This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to si…Read more
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This book describes computational finance tools. It covers fundamental numerical analysis and computational techniques, such as option pricing, and gives special attention to simulation and optimization. Many chapters are organized as case studies around portfolio insurance and risk estimation problems. In particular, several chapters explain optimization heuristics and how to use them for portfolio selection and in calibration of estimation and option pricing models. Such practical examples allow readers to learn the steps for solving specific problems and apply these steps to others. At the same time, the applications are relevant enough to make the book a useful reference. Matlab and R sample code is provided in the text and can be downloaded from the book's website.
Shows ways to build and implement tools that help test ideas
Focuses on the application of heuristics; standard methods receive limited attention
Presents as separate chapters problems from portfolio optimization, estimation of econometric models, and calibration of option pricing models
List of Algorithms
Acknowledgements
Chapter One. Introduction
Publisher Summary
1.1 About this book
1.2 Principles
1.3 On software
1.4 On approximations and accuracy
1.5 Summary: the theme of the book
Part One: Fundamentals
Chapter Two. Numerical Analysis in a Nutshell
Publisher Summary
2.1 Computer Arithmetic
2.2 Measuring Errors
2.3 Approximating Derivatives with Finite Differences
2.4 Numerical Instability and Ill-Conditioning
2.5 Condition Number of a Matrix
2.6 A Primer on Algorithmic and Computational Complexity
2.A Operation Count for Basic Linear Algebra Operations
Chapter Three. Linear Equations and Least Squares Problems
Publisher Summary
3.1 Direct Methods
3.2 Iterative Methods
3.3 Sparse Linear Systems
3.4 The Least Squares Problem
Chapter Four. Finite Difference Methods
Publisher Summary
4.1 An example of a numerical solution
4.2 Classification of differential equations
4.3 The Black–Scholes equation
4.4 American options
4.A A note on Matlab's function spdiags
Chapter Five. Binomial Trees
Publisher Summary
5.1 Motivation
5.2 Growing the Tree
5.3 Early Exercise
5.4 Dividends
5.5 The Greeks
Part Two: Simulation
Chapter Six. Generating Random Numbers
Publisher Summary
6.1 Monte Carlo Methods and Sampling
6.2 Uniform Random Number Generators
6.3 Nonuniform Distributions
6.4 Specialized Methods for Selected Distributions
6.5 Sampling from a Discrete Set
6.6 Sampling Errors—and How to Reduce them
6.7 Drawing from Empirical Distributions
6.8 Controlled Experiments and Experimental Design
Chapter Seven. Modeling Dependencies
Publisher Summary
7.1 Transformation Methods
7.2 Markov Chains
7.3 Copula Models
Chapter Eight. A Gentle Introduction to Financial Simulation
Publisher Summary
8.1 Setting the Stage
8.2 Single-Period Simulations
8.3 Simple Price Processes
8.4 Processes with Memory in the Levels of Returns
8.5 Time-Varying Volatility
8.6 Adaptive expectations and patterns in Price Processes
8.7 Historical Simulation
8.8 Agent-based Models and Complexity
Chapter Nine. Financial Simulation at Work: Some Case Studies
Manfred Gilli is Professor emeritus at the Geneva School of Economics and Management at the University of Geneva, Switzerland, where he has taught numerical methods in economics and finance. He is also a Faculty member of the Swiss Finance Institute, a member of the Advisory Board of Computational Statistics and Data Analysis, and a member of the editorial board of Computational Economics. He formerly served as president of the Society for Computational Economics.
Affiliations and expertise
University of Geneva, Geneva School of Economics and Management (GSEM) and Swiss Finance Institute
DM
Dietmar Maringer
Dietmar Maringer is Professor of Computational Economics and Finance at the University of Basel, Switzerland, and a faculty member at the Geneva School of Economics and Management. His research interests include non-deterministic methods such as heuristic optimization and simulations, computational learning, and empirical methods, typically with applications in trading, risk, and financial management.
Affiliations and expertise
University of Basel and University of Geneva, Switzerland
ES
Enrico Schumann
Enrico Schumann holds a Ph.D. in econometrics, an MSC in economics, and a BA in economics and law. He has written on numerical methods and their application in finance, with a focus on asset allocation. His research interests include quantitative investment strategies and portfolio construction, computationally-intensive methods (in particular, optimization), and automated data processing and analysis.
Affiliations and expertise
Portfolio Manager at a large Swiss pension fund
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