Handbook in Monte Carlo Simulation - Applications in Financial Engineering, Risk Management, and Economics

Informationen zum Autor PAOLO BRANDIMARTE is Full Professor of Quantitative Methods for Finance and Logistics in the Department of Mathematical Sciences at Politecnico di Torino in Italy. He has extensive teaching experience in engineering and economics faculties, including master's- and PhD-level courses. Dr. Brandimarte is the author or coauthor of Introduction to Distribution Logistics, Quantitative Methods: An Introduction for Business Management , and Numerical Methods in Finance and Economics: A MATLAB-Based Introduction, Second Edition , all published by Wiley. Klappentext An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economicsProviding readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization.The Handbook in Monte Carlo Simulation features:* An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials* Carefully crafted examples in order to spot potential pitfalls and drawbacks of each approach* An accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methods* Numerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentationThe Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation. Zusammenfassung Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applications of Monte Carlo methods in financial engineering and economics. Inhaltsverzeichnis Preface xiii Part I Overview and Motivation 1 Introduction to Monte Carlo Methods 3 1.1 Historical origin of Monte Carlo simulation 4 1.2 Monte Carlo Simulation vs. Monte Carlo Sampling 7 1.3 System dynamics and the mechanics of Monte Carlo simulation 10 1.4 Simulation and optimization 21 1.5 Pitfalls in Monte Carlo simulation 30 1.6 Software tools for Monte Carlo simulation 35 1.7 Prerequisites 37 For further reading 38 Chapter References 38 2 Numerical Integration Methods 41 2.1 Classical quadrature formulae 43 2.2 Gaussian quadrature 48 2.3 Extension to higher dimensions: Product rules 53 2.4 Alternative approaches for high-dimensional integration 55 2.5 Relationship with moment matching 67 2.6 Numerical integration in R 69 For further reading 71 Chapter References 71 Part II Input Analysis: Modeling and Estimation 3 Stochastic Modeling in Finance and Economics 75 3.1 Introductory examples 77 3.2 Some common probability distributions 86 3.3 Multivariate distri...

List of contents

Preface xiii
 
Part I Overview and Motivation
 
1 Introduction to Monte Carlo Methods 3
 
1.1 Historical origin of Monte Carlo simulation 4
 
1.2 Monte Carlo Simulation vs. Monte Carlo Sampling 7
 
1.3 System dynamics and the mechanics of Monte Carlo simulation 10
 
1.4 Simulation and optimization 21
 
1.5 Pitfalls in Monte Carlo simulation 30
 
1.6 Software tools for Monte Carlo simulation 35
 
1.7 Prerequisites 37
 
For further reading 38
 
Chapter References 38
 
2 Numerical Integration Methods 41
 
2.1 Classical quadrature formulae 43
 
2.2 Gaussian quadrature 48
 
2.3 Extension to higher dimensions: Product rules 53
 
2.4 Alternative approaches for high-dimensional integration 55
 
2.5 Relationship with moment matching 67
 
2.6 Numerical integration in R 69
 
For further reading 71
 
Chapter References 71
 
Part II Input Analysis: Modeling and Estimation
 
3 Stochastic Modeling in Finance and Economics 75
 
3.1 Introductory examples 77
 
3.2 Some common probability distributions 86
 
3.3 Multivariate distributions: Covariance and correlation 111
 
3.4 Modeling dependence with copulae 127
 
3.5 Linear regression models: a probabilistic view 136
 
3.6 Time series models 137
 
3.7 Stochastic differential equations 158
 
3.8 Dimensionality reduction 177
 
S3.1 Risk-neutral derivative pricing 190
 
S3.1.1 Option pricing in the binomial model 192
 
S3.1.2 A continuous-time model for option pricing: The Black-Scholes-Merton formula 194
 
S3.1.3 Option pricing in incomplete markets 199
 
For further reading 202
 
Chapter References 203
 
4 Estimation and Fitting 205
 
4.1 Basic inferential statistics in R 207
 
4.2 Parameter estimation 215
 
4.3 Checking the fit of hypothetical distributions 224
 
4.4 Estimation of linear regression models by ordinary least squares 229
 
4.5 Fitting time series models 232
 
4.6 Subjective probability: the Bayesian view 235
 
For further reading 244
 
Chapter References 245
 
Part III Sampling and Path Generation
 
5 Random Variate Generation 249
 
5.1 The structure of a Monte Carlo simulation 250
 
5.2 Generating pseudo-random numbers 252
 
5.3 The inverse transform method 263
 
5.4 The acceptance-rejection method 265
 
5.5 Generating normal variates 269
 
5.6 Other ad hoc methods 274
 
5.7 Sampling from copulae 276
 
For further reading 277
 
Chapter References 279
 
6 Sample Path Generation for Continuous-Time Models 281
 
6.1 Issues in path generation 282
 
6.2 Simulating geometric Brownian motion 287
 
6.3 Sample paths of short-term interest rates 298
 
6.4 Dealing with stochastic volatility 306
 
6.5 Dealing with jumps 308
 
For further reading 310
 
Chapter References 311
 
Part IV Output Analysis and Efficiency Improvement
 
7 Output Analysis 315
 
7.1 Pitfalls in output analysis 317
 
7.2 Setting the number of replications 323
 
7.3 A world beyond averages 325
 
7.4 Good and bad news 327
 
For further reading 327
 
Chapter References 328
 
8 Variance Reduction Methods 329
 
8.1 Antithetic sampling 330
 
8.2 Common random numbers 336
 
8.3 Control variates 337
 
8.4 Conditional Monte Carlo 341
 
8.5 Stratified sampling 344
 
8.6 Importan

Product details

• Authors: Brandimarte, P Brandimarte, Paolo Brandimarte, Brandimarte Paolo
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 06.06.2014
• EAN: 9780470531112
• ISBN: 978-0-470-53111-2
• No. of pages: 688
• Series: Wiley Handbooks in Financial Engineering and Econometrics; Wiley Handbooks in Financial E; Wiley Handbooks in Financial Engineering and Econometrics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics; Social sciences, law, business > Business > Economics; Statistik, Volkswirtschaftslehre, Economics, Statistics, Finanzökonomie, Financial Economics, Financial Engineering, Finance & Investments, Finanz- u. Anlagewesen, Finanztechnik, Econometric & Statistical Methods, Ökonometrie u. statistische Methoden, Monte Carlo Methode