Handbook In monte carlo simulation : applications in financial engineering, risk management and economics/

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.