Numerical Methods and Optimization in Finance 2nd Edition by Manfred Gilli, Dietmar Maringer, Enrico Schumann – Ebook PDF Instant Download/Delivery: 0128150661, 9780128150665
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ISBN 10: 0128150661
ISBN 13: 9780128150665
Author: Manfred Gilli, Dietmar Maringer, Enrico Schumann
Computationally-intensive tools play an increasingly important role in financial decisions. Many financial problems—ranging from asset allocation to risk management and from option pricing to model calibration—can be efficiently handled using modern computational techniques. Numerical Methods and Optimization in Finance presents such computational techniques, with an emphasis on simulation and optimization, particularly so-called heuristics. This book treats quantitative analysis as an essentially computational discipline in which applications are put into software form and tested empirically.
This revised edition includes two new chapters, a self-contained tutorial on implementing and using heuristics, and an explanation of software used for testing portfolio-selection models. Postgraduate students, researchers in programs on quantitative and computational finance, and practitioners in banks and other financial companies can benefit from this second edition of Numerical Methods and Optimization in Finance.
- Introduces numerical methods to readers with economics backgrounds
- Emphasizes core simulation and optimization problems
- Includes MATLAB and R code for all applications, with sample code in the text and freely available for download
Numerical Methods and Optimization in Finance 2nd Table of contents:
Part I: Fundamentals
Chapter 1: Introduction
1.1. Abstract
1.2. About this book
1.3. Principles
1.4. On software
1.5. On approximations and accuracy
1.6. Summary: the theme of the book
1.7. Bibliography
Chapter 2: Numerical analysis in a nutshell
2.1. Abstract
2.2. Computer arithmetic
2.3. Measuring errors
2.4. Approximating derivatives with finite differences
2.5. Numerical instability and ill-conditioning
2.6. Condition number of a matrix
2.7. A primer on algorithmic and computational complexity
- Appendix 2.A. Operation count for basic linear algebra operations
2.8. Bibliography
Chapter 3: Linear equations and Least Squares problems
3.1. Abstract
3.2. Direct methods
3.3. Iterative methods
3.4. Sparse linear systems
3.5. The Least Squares problem
- Appendix 3.A. Solving linear systems in R
3.6. Bibliography
Chapter 4: Finite difference methods
4.1. Abstract
4.2. An example of a numerical solution
4.3. Classification of differential equations
4.4. The Black–Scholes equation
4.5. American options
- Appendix 4.A. A note on MATLAB’s function spdiags
4.6. Bibliography
Chapter 5: Binomial trees
5.1. Abstract
5.2. Motivation
5.3. Growing the tree
5.4. Early exercise
5.5. Dividends
5.6. The Greeks
5.7. Bibliography
Part II: Simulation
Chapter 6: Generating random numbers
6.1. Abstract
6.2. Monte Carlo methods and sampling
6.3. Uniform random number generators
6.4. Nonuniform distributions
6.5. Specialized methods for selected distributions
6.6. Sampling from a discrete set
6.7. Sampling errors—and how to reduce them
6.8. Drawing from empirical distributions
6.9. Controlled experiments and experimental design
6.10. Bibliography
Chapter 7: Modeling dependencies
7.1. Abstract
7.2. Transformation methods
7.3. Markov chains
7.4. Copula models
7.5. Bibliography
Chapter 8: A gentle introduction to financial simulation
8.1. Abstract
8.2. Setting the stage
8.3. Single-period simulations
8.4. Simple price processes
8.5. Processes with memory in the levels of returns
8.6. Time-varying volatility
8.7. Adaptive expectations and patterns in price processes
8.8. Historical simulation
8.9. Agent-based models and complexity
8.10. Bibliography
Chapter 9: Financial simulation at work: some case studies
9.1. Abstract
9.2. Constant proportion portfolio insurance (CPPI)
9.3. VaR estimation with Extreme Value Theory
9.4. Option pricing
9.5. Bibliography
Part III: Optimization
Chapter 10: Optimization problems in finance
10.1. Abstract
10.2. What to optimize?
10.3. Solving the model
10.4. Evaluating solutions
10.5. Examples
10.6. Summary
10.7. Bibliography
Chapter 11: Basic methods
11.1. Abstract
11.2. Finding the roots of f(x)=0
11.3. Classical unconstrained optimization
11.4. Unconstrained optimization in one dimension
11.5. Unconstrained optimization in multiple dimensions
11.6. Nonlinear Least Squares
11.7. Solving systems of nonlinear equations F(x)=0
11.8. Synoptic view of solution methods
11.9. Bibliography
Chapter 12: Heuristic methods in a nutshell
12.1. Abstract
12.2. Heuristics
12.3. Single-solution methods
12.4. Population-based methods
12.5. Hybrids
12.6. Constraints
12.7. The stochastics of heuristic search
12.8. General considerations
12.9. Outlook
- Appendix 12.A. Implementing heuristic methods with MATLAB
- Appendix 12.B. Parallel computations in MATLAB
- Appendix 12.C. Heuristic methods in the NMOF package
12.10. Bibliography
Chapter 13: Heuristics: a tutorial
13.1. Abstract
13.2. On Optimization
13.3. The problem: choosing few from many
13.4. Solution strategies
13.5. Heuristics
13.6. Application: selecting variables in a regression
13.7. Application: portfolio selection
13.8. Bibliography
Chapter 14: Portfolio optimization
14.1. Abstract
14.2. The investment problem
14.3. Mean–variance optimization
14.4. Optimization with heuristics
14.5. Portfolios under Value-at-Risk
- Appendix 14.A. Computing returns
- Appendix 14.B. More implementation issues in R
- Appendix 14.C. A neighborhood for switching elements
14.6. Bibliography
Chapter 15: Backtesting
15.1. Abstract
15.2. What is (the problem with) backtesting?
15.3. Data and software
15.4. Simple backtests
15.5. Backtesting portfolio strategies
- Appendix 15.A. Prices in btest
- Appendix 15.B. Notes on zoo
- Appendix 15.C. Parallel computations in R
15.6. Bibliography
Chapter 16: Econometric models
16.1. Abstract
16.2. Term structure models
16.3. Robust and resistant regression
16.4. Estimating Time Series Models
- Appendix 16.A. Maximizing the Sharpe ratio
16.5. Bibliography
Chapter 17: Calibrating option pricing models
17.1. Abstract
17.2. Implied volatility with Black–Scholes
17.3. Pricing with the characteristic function
17.4. Calibration
17.5. Final remarks
- Appendix 17.A. Quadrature rules for infinity
17.6. Bibliography
Appendix A: The NMOF package
A.1. Installing the package
A.2. News, feedback and discussion
A.3. Using the package
A.4. Bibliography
Bibliography
Index
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