computation of L-stable distributions (power or scaling laws) of high frequency speculative pricing series, and via the computation of Lipschitz-Hölder exponents and multifractal spectra from wavelet multi-resolution analysis (MRA). He also assesses the impact of long term dependence on investment opportunity sets. He has more than 20 years experience in financial services and he has been a Senior Economist of the Federal Reserve Bank of NY and of Nomura Research Institute (America) and the Chief Economist of ING Bank in New York City. He has taught at Columbia University, and at Baruch, City and Hunter Colleges in New York City, at the Nanyang Technological University in Singapore and at Adelaide and Deakin Universities in Australia. His bio is recorded in several of Marquis' Who's Whos, i.a., Who's Who in America.

Table of Contents

Preface
0.1 Objective
0.2 History
0.3 Outline and Readers Guide
0.4 Acknowledgements
1 A Scientific Perspective
1.1 Introduction
1.2 Financial Modeling and Computers
1.3 Epistemic Uncertainty: Exact and Inexact Models
1.3.1 Exact Models, e.g., Financial Statements
1.3.2 Inexact Models, e.g., Behavioral Relationships
1.4 Identification, Simulation and Extrapolation
1.5 Pro Forma Financial Statement Projections
1.6 Envisioning Information: Unique Mappings
1.7 Exercises
1.8 Bibliography
2 Capital Budgeting and Analytic Formulas
2.1 Introduction
2.2 Present and Future Value Calculations
2.3 Continuous and Discrete Compounding
2.4 Expansions and Euler Formulas
2.4.1 Imaginary and Conjugate Complex Numbers and the Euler Relations
2.5 Fourier and Wavelet Analysis
2.5.1 Fourier Series
2.5.2 Fourier Transform
2.5.3 Wavelet Transform
2.5.4 Multiresolution Analysis
2.6 Exercises
2.7 Bibliography
3 Fundamental Security Valuation
3.1 Introduction
3.2 Valuation of Bonds
3.3 Yield Curve and Term Structure Analysis
3.3.1 Custom-fitting of Bond Maturities
3.3.2 Computing Forward Interest Rates
3.4 Risk-Based Credit Ratings
3.5 Valuation of Stocks by Dividend Discount Models
3.6 Cash Flow and Ratio Analysis
3.7 Exercises
3.8 Bibliography
4 Analysis of Inexact Data I
4.1 Introduction
4.2 First Two Moments
4.2.1 Expected Value and Variance
4.2.2 Covariance Matrix and Correlations
4.3 Iso-Information Ellipsoids
4.3.1 Iso-Information Ellipsoids and Projections
4.3.2 Linear Loci of Certainty
4.3.3 Bivariate Least Squares Projections
4.4 Envisoning Bivariate Modeling Uncertainty
4.5 Exercises
4.6 Bibliography
5 Analysis of Inexact Data II
5.1 Introduction
5.2 Complete Least Squares Projections
5.2.1 Two Important System Identification Theorems
5.2.2 Noise and Signal Projections
5.2.3 Noise/Data Ratios in Two-Dimensional Data
5.3 Hypotheses Non Fingo
5.3.1 Examples of an Uncertain (n,q) = (3,2) Model
5.3.2 Observed Relative Frequencies and Theoretical Distributions
5.4 Model Quality Measurement by Noise/Data Ratios
5.4.1 The Directionless t-Statistic
5.4.2 Modeling n-Dimensional Financial Risk
5.4.3 Noise/Data Ratios In n-Dimensional Data
5.4.4 Modeling 3-Dimensional Uncertainty and Inexactness
5.5 Stationarity Tests
5.5.1 Stationarity Windowing
5.5.2 Inertia-Based Prediction
5.6 Exercises
5.6.1 Basic Understanding of CLS
5.6.2 Bank Performance Identification From Inexact Data - Trivariate Data Set
5.6.3 Identification of 1928 Cobb-Douglas Production Model -Trivariate Data Set
5.7 Bibliography
6 Optimal Portfolio Formation
6.1 Introduction
6.2 Mean-Variance Analysis
6.3 Efficient Frontier With Two Assets
6.4 Efficient Frontier With Multiple Assets
6.5 Value-at-Risk and RiskMetricsTM
6.5.1 Value-at-Risk
6.5.2 Singularity Problems of RiskMetricsTM and CreditMetricsTM
6.6 Exercises
6.7 Bibliography
7 Systematic Financial Risk Analysis
7.1 Introduction
7.2 Fundamental Market Model
7.2.1 Systematic and Unsystematic Risk
7.2.2 Absolute and Relative Risk
7.2.3 Sharpe Ratio
7.3 CAPM, Beta and Epistemic Risk
7.3.1 Mutual Funds Selection Based on Beta
7.4 Related Topics
7.4.1 Multi-Factor Models
7.4.2 Mdmv Model Comparison Between CAPM and APT
7.5 Risk Aversion, Neutrality and Gambling
7.6 Exercises
7.7 Bibliography
8 Complete Valuation and Dynamic Risk Theory
8.1 Introduction
8.2 Expected Return and Risk
8.3 Complete Capital Market Pricing
8.4 Risk-Neutral Pricing
8.4.1 Single Price Law of Efficient Markets
8.4.2 Arbitrage-Free Securities Design
8.5 Markov State Transition Theory
8.5.1 Exact Markov Dynamics
8.5.2 Limiting Markov Chain Distribution
8.5.3 Ehrenfest's Heat Exchange Example
8.6 Default and Credit Migration Frequencies
8.7 Exercises
8.8 Bibliography
9 Option Pricing I
9.1 Introduction
9.2 Pricing By Arbitrage
9.3 Single-Period Binomial Option Pricing
9.3.1 Using Portfolio Theory
9.3.2 Pseudo-Probabilities
9.3.3 Using CCMP Theory
9.4 Multi-Period Binomial Option Pricing
9.5 Put-Call Parity
9.6 European, American and Asian Options
9.7 Random Walks and Brownian Motion
9.8 Exercises
9.9 Bibliography
10 Option Pricing II
10.1 Introduction
10.2 Black-Scholes Option Pricing
10.2.1 Non-Dividend-Paying Stock
10.2.2 Continuous-Dividend-Paying Stock
10.3 Historical and Implied Volatility
10.3.1 Volatility Computation by "Trial and Error"
10.3.2 Volatility Computation by At-the-Money Formula
10.4 Options' Greek Alphabet
10.5 Dynamic Hedging Strategies
10.6 Exercises
10.7 Bibliography
11 Bond Portfolio Valuation and Management
11.1 Introduction
11.2 Bond Price Volatility
11.2.1 Risks in Fixed Income Securities
11.2.2 Measures of Interest Rate Risk
11.3 Macauley and Modified Durations
11.3.1 Modified Duration
11.3.2 Interpretation and Various Definitions
11.3.3 Macauley Duration
11.3.4 Dollar Duration
11.3.5 Effective Duration
11.4 Option-Adjusted Spreads and Imbedded Options
11.5 Convexity
11.5.1 Definition of Convexity
11.5.2 Positive and Negative Convexity
11.6 Default Risk and Effective Duration of Bonds
11.7 Bond Portfolio Immunization
11.8 Duration of Common Stocks
11.9 Interest Rate Risk Management
11.9.1 Horizon Hedging
11.10 Exercises
11.11 Bibliography
12 Forwards and Futures
12.1 Introduction
12.2 Forwards and Futures Valuation
12.2.1 Forwards and Futures Pricing
12.2.2 Foreign Exchange Futures
12.3 Risks in the Futures Markets
12.3.1 Basis Risk
12.3.2 Calendar Spread Risk
12.4 Hedging with Futures
12.4.1 Imperfect Insurance
12.4.2 Portfolio Insurance
12.5 Exercises
12.6 Bibliography
13 Swaps
13.1 Introduction
13.1.1 Reasons for Using Swaps
13.2 Valuation of Interest Rate Swaps
13.2.1 Interest Rate Swaps
13.2.2 Valuation of Interest Rate Swaps
13.2.3 Constructing a Swap Yield Curve
13.2.4 Computing the Discount Function
13.3 Valuation of Currency Swaps
13.3.1 Quoting Conventions
13.3.2 Valuation of Currency Swaps
13.4 Risks of Swaps Contracts
13.4.1 Market and Credit Risk
13.4.2 Duration of a Swap
13.5 Exercises
13.6 Bibliography
14 Multi-Currency Investments and Exact Performance Attribution
14.1 Introduction
14.2 Multi-Currency Investment Return Accounting
14.2.1 Investment Strategy Return Attribution
14.2.2 Exact Cash Growth Accounting
14.2.3 Strategy Return Matrices
14.3 Portfolio of Multi-Currency Investment Strategies
14.3.1 Growth Accounting of Portfolio Investments
14.3.2 Vectorization of Sequence of Strategy Matrices
14.3.3 Strategy Risk Matrices
14.3.4 Singularity of Strategy Risk Matrix
14.4 Multi-Currency Portfolio Optimization
14.4.1 Extended Markowitz Procedure
14.5 Exact Investment Performance Attribution
14.6 Exercises
14.7 Bibliography
A Algebraic Geometric Measurements of the Bivariate Model
B Flow Chart of Linear Model Identification
C 3D Noise/Signal Ratio
D 1986 Manifesto for Identification of Models From Inexact Data
D.1 Background
D.2 Proposed Research Path
D.3 Biographical Background
E List of (Computational) Finance Journals on the Internet
E.1 Electronic Journals
Index