Format:
Online-Ressource (1 online resource (xv, 584 p.))
Edition:
Online-Ausg.
ISBN:
9780123756626
,
0123756626
,
0123756626
Content:
Fundamentals -- Simulation -- Optimization
Content:
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
Content:
Includes bibliographical references and index
Note:
Includes bibliographical references and index
,
Front Cover; Numerical Methods and Optimization in Finance; Copyright; Table of Contents; List of Algorithms; Acknowledgements; Chapter 1. Introduction; 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 2. Numerical analysis in a nutshell; 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
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2.A. Operation count for basic linear algebra operationsChapter 3. Linear equations and Least Squares problems; 3.1. Direct methods; 3.2. Iterative methods; 3.3. Sparse linear systems; 3.4. The Least Squares problem; Chapter 4. Finite difference methods; 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 5. Binomial trees; 5.1. Motivation; 5.2. Growing the tree; 5.3. Early exercise; 5.4. Dividends; 5.5. The Greeks; Part Two Simulation
,
Chapter 6. Generating random numbers6.1. 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 7. Modeling dependencies; 7.1. Transformation methods; 7.2. Markov chains; 7.3. Copula models; Chapter 8. A gentle introduction to financial simulation; 8.1. Setting the stage; 8.2. Single-period simulations
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8.3. Simple price processes8.4. 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 9. Financial simulation at work: some case studies; 9.1. Constant proportion portfolio insurance (CPPI); 9.2. VaR estimation with Extreme Value Theory; 9.3. Option pricing; Part Three Optimization; Chapter 10. Optimization problems in finance; 10.1. What to optimize?; 10.2. Solving the model; 10.3. Evaluating solutions; 10.4. Examples; 10.5. Summary
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Chapter 11. Basic methods11.1. Finding the roots of f(x) = 0; 11.2. Classical unconstrained optimization; 11.3. Unconstrained optimization in one dimension; 11.4. Unconstrained optimization in multiple dimensions; 11.5. Nonlinear Least Squares; 11.6. Solving systems of nonlinear equations F(x) = 0; 11.7. Synoptic view of solution methods; Chapter 12. Heuristic methods in a nutshell; 12.1. Heuristics; 12.2. Trajectory methods; 12.3. Population-based methods; 12.4. Hybrids; 12.5. Constraints; 12.6. The stochastics of heuristic search; 12.7. General considerations; 12.8. Summary
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12.A. Implementing heuristic methods with Matlab
Additional Edition:
ISBN 9786613163950
Additional Edition:
ISBN 6613163953
Additional Edition:
ISBN 9780123756633
Additional Edition:
ISBN 0123756634
Additional Edition:
ISBN 9780123756626
Additional Edition:
Druckausg. Gilli, Manfred, 1942 - Numerical methods and optimization in finance Amsterdam, Heidelberg [u.a.] : Academic Press Elsevier, 2011 ISBN 9781493301188
Additional Edition:
ISBN 0123756626
Additional Edition:
ISBN 9780123756626
Language:
English
Subjects:
Economics
,
Mathematics
Keywords:
Finanzierung
;
Finanzmathematik
;
Optimierung
;
Finanzplanungsmodell
;
Electronic books
;
Electronic books
;
Electronic resource
Author information:
Gilli, Manfred 1942-
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