Handbook in Monte Carlo Simulation by Brandimarte, Paolo -- Read -- Imperial Library of Trantor

Index

Cover Half Title page Title page Copyright page Preface Part One: Overview and Motivation

Chapter One: Introduction to Monte Carlo Methods

1.1 Historical origin of Monte Carlo simulation 1.2 Monte Carlo simulation vs. Monte Carlo sampling 1.3 System dynamics and the mechanics of Monte Carlo simulation 1.4 Simulation and optimization 1.5 Pitfalls in Monte Carlo simulation 1.6 Software tools for Monte Carlo simulation 1.7 Prerequisites For further reading References

Chapter Two: Numerical Integration Methods

2.1 Classical quadrature formulas 2.2 Gaussian quadrature 2.3 Extension to higher dimensions: Product rules 2.4 Alternative approaches for high-dimensional integration 2.5 Relationship with moment matching 2.6 Numerical integration in R For further reading References

Part Two: Input Analysis: Modeling and Estimation

Chapter Three: Stochastic Modeling in Finance and Economics

3.1 Introductory examples 3.2 Some common probability distributions 3.3 Multivariate distributions: Covariance and correlation 3.4 Modeling dependence with copulas 3.5 Linear regression models: A probabilistic view 3.6 Time series models 3.7 Stochastic differential equations 3.8 Dimensionality reduction 3.9 Risk-neutral derivative pricing For further reading References

Chapter Four: Estimation and Fitting

4.1 Basic inferential statistics in R 4.2 Parameter estimation 4.3 Checking the fit of hypothetical distributions 4.4 Estimation of linear regression models by ordinary least squares 4.5 Fitting time series models 4.6 Subjective probability: The Bayesian view For further reading References

Part Three: Sampling and Path Generation

Chapter Five: Random Variate Generation

5.1 The structure of a Monte Carlo simulation 5.2 Generating pseudorandom numbers 5.3 The inverse transform method 5.4 The acceptance-rejection method 5.5 Generating normal variates 5.6 Other ad hoc methods 5.7 Sampling from copulas For further reading References

Chapter Six: Sample Path Generation for Continuous-Time Models

6.1 Issues in path generation 6.2 Simulating geometric Brownian motion 6.3 Sample paths of short-term interest rates 6.4 Dealing with stochastic volatility 6.5 Dealing with jumps For further reading References

Part Four: Output Analysis and Efficiency Improvement

Chapter Seven: Output Analysis

7.1 Pitfalls in output analysis 7.2 Setting the number of replications 7.3 A world beyond averages 7.4 Good and bad news For further reading References

Chapter Eight: Variance Reduction Methods

8.1 Antithetic sampling 8.2 Common random numbers 8.3 Control variates 8.4 Conditional Monte Carlo 8.5 Stratified sampling 8.6 Importance sampling For further reading References

Chapter Nine: Low-Discrepancy Sequences

9.1 Low-discrepancy sequences 9.2 Halton sequences 9.3 Sobol low-discrepancy sequences 9.4 Randomized and scrambled low-discrepancy sequences 9.5 Sample path generation with low-discrepancy sequences For further reading References

Part Five: Miscellaneous Applications

Chapter Ten: Optimization

10.1 Classification of optimization problems 10.2 Optimization model building 10.3 Monte Carlo methods for global optimization 10.4 Direct search and simulation-based optimization methods 10.5 Stochastic programming models 10.6 Stochastic dynamic programming 10.7 Numerical dynamic programming 10.8 Approximate dynamic programming For further reading References

Chapter Eleven: Option Pricing

11.1 European-style multidimensional options in the BSM world 11.2 European-style path-dependent options in the BSM world 11.3 Pricing options with early exercise features 11.4 A look outside the BSM world: Equity options under the Heston model 11.5 Pricing interest rate derivatives For further reading References

Chapter Twelve: Sensitivity Estimation

12.1 Estimating option greeks by finite differences 12.2 Estimating option greeks by pathwise derivatives 12.3 Estimating option greeks by the likelihood ratio method For further reading References

Chapter Thirteen: Risk Measurement and Management

13.1 What is a risk measure? 13.2 Quantile-based risk measures: Value-at-risk 13.3 Issues in Monte Carlo estimation of V@R 13.4 Variance reduction methods for V@R 13.5 Mean–risk models in stochastic programming 13.6 Simulating delta hedging strategies 13.7 The interplay of financial and nonfinancial risks For further reading References

Chapter Fourteen: Markov Chain Monte Carlo and Bayesian Statistics

14.1 Acceptance–rejection sampling in Bayesian statistics 14.2 An introduction to Markov chains 14.3 The Metropolis–Hastings algorithm 14.4 A re-examination of simulated annealing For further reading References

Index