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More About This Title Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics
English
An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics
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 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 experimentation
The 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.
English
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.
English
Preface xiii
Part I Overview and Motivation
1 Introduction to Monte Carlo Methods3
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 Methods41
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 Economics75
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 Fitting205
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 Generation249
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 Models281
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 Analysis315
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 Methods329
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 Importance sampling 350
For further reading 363
Chapter References 363
9 Low-Discrepancy Sequences365
9.1 Low-discrepancy sequences 366
9.2 Halton sequences 367
9.3 Sobol low-discrepancy sequences 374
9.4 Randomized and scrambled low-discrepancy sequences 379
9.5 Sample path generation with low-discrepancy sequences 381
For further reading 385
Chapter References 385
Part V Miscellaneous Applications
10 Optimization389
10.1 Classification of optimization problems 390
10.2 Optimization model building 405
10.3 Monte Carlo methods for global optimization 412
10.4 Direct search and simulation-based optimization methods 416
10.5 Stochastic programming models 420
10.6 Scenario generation and Monte Carlo methods for stochastic programming 428
10.7 Stochastic dynamic programming 433
10.8 Numerical dynamic programming 440
10.9 Approximate dynamic programming 451
For further reading 453
Chapter References 453
11 Option Pricing455
11.1 European-style multidimensional options in the BSM world 456
11.2 European-style path-dependent options in the BSM world 462
11.3 Pricing options with early exercise features 475
11.4 A look outside the BSM world 487
11.5 Pricing interest-rate derivatives 490
For further reading 497
Chapter References 498
12 Sensitivity Estimation501
12.1 Estimating option greeks by finite differences 503
12.2 Estimating option greeks by pathwise derivatives 509
12.3 Estimating option greeks by the likelihood ratio method 513
For further reading 517
Chapter References 518
13 Risk Measurement and Management519
13.1 What is a risk measure? 520
13.2 Quantile-based risk measures: value at risk 522
13.3 Monte Carlo methods for V@R 533
13.4 Mean-risk models in stochastic programming 537
13.5 Simulating delta-hedging strategies 540
13.6 The interplay of financial and nonfinancial risks 546
For further reading 548
Chapter References 548
14 Markov Chain Monte Carlo and Bayesian Statistics551
14.1 An introduction to Markov chains 552
14.2 The Metropolis–Hastings algorithm 555
14.3 A re-examination of simulated annealing 558
For further reading 560
Chapter References 561
Index 563
