Monte Carlo Methods in Financial Engineering

(Paul Glasserman)

614页 　　12.6M 英文

Author: Paul Glasserman　　

Publication Date: October 2003

The subject is covered broadly and in a systematic manner. Chapter 1 is an introduction and Chapter 2 discusses pseudorandom number and variate generation. Neither is special. Things start to get interesting in Chapter 3, which covers the generation of sample paths, starting with Brownian motion and proceeding along to the HJM and Libor market model. The discussion is simultaneously sophisticated and practical. Glasserman builds up concepts nicely. For example, he introduces the Brownian bridge in the simple case of one-dimensional Brownian motion and then extends it as he considers more elaborate models.

Contents

1. Foundations
Principles of Monte Carlo
Principles of Derivatives Pricing

2. Generating Random Numbers and Random Variables
Random Number Generation
General Sampling Methods
Normal Random Variables and Vectors

3. Generating Sample Paths
Brownian Motion
Geometric Brownian Motion
Gaussian Short Rate Models
Square-Root Diffusions
Processes With Jumps
Forward Rate Models: Continuous Rates
Forward Rate Models: Simple Rates

4. Variance Reduction Techniques
Control Variates
Antithetic Variates
Stratified Sampling
Latin Hypercube Sampling
Matching Underlying Assets
Importance Sampling

5. Quasi-Monte Carlo
General Principles
Low-Discrepancy Sequences
Lattice Rules
Randomized QMC
The Finance Setting

6. Discretization Methods
Introduction
Second-Order Methods
Extensions
Extremes and Barrier Crossings: Brownian Interpolation
Changing Variables

7. Estimating Sensitivities
Finite Difference Approximations
Pathwise Derivative Estimates
The Likelihood Ratio Method

8. Pricing American Options
Problem Formulation
Parametric Approximations
Random Tree Methods
State Space Partitioning
Stochastic Mesh Methods
Regression-Based Methods and Weights
Duality

9. Applications in Risk Management
Loss Probabilities and Value-at-Risk
Variance Reduction Using the Delta-Gamma Approximation
A Heavy-Tailed Setting
Credit Risk

App. A Convergence and Confidence Intervals

App. B Results from Stochastic Calculus

App. C The Term Structure of Interest Rates

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