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

Book Description

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.

    Table of Contents

    1. Cover
    2. Half Title page
    3. Title page
    4. Copyright page
    5. Preface
    6. Part One: Overview and Motivation
      1. Chapter One: Introduction to Monte Carlo Methods
        1. 1.1 Historical origin of Monte Carlo simulation
        2. 1.2 Monte Carlo simulation vs. Monte Carlo sampling
        3. 1.3 System dynamics and the mechanics of Monte Carlo simulation
        4. 1.4 Simulation and optimization
        5. 1.5 Pitfalls in Monte Carlo simulation
        6. 1.6 Software tools for Monte Carlo simulation
        7. 1.7 Prerequisites
        8. For further reading
        9. References
      2. Chapter Two: Numerical Integration Methods
        1. 2.1 Classical quadrature formulas
        2. 2.2 Gaussian quadrature
        3. 2.3 Extension to higher dimensions: Product rules
        4. 2.4 Alternative approaches for high-dimensional integration
        5. 2.5 Relationship with moment matching
        6. 2.6 Numerical integration in R
        7. For further reading
        8. References
    7. Part Two: Input Analysis: Modeling and Estimation
      1. Chapter Three: Stochastic Modeling in Finance and Economics
        1. 3.1 Introductory examples
        2. 3.2 Some common probability distributions
        3. 3.3 Multivariate distributions: Covariance and correlation
        4. 3.4 Modeling dependence with copulas
        5. 3.5 Linear regression models: A probabilistic view
        6. 3.6 Time series models
        7. 3.7 Stochastic differential equations
        8. 3.8 Dimensionality reduction
        9. 3.9 Risk-neutral derivative pricing
        10. For further reading
        11. References
      2. Chapter Four: Estimation and Fitting
        1. 4.1 Basic inferential statistics in R
        2. 4.2 Parameter estimation
        3. 4.3 Checking the fit of hypothetical distributions
        4. 4.4 Estimation of linear regression models by ordinary least squares
        5. 4.5 Fitting time series models
        6. 4.6 Subjective probability: The Bayesian view
        7. For further reading
        8. References
    8. Part Three: Sampling and Path Generation
      1. Chapter Five: Random Variate Generation
        1. 5.1 The structure of a Monte Carlo simulation
        2. 5.2 Generating pseudorandom numbers
        3. 5.3 The inverse transform method
        4. 5.4 The acceptance-rejection method
        5. 5.5 Generating normal variates
        6. 5.6 Other ad hoc methods
        7. 5.7 Sampling from copulas
        8. For further reading
        9. References
      2. Chapter Six: Sample Path Generation for Continuous-Time Models
        1. 6.1 Issues in path generation
        2. 6.2 Simulating geometric Brownian motion
        3. 6.3 Sample paths of short-term interest rates
        4. 6.4 Dealing with stochastic volatility
        5. 6.5 Dealing with jumps
        6. For further reading
        7. References
    9. Part Four: Output Analysis and Efficiency Improvement
      1. Chapter Seven: Output Analysis
        1. 7.1 Pitfalls in output analysis
        2. 7.2 Setting the number of replications
        3. 7.3 A world beyond averages
        4. 7.4 Good and bad news
        5. For further reading
        6. References
      2. Chapter Eight: Variance Reduction Methods
        1. 8.1 Antithetic sampling
        2. 8.2 Common random numbers
        3. 8.3 Control variates
        4. 8.4 Conditional Monte Carlo
        5. 8.5 Stratified sampling
        6. 8.6 Importance sampling
        7. For further reading
        8. References
      3. Chapter Nine: Low-Discrepancy Sequences
        1. 9.1 Low-discrepancy sequences
        2. 9.2 Halton sequences
        3. 9.3 Sobol low-discrepancy sequences
        4. 9.4 Randomized and scrambled low-discrepancy sequences
        5. 9.5 Sample path generation with low-discrepancy sequences
        6. For further reading
        7. References
    10. Part Five: Miscellaneous Applications
      1. Chapter Ten: Optimization
        1. 10.1 Classification of optimization problems
        2. 10.2 Optimization model building
        3. 10.3 Monte Carlo methods for global optimization
        4. 10.4 Direct search and simulation-based optimization methods
        5. 10.5 Stochastic programming models
        6. 10.6 Stochastic dynamic programming
        7. 10.7 Numerical dynamic programming
        8. 10.8 Approximate dynamic programming
        9. For further reading
        10. References
      2. Chapter Eleven: Option Pricing
        1. 11.1 European-style multidimensional options in the BSM world
        2. 11.2 European-style path-dependent options in the BSM world
        3. 11.3 Pricing options with early exercise features
        4. 11.4 A look outside the BSM world: Equity options under the Heston model
        5. 11.5 Pricing interest rate derivatives
        6. For further reading
        7. References
      3. Chapter Twelve: Sensitivity Estimation
        1. 12.1 Estimating option greeks by finite differences
        2. 12.2 Estimating option greeks by pathwise derivatives
        3. 12.3 Estimating option greeks by the likelihood ratio method
        4. For further reading
        5. References
      4. Chapter Thirteen: Risk Measurement and Management
        1. 13.1 What is a risk measure?
        2. 13.2 Quantile-based risk measures: Value-at-risk
        3. 13.3 Issues in Monte Carlo estimation of V@R
        4. 13.4 Variance reduction methods for V@R
        5. 13.5 Mean–risk models in stochastic programming
        6. 13.6 Simulating delta hedging strategies
        7. 13.7 The interplay of financial and nonfinancial risks
        8. For further reading
        9. References
      5. Chapter Fourteen: Markov Chain Monte Carlo and Bayesian Statistics
        1. 14.1 Acceptance–rejection sampling in Bayesian statistics
        2. 14.2 An introduction to Markov chains
        3. 14.3 The Metropolis–Hastings algorithm
        4. 14.4 A re-examination of simulated annealing
        5. For further reading
        6. References
    11. Index