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[美] 卡莫纳 著

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出版社： 世界图书出版公司

ISBN：9787510052774

版次：1

商品编码：11181634

包装：平装

开本：24开

出版时间：2013-01-01

页数：235

内容简介

　　卡莫纳编著的《利率模型》内容介绍：The main goal of the book is to present, in a self-contained manner, the empirical facts needed to understand the sophisticated mathematical models developed by the financial mathematics community over the last decade. So after a very elementary introduction to the mechanics of the bond market,and a thorough statistical analysis of the data available to any curious spectator without any special inside track information, we gradually introduce the mathematical tools needed to analyze the stochastic models most widely used in the industry. Our point of view has been strongly influenced by recent works of Cont and his collaborators and the Ph.D. of Filipovid. They merge the original proposal of Musiela inviting us to rewrite the HJM model as a stochastic partial differential equation, together with Bjork's proposal to recast the HJM model in the framework of stochastic differential equations in a Baoach space.

目录

Part Ⅰ The Term Structure of Interest Rates
Data and Instruments of the Term Structure of Interest Rates
1.1 Time Value of Money and Zero Coupon Bonds
1.1.1 Treasury Bills
1.1.2 Discount Factors and Interest Rates
1.2 Coupon Bearing Bonds
1.2.1 Treasury Notes and Treasury Bonds
1.2.2 The STRIPS Program
1.2.3 Clean Prices
1.3 Term Structure as Given by Curves
1.3.1 The Spot （Zero Coupon） Yield Curve
1.3.2 The Forward Rats Curve and Duration
1.3.3 Swap Rate Curves
1.4 Continuous Compounding and Market Conventions
1.4.1 Day Count Conventions
1.4.2 Compounding Conventions
1.4.3 Summary
1.5 Related Markets
1.5.1 Municipal Bonds
1.5.2 Indsx Linked Bonds
1.5.3 Corporate Bonds and Credit Markets
1.5.4 Tax Issues
1.5.5 Asset Backed Securities
1.6 Statistical Estimation of the Term Structure
1.6.1 Yield Curve Estimation
1.6.2 Parametric Estimation Procedures
1.6.3 Nonparametric Estimation Procedures
1.7 Principal Component Analysis
1.7.1 Principal Components of a Random Vector
1.7.2 Multivariate Data PCA
1.7.3 PCA of the Yield Curve
1.7.4 PCA of the Swap Rate Curve
Notes & Complements
Term Structure Factor Models
2.1 Factor Models for the Term Structure
2.2 Afllne Models
2.3 Short Rate Models as One-Factor Models
2.3.1 IncompleteneSs and Pricing
2.3.2 Specific Models
2.3.3 A PDE for Numerical Purposes
2.3.4 Explicit Pricing Formulae
2.3.5 Rigid Term Structures for Calibration
2.4 Term Structure Dynamics
2.4.1 The Heath Jarrow-Morton Framework
2.4.2 Hedging Contingent Claims
2.4.3 A Shortcoming of the Finite-Rank Models
2.4.4 The Musiela Notation
2.4.5 Random Field Formulation
2.5 Appendices
Notes & Complements
Part Ⅱ Infinite Dimensional Stochastic Analysis
Infinite Dimensional Integration Theory
3.1 Introduction
3.1.1 The Setting
3.1.2 Distributions of Gaussian Processes
3.2 Ganssian Measures in Banach Spaces and Examples
3.2.1 Integrability Properties
3.2.2 Isouormal Processes
3.3 Reproducing Kernel Hilbert Space
3.3.1 RKHS of Gaussian Processes
3.3.2 The RKHS of the Classical Wiener Measure
3.4 Topological Supports. Carriers. Equivalence and Singularity
3.4.1 Topological Supports of Gaussian Measures
3.4.2 Equivalence and Singularity of Gaussian Measures
3.5 Series Expansions
3.6 Cylindrical Measures
3.6.1 The Canonical （Ganssian） Cylindrical Measure
of a Hilbert Space
3.6.2 Integration with Respect to a Cylindrical Measure
3.6.3 Characteristic Functions and Bochner's Theorem
3.6.4 Radonification of Cylindrical Measures
3.7 Appendices
Notes & Complements
Stochastic Analysis in Infinite Dimensions
4.1 Infinite Dimensional Wiener Processes
4.1.1 Revisiting some Known Two-Parameter Processes
4.1.2 Bannch Space Valued Wiener Process
4.1.3 Sample Path Regularity
4.1.4 Absolute Continuity Issues
4.1.5 Series Expansions
4.2 Stochastic Integral and It6 Processes
4.2.1 The Case of E*- and H*-Valued Integrands
4.9.2 The Case of Operator Valued Integrands
4.2.3 Stochastic Convolutions
4.3 Martingale Representation Theorems
4.4 Girsanov's Theorem and Changes of Measures
4.5 Infinite Dimensional Ornstein Uhtenbeck Processes
4.5.1 Finite Dimensional OU Processes
4.5.2 Infinite Dimensional OU Processes
4.5.3 The SDE Approach in Infinite Dimensions
4.6 Stochastic Differential Equations
Notes & Complements
The Malliavin Calculus
5.1 The Malliavin Derivative
5.1.1 Various Notions of Differentiability
5.1.2 The Definition of the Malliavin Derivative
5.2 The Chain Rule
5.3 The Skorohod Integral
5.4 The Clark Ocone Formula
5.4.1 Sobolev and Logarithmic Sebolev Inequalities
5.5 Maniavin Derivatives and SDEs
5.5.1 Random Operators
5.5.2 A Useful Formula
5.6 Applications in Numerical Finance
5.6.1 Computation of the Delta
5.6.2 Computation of Conditional Expectations
Notes & Complements
Part Ⅲ Generalized Models for the Term Structure
6 General Models
6.1 Existence of a Bond Market
6.2 The HJM Evolution Equation
6.2.1 Function Spaces for Forward Curves
6.3 The Abstract HJM Model
6.3.1 Drift Condition and Absence of Arbitrage
6.3.2 Long Rates Never Fall
6.3.3 A Concrete Example
6.4 Geometry of the Term Structure Dynamics
6.4.1 The Consistency Problem
6.4.2 Finite Dimensional Realizations
6.5 Generalized Bond Portfolios
6.5.1 Models of the Discounted Bond Price Curve
6.5.2 Trading Strategies
6.5.3 Uniqueness of Hedging Strategies
6.5.4 Approximate Completeness of the Bond Market
6.5.5 Hedging Strategies for Lipscbitz Claims
Notes & Complements
7 Specific Models
7.1 Markovian HJM Models
7.1.1 Gaussian Markov Models
7.1.2 Assumptions on the State Space
7.1.3 Invariant Measures for Gauss-Markov HJM Models
7.1.4 Non-Uniqueness of the Invariant Measure
7.1.5 Asymptotic Behavior
7.1.6 The Short Rate is a Maximum on Average
7.2 SPDEs and Term Structure Models
7.2.1 The Deformation Process
7.2.2 A Model of the Deformation Process
7.2.3 Analysis of the SPDE
7.2.4 Regularity of the Solutions
7.3 Market Models
7.3.1 The Forward Measure
7.3.2 LIBOR Rates Revisited
Notes & Complements
References
Notation Index
Author Index
Subject Index

前言/序言

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用到的数学比较高深，值得看看！

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此外还有承诺交付货币的时间长度以及所承担风险的程度。利息率政策是宏观货币政策的主要措施，政府为了干预经济，可通过变动利息率的办法来间接调节国内通货膨胀水平。

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利息率的高低，影响利息率的因素，主要有资本的边际生产力或资本的供求关系

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当经济过热、通货膨胀上升时，便提高利率、收紧信贷；当过热的经济和通货膨胀得到控制时，便会把利率适当地调低。因此，利率是重要的基本经济因素之一。利率是经济学中一个重要的金融变量，几乎所有的金融现象、金融资产均与利率有着或多或少的联系。

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从借款人的角度来看，利率是使用资本的单位成本，是借款人使用贷款人的货币资本而向贷款人支付的价格；从贷款人的角度来看，利率是贷款人借出货币资本所获得的报酬率。如果用i表示利率、用I表示利息额、用P表示本金，则利率可用公式表示为：i=I/P