Handbook in Monte Carlo Simulation Applications in Financial Engineering Risk Management and Economics 1st Edition by Paolo Brandimarte 0470531118 9780470531112

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ISBN 10: 0470531118

ISBN 13: 9780470531112

Author: Paolo Brandimarte

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.

Handbook in Monte Carlo Simulation Applications in Financial Engineering Risk Management and Economics 1st Table of contents:

Part I Overview and Motivation

1 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

1.3.1 Discrete-time models

1.3.2 Continuous-time models

1.3.3 Discrete-event models

1.4 Simulation and optimization

1.4.1 Nonconvex optimization

1.4.2 Stochastic optimization

1.4.3 Stochastic dynamic programming

1.5 Pitfalls in Monte Carlo simulation

1.5.1 Technical issues

1.5.2 Philosophical issues

1.6 Software tools for Monte Carlo simulation

1.7 Prerequisites

1.7.1 Mathematical background

1.7.2 Financial background

1.7.3 Technical background

For further reading

References

2 Numerical Integration Methods

2.1 Classical quadrature formulas

2.1.1 The rectangle rule

2.1.2 Interpolatory quadrature formulas

2.1.3 An alternative derivation

2.2 Gaussian quadrature

2.2.1 Theory of Gaussian quadrature: The role of orthogonal polynomials

2.2.2 Gaussian quadrature in R

2.3 Extension to higher dimensions: Product rules

2.4 Alternative approaches for high-dimensional integration

2.4.1 Monte Carlo integration

2.4.2 Low-discrepancy sequences

2.4.3 Lattice methods

2.5 Relationship with moment matching

2.5.1 Binomial lattices

2.5.2 Scenario generation in stochastic programming

2.6 Numerical integration in R

For further reading

References

Part II Input Analysis: Modeling and Estimation

3 Stochastic Modeling in Finance and Economics

3.1 Introductory examples

3.1.1 Single-period portfolio optimization and modeling returns

3.1.2 Consumption-saving with uncertain labor income

3.1.3 Continuous-time models for asset prices and interest rates

3.2 Some common probability distributions

3.2.1 Bernoulli, binomial, and geometric variables

3.2.2 Exponential and Poisson distributions

3.2.3 Normal and related distributions

3.2.4 Beta distribution

3.2.5 Gamma distribution

3.2.6 Empirical distributions

3.3 Multivariate distributions: Covariance and correlation

3.3.1 Multivariate distributions

3.3.2 Covariance and Pearson’s correlation

3.3.3 R functions for covariance and correlation

3.3.4 Some typical multivariate distributions

3.4 Modeling dependence with copulas

3.4.1 Kendall’s tau and Spearman’s rho

3.4.2 Tail dependence

3.5 Linear regression models: A probabilistic view

3.6 Time series models

3.6.1 Moving-average processes

3.6.2 Autoregressive processes

3.6.3 ARMA and ARIMA processes

3.6.4 Vector autoregressive models

3.6.5 Modeling stochastic volatility

3.7 Stochastic differential equations

3.7.1 From discrete to continuous time

3.7.2 Standard Wiener process

3.7.3 Stochastic integration and Itô’s lemma

3.7.4 Geometric Brownian motion

3.7.5 Generalizations

3.8 Dimensionality reduction

3.8.1 Principal component analysis (PCA)

3.8.2 Factor models

3.9 Risk-neutral derivative pricing

3.9.1 Option pricing in the binomial model

3.9.2 A continuous-time model for option pricing: The Black-Scholes-Merton formula

3.9.3 Option pricing in incomplete markets

For further reading

References

4 Estimation and Fitting

4.1 Basic inferential statistics in R

4.1.1 Confidence intervals

4.1.2 Hypothesis testing

4.1.3 Correlation testing

4.2 Parameter estimation

4.2.1 Features of point estimators

4.2.2 The method of moments

4.2.3 The method of maximum likelihood

4.2.4 Distribution fitting in R

4.3 Checking the fit of hypothetical distributions

4.3.1 The chi-square test

4.3.2 The Kolmogorov-Smirnov test

4.3.3 Testing normality

4.4 Estimation of linear regression models by ordinary least squares

4.5 Fitting time series models

4.6 Subjective probability: The Bayesian view

4.6.1 Bayesian estimation

4.6.2 Bayesian learning and coin flipping

For further reading

References

Part III Sampling and Path Generation

5 Random Variate Generation

5.1 The structure of a Monte Carlo simulation

5.2 Generating pseudorandom numbers

5.2.1 Linear congruential generators

5.2.2 Desirable properties of random number generators

5.2.3 General structure of random number generators

5.2.4 Random number generators in R

5.3 The inverse transform method

5.4 The acceptance-rejection method

5.5 Generating normal variates

5.5.1 Sampling the standard normal distribution

5.5.2 Sampling a multivariate normal distribution

5.6 Other ad hoc methods

5.7 Sampling from copulas

For further reading

References

6 Sample Path Generation for Continuous-Time Models

6.1 Issues in path generation

6.1.1 Euler vs. Milstein schemes

6.1.2 Predictor-corrector methods

6.2 Simulating geometric Brownian motion

6.2.1 An application: Pricing a vanilla call option

6.2.2 Multidimensional GBM

6.2.3 The Brownian bridge

6.3 Sample paths of short-term interest rates

6.3.1 The Vasicek short-rate model

6.3.2 The Cox-Ingersoll-Ross short-rate model

6.4 Dealing with stochastic volatility

6.5 Dealing with jumps

For further reading

References

Part IV Output Analysis and Efficiency Improvement

7 Output Analysis

7.1 Pitfalls in output analysis

7.1.1 Bias and dependence issues: A financial example

7.2 Setting the number of replications

7.3 A world beyond averages

7.4 Good and bad news

For further reading

References

8 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

8.6.1 Importance sampling and rare events

8.6.2 A digression: Moment and cumulant generating functions

8.6.3 Exponential tilting

For further reading

References

9 Low-Discrepancy Sequences

9.1 Low-discrepancy sequences

9.2 Halton sequences

9.3 Sobol low-discrepancy sequences

9.3.1 Sobol sequences and the algebra of polynomials

9.4 Randomized and scrambled low-discrepancy sequences

9.5 Sample path generation with low-discrepancy sequences

For further reading

References

Part V Miscellaneous Applications

10 Optimization

10.1 Classification of optimization problems

10.2 Optimization model building

10.2.1 Mean-variance portfolio optimization

10.2.2 Modeling with logical decision variables: Optimal portfolio tracking

10.2.3 A scenario-based model for the newsvendor problem

10.2.4 Fixed-mix asset allocation

10.2.5 Asset pricing

10.2.6 Parameter estimation and model calibration

10.3 Monte Carlo methods for global optimization

10.3.1 Local search and other metaheuristics

10.3.2 Simulated annealing

10.3.3 Genetic algorithms

10.3.4 Particle swarm optimization

10.4 Direct search and simulation-based optimization methods

10.4.1 Simplex search

10.4.2 Metamodeling

10.5 Stochastic programming models

10.5.1 Two-stage stochastic linear programming with recourse

10.5.2 A multistage model for portfolio management

10.5.3 Scenario generation and stability in stochastic programming

10.6 Stochastic dynamic programming

10.6.1 The shortest path problem

10.6.2 The functional equation of dynamic programming

10.6.3 Infinite-horizon stochastic optimization

10.6.4 Stochastic programming with recourse vs. dynamic programming

10.7 Numerical dynamic programming

10.7.1 Approximating the value function: A deterministic example

10.7.2 Value iteration for infinite-horizon problems

10.7.3 A numerical approach to consumption-saving

10.8 Approximate dynamic programming

10.8.1 A basic version of ADP

10.8.2 Post-decision state variables in ADP

10.8.3 Q-learning for a simple MDP

For further reading

References

11 Option Pricing

11.1 European-style multidimensional options in the BSM world

11.2 European-style path-dependent options in the BSM world

11.2.1 Pricing a barrier option

11.2.2 Pricing an arithmetic average Asian option

11.3 Pricing options with early exercise features

11.3.1 Sources of bias in pricing options with early exercise features

11.3.2 The scenario tree approach

11.3.3 The regression-based approach

11.4 A look outside the BSM world: Equity options under the Heston model

11.5 Pricing interest rate derivatives

11.5.1 Pricing bonds and bond options under the Vasicek model

11.5.2 Pricing a zero-coupon bond under the CIR model

For further reading

References

12 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

13 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

14 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

14.3.1 The Gibbs sampler

14.4 A re-examination of simulated annealing

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