金融工程中的蒙特卡罗方法(影印版)(金融数学丛书)(Monte Carlo Methods in Financial Engineering)
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品牌: 格拉瑟曼
基本信息·出版社：高等教育出版社
·页码：595 页
·出版日期：2008年
·ISBN：9787040247527
·包装版本：1版
·装帧：平装
·开本：16
·正文语种：英语
·丛书名：金融数学丛书
·外文书名：Monte Carlo Methods in Financial Engineering
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内容简介《金融工程中的蒙特卡罗方法》（影印版）中介绍了蒙特卡罗方法在金融中的用途，并且将模拟用作呈现金融工程中模型和思想的工具。《金融工程中的蒙特卡罗方法》大致分为三个部分。第一部分介绍了蒙特卡罗方法的基本原理，衍生定价基础以及金融工程中一些最重要模型的实现。第二部分描述了如何改进模拟精确度和效率。最后的第三部分讲述了几个特别的论题：价格敏感度估计，美式期权定价以及金融投资组合中的市场风险和信贷风险评估。
作者简介Paul Glasserman，哥伦比亚大学商学院高级副院长、Jack R．Anderson教授，美国联邦储蓄保险公司(FDIC)金融研究中心成员。长期从事风险管理、衍生证券定价、Monte Carlo模拟等方向的教学和研究，曾发表许多有影响力的研究论文，并担任著名刊物Management Science、Finance&Stochastics、Mathematical Finance等的编委。
媒体推荐“……我鼓励对金融学中蒙特卡罗方法有兴趣的每一个人都阅读此书。这本书写得很出色，并且配有精选的参考书目和一个有帮助的索引，确实值得购买。”.
——Ralf Werner，OR Spectrum Operations Research Spectrum，Issue 27，2005
“本书的出版是计算金融学的一件大事。多年来，蒙特卡罗方法成功地应用于解决各式各样的金融数学问题。通过本书的出版，作者应为将这些应用提升到一个新水平的这次不错的尝试而得到更高的声誉。……”...
——A Zhigljavsky，Journal of the Operational Research Society，Vol．57，2006
编辑推荐《金融工程中的蒙特卡罗方法》（影印版）源于作者在哥伦比亚大学多年教学的讲稿。
《金融工程中的蒙特卡罗方法》（影印版）可供金融工程、金融数学、统计学等专业的研究生阅读，也可供金融行业的从业人员及相关领域的专业人士和技术人员参考。
目录
1 Foundations .
1.1 Principles of Monte Carlo
1.1.1 Introduction
1.1.2 First Examples
1.1.3 Efficiency of Simulation Estimators
1.2 Principles of Derivatives Pricing
1.2.1 Pricing and Replication
1.2.2 Arbitrage and Risk-Neutral Pricing
1.2.3 Change of Numeraire
1.2.4 The Market Price of Risk
2 Generating Random Numbers and Random Variables
2.1 Random Number Generation
2.1.1 General Considerations
2.1.2 Linear Congruential Generators
2.1.3 Implementation of Linear Congruential Generators
2.1.4 Lattice Structure
2.1.5 Combined Generators and Other Methods
2.2 General Sampling Methods
2.2.1 Inverse Transform Method
2.2.2 Acceptance-Rejection Method
2.3 Normal Random Variables and Vectors
2.3.1 Basic Properties
2.3.2 Generating Univariate Normals
2.3.3 Generating Multivariate Normals
3 Generating Sample Paths
3.1 Brownian Motion
3.1.1 One Dimension
3.1.2 Multiple Dimensions
3.2 Geometric Brownian Motion
3.2.1 Basic Properties
3.2.2 Path-Dependent Options
3.2.3 Multiple Dimensions
3.3 Gaussian Short Rate Models
3.3.1 Basic Models and Simulation
3.3.2 Bond Prices
.3.3 Multifactor Models
3.4 Square-Root Diffusions
3.4.1 Transition Density
3.4.2 Sampling Gamma and Poisson
3.4.3 Bond Prices
3.4.4 Extensions
3.5 Processes with Jumps
3.5.1 A Jump-Diffusion Model
3.5.2 Pure-Jump Processes
3.6 Forward Rate Models: Continuous Rates
3.6.1 The HJM Framework
3.6.2 The Discrete Drift
3.6.3 Implementation
3.7 Forward Rate Models: Simple Rates
3.7.1 LIBOR Market Model Dynamics
3.7.2 Pricing Derivatives
3.7.3 Simulation
3.7.4 Volatility Structure and Calibration
4 Variance Reduction Techniques
4.1 Control Variates
4.1.1 Method and Examples
4.1.2 Multiple Controls
4.1.3 Small-Sample Issues
4.1.4 Nonlinear Controls
4.2 Antithetic Variates
4.3 Stratified Sampling
4.3.1 Method and Examples
4.3.2 Applications
4.3.3 Poststratification
4.4 Latin Hypercube Sampling
4.5 Matching Underlying Assets
4.5.1 Moment Matching Through Path Adjustments
4.5.2 Weighted Monte Carlo
4.6 Importance Sampling
4.6.1 Principles and First Examples
4.6.2 Path-Dependent Options
4.7 Concluding Remarks
5 Quasi-Monte Carlo
5.1 General Principles
5.1.1 Discrepancy
5.1.2 Van der Corput Sequences
5.1.3 The Koksma-Hlawka Bound
5,1.4 Nets and Sequences
5.2 Low-Discrepancy Sequences
5.2.1 Halton and Hammersley
5.2.2 Faure
5.2.3 Sobol'
5.2.4 Further Constructions ..
5.3 Lattice Rules
5.4 Randomized QMC
5.5 The Finance Setting
5.5.1 Numerical Examples
5.5.2 Strategic Implementation
5.6 Concluding Remarks
6 Discretization Methods
6.1 Introduction
6.1.1 The Euler Scheme and a First Refinement
6.1.2 Convergence Order
6.2 Second-Order Methods
6.2.1 The Scalar Case
6.2.2 The Vector Case
6.2.3 Incorporating Path-Dependence
6.2.4 Extrapolation
6.3 Extensions
6.3.1 General Expansions
6.3.2 Jump-Diffusion Processes
6.3.3 Convergence of Mean Square Error
6.4 Extremes and Barrier Crossings: Brownian Interpolation
6.5 Changing Variables
6.6 Concluding Remarks
7 Estimating Sensitivities
7.1 Finite-Difference Approximations
7.1.1 Bias and Variance
7.1.2 Optimal Mean Square Error
7.2 Pathwise Derivative Estimates
7.2.1 Method and Examples
7.2.2 Conditions for Unbiasedness
7.2.3 Approximations and Related Methods
7.3 The Likelihood Ratio Method
7.3.1 Method and Examples
7.3.2 Bias and Variance Properties
7.3.3 Gamma
7.3.4 Approximations and Related Methods
7.4 Concluding Remarks
8 Pricing American Options
8.1 Problem Formulation
8.2 Parametric Approximations
8.3 Random Tree Methods
8.3.1 High Estimator
8.3.2 Low Estimator
8.3.3 Implementation
8.4 State-Space Partitioning
8.5 Stochastic Mesh Methods
8.5.1 General Framework
8.5.2 Likelihood Ratio Weights
8.6 Regression-Based Methods and Weights
8.6.1 Approximate Continuation Values
8.6.2 Regression and Mesh Weights
8.7 Duality
8.8 Concluding Remarks
9 Applications in Risk Management
9.1 Loss Probabilities and Value-at-Risk
9.1.1 Background
9.1.2 Calculating VAR
9.2 Variance Reduction Using the Delta-Gamma Approximation
9.2.1 Control Variate
9.2.2 Importance Sampling
9.2.3 Stratified Sampling
9.3 A Heavy-Tailed Setting
9.3.1 Modeling Heavy Tails
9.3.2 Delta-Gamma Approximation
9.3.3 Variance Reduction
9.4 Credit Risk
9.4.1 Default Times and Valuation
9.4.2 Dependent Defaults
9.4.3 Portfolio Credit Risk
9.5 Concluding Remarks
A Appendix: Convergence and Confidence Intervals
A.1 Convergence Concepts
A.2 Central Limit Theorem and Confidence Intervals
B Appendix: Results from Stochastic Calculus
B.1 It6's Formula
B.2 Stochastic Differential Equations
B.3 Martingales
B.4 Change of Measure
C Appendix: The Term Structure of Interest Rates
C.1 Term Structure Terminology
C.2 Interest Rate Derivatives
References
Index
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